November 18, 26, and December 2, 9, 15, 23, 2021, and March 7, 2022

*Mathematical Physics is neither physics with a lot of math, nor is it math with a lot of physics, but a distinct field in which the rigor of math is applied to problems that come from physics. Barry Simon's research career is testament to the value of this approach. His work on the spectral theory of orthogonal polynomials is considered a landmark in the field, and he has made fundamental contributions in areas ranging from quantum field theory to statistical mechanics.*

*Mathematical Physics is neither physics with a lot of math, nor is it math with a lot of physics, but a distinct field in which the rigor of math is applied to problems that come from physics. Barry Simon's research career is testament to the value of this approach. His work on the spectral theory of orthogonal polynomials is considered a landmark in the field, and he has made fundamental contributions in areas ranging from quantum field theory to statistical mechanics.*

*From winning math contests in New York City to college at Harvard, and from Princeton graduate school to Princeton faculty, Simon distinguished himself with his sheer energy - energy for solving complex mathematical proofs, energy for writing and reviewing manuscripts, and energy for collaborating with peers in the tight-knit world of mathematical physics.*

*From winning math contests in New York City to college at Harvard, and from Princeton graduate school to Princeton faculty, Simon distinguished himself with his sheer energy - energy for solving complex mathematical proofs, energy for writing and reviewing manuscripts, and energy for collaborating with peers in the tight-knit world of mathematical physics.*

*Early in his career, Simon decided to become observantly Jewish, and the ease of this transition demonstrates that if one is comfortable with oneself, so too will others, even in the highly secular world of scientific academia. Midway through his career, Simon moved to Caltech, where he has served in numerous formal and informal roles that have enhanced both the Math and Physics programs at the Institute.*

*Early in his career, Simon decided to become observantly Jewish, and the ease of this transition demonstrates that if one is comfortable with oneself, so too will others, even in the highly secular world of scientific academia. Midway through his career, Simon moved to Caltech, where he has served in numerous formal and informal roles that have enhanced both the Math and Physics programs at the Institute.*

*Among his many honors are his election as a Fellow to the American Physical Society and the American Mathematical Society, as a member of the National Academy of Sciences, and winning the Henri Poincaré, Steele, and Dannie Heineman Prizes. Simon is currently working on a book-length manuscript on statistical mechanics.*

*Among his many honors are his election as a Fellow to the American Physical Society and the American Mathematical Society, as a member of the National Academy of Sciences, and winning the Henri Poincaré, Steele, and Dannie Heineman Prizes. Simon is currently working on a book-length manuscript on statistical mechanics.*

### Interview Transcript

**DAVID ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It is Thursday, November 18, 2021. It is my great pleasure to be here with Professor Barry Simon. Barry, it's wonderful to be with you. Thank you for joining me.

**BARRY SIMON:** My pleasure.

**ZIERLER:** To start, would you tell me, please, your title and institutional affiliation?

**SIMON:** I am the I.B.M. Professor of Mathematics and Theoretical Physics, Emeritus at the California Institute of Technology.

**ZIERLER:** We'll unpack the title right from the beginning. Professor of Mathematics and Theoretical Physics, is that a joint appointment between two departments?

**SIMON:** Yes, and no. You have to remember that Caltech officially doesn't have "departments," it has divisions. Because when I came from Princeton, I had a joint appointment. I insisted on a joint appointment, so that was the title that was arrived at.

**ZIERLER:** In terms of administrative responsibilities, I understand it's one division chair, but are there two faculty committees you sit on, two tenure committees you've sat on?

**SIMON:** Again, the tenure committees are divisional. All mathematicians are invited to the tenure committees for physics, astronomy, as well as mathematics. There was a decision, I think, made quite a while ago, I'm not sure how early, but before I came to Caltech, to avoid overwhelming the mathematicians because mathematics is a small part of the Division of Physics, Mathematics, and Astronomy. Only the theoretical physicists and astrophysicists are invited to the math tenure meetings. But even if I were just a professor of physics, I would be invited to meetings in both, and even if I were just a professor of mathematics, I'd be invited. In that sense, it's no different. Teaching, in principle, it could be either. At Princeton, in fact, my teaching load was one course in math and a half course in physics because the physics load was half of what it was in math. At Caltech, I've done all my teaching essentially in mathematics, but it didn't have to be that way. It was decided, because there were fewer math faculty and more need for mathematical teachers, that I should be teaching math courses.

**ZIERLER:** What about in terms of all of the graduate students and mentees you've had over the course of your career?

**SIMON:** I think that if I go back and look at official majors, the bulk of my graduate students at Caltech have been in math, but probably roughly a third were officially, a quarter, maybe, in physics. Some of them wound up with jobs in physics departments. They were more earlier in my career somehow. One of my graduate students tells the story, he was a physics student and decided he wanted to do mathematical physics. When he came and said he wanted to work with me, I was a little concerned because in physics, most of the students are supported by grants, but there really is not that much term-time support in mathematics, so it's almost all teaching in mathematics. Since he was a physics graduate student, he wouldn't do that. I said he should check that it might be difficult, and he went to see the overall physics graduate advisor at the time, who told him, "Oh, well, Simon did Berry's phase, so he's a physicist, you can certainly work with him. We'll find a way to support you." And the student tells the story that he was very confused because he'd never heard of something being named after someone's first name. Because, of course, he didn't hear Berry's phase, he heard Barry's phase.

**ZIERLER:** Going emeritus in 2016, is there any significance to that year in particular? Perhaps turning 70 years old?

**SIMON:** Caltech has a program to encourage people to retire by age 70 by offering them an extra benefit. I was told roughly 75% of the Caltech faculty take the bribe, almost all at the last minute. You can do it between ages 62 and 70, and almost everyone does it so they're finishing at age 70.

**ZIERLER:** Last question as it relates specifically to your title. Being named I.B.M. Professor in 1984, I'm curious if you ever thought about potential controversies related to I.B.M.'s alleged work with the Germans during World War II.

**SIMON:** That was essentially totally unknown, I think, until the last ten years, roughly. It wasn't that it was hidden, but no one talked about it, so I certainly didn't know about it. It's sort of strange and always puzzled me, that I.B.M. made absolutely no attempt to make any contact with me. The history is that Thomas Watson, Jr., the one who essentially turned I.B.M. from a relatively small typewriter company into the I.B.M. that we know, was on the Caltech board of trustees for about a dozen years, and I think he's the one who arranged the endowment in about 1960. The only person who held it before me was Marshall Hall, who was probably Caltech's most distinguished mathematician in that era. And after he retired, the position was actually open for several years because the idea was to use it to recruit a superstar. We made offers–I was very involved with hiring then–to two Fields medalists, both of whom turned us down. Basically, people roughly my age. They were very good, still very well-known. And then, at some point, it was decided, "Well, we're not doing it for that. We'll appoint you."

At some point, about three years ago, a new vice president for I.B.M.'s educational division took over, and they suddenly realized that, "Gee, there seem to be these I.B.M. professors," and they had no way of figuring out who or where they were because the internal records were so bad. They actually used Google to try to search for I.B.M. professor, and they located some of us. They actually missed probably the most famous, Jean Bourgain, who was at the Institute for Advanced Study, the von Neumann I.B.M. Professor. Because it was called the von Neumann I.B.M. Professor, they missed it when they just searched for I.B.M. professor. Nets Katz, who's the current I.B.M. professor, actually, told them about it. They had one meeting of us where they just talked to us and wanted to see about making some kind of connection. There was no real attempt to make contact until then. I found it very strange.

**ZIERLER:** I'm not sure if you're aware, but when the Renaming Report came out last year, there was an investigation about…

**SIMON:** I am. I am. It dealt with Watson. I read it as, "We're not sure enough. There's probably some case, but it's not strong enough for us to take action at this point."

**ZIERLER:** For you, when this information came out about I.B.M.–there was a book, of course, *I.B.M. and the Holocaust*–in light of the fact that, for example, somebody like Ed Stolper gave up the Millikan name last year, did you ever give thought to renouncing the I.B.M. professorship?

**SIMON:** No, absolutely not. Particularly in the I.B.M. case, it's not central to what I.B.M. has done. It had nothing to do with why they gave the money. I didn't realize Stolper had a choice. I thought that the Institute decided–as I went out to have my pictures taken this week, I saw the building I refer to as the Library Formerly Known as Millikan. I thought Caltech made the decision that Millikan's name couldn't be used. If Ed wanted to keep the name, he could have? I would've thought he couldn't. It was Caltech policy. And if Caltech had said I'd have to remove I.B.M., I would've said, "That's your chair. Do what you need to do." It never occurred to me to renounce it. While I think there's more justification for Millikan, I really do not approve. Caltech is Caltech because of Millikan.

I agree that what Millikan said, committees he served on–there's no sign of his having made many actions, and it's just crazy because Caltech is Caltech because of him. Even Woodrow Wilson, not as president of Princeton but as President of the US, took actions that are reprehensible. Given that Princeton became a research institution because of Wilson–I had mixed feelings. But there, at least, you look at the balance, it's close, and I can understand un-naming Wilson. I definitely do not approve of what Caltech did. I thought to do it, and I think I did send a letter of protest to the president. I just thought it was wrong. These are complicated issues, but Caltech is what it is because of Millikan. It's not that he's a minor figure. He made Caltech what it is.

**ZIERLER:** And is it particularly significant to you that Millikan, even if he held some anti-Semitic views, that that didn't stop him from going after some Jewish professors who were of the highest ranking?

**SIMON:** But it did. At least the story I've heard, and I've never been able to verify it. But the story I heard. I can't remember from whom, and I actually asked Judy Goodstein. She said she wasn't sure. I heard a story that Norbert Wiener really wanted to come to Caltech in the 30s, and Millikan said, "In an important area like physics, where I hired Einstein, I'll certainly be willing to hire a Jew. But I'll be damned if I'll hire a Jewish mathematician." Which says something about Caltech's attitude towards mathematics.

**ZIERLER:** So he was doubly bigoted towards Jews and mathematicians. [Laugh]

**SIMON:** Correct.

**ZIERLER:** To go back to going emeritus in 2016, just as a snapshot of what you've been doing in the research world in the last five years, to what extent did going emeritus and unburdening yourself of committee work, advisory work, and teaching increase your bandwidth to focus on the research most important to you?

**SIMON:** I focused more, but you get a little older, you slow down a little. I was always noted for my incredible energy, he said modestly. I still have a lot of energy compared to my peers. There were periods in the late 70s and 80s that I wrote 25 papers in a year. I've had, a five-volume series of books. You say going emeritus in 2016, but it's actually 2014 because I had these two years before that. The first thing I did is actually finish up this set of five volumes, *A Comprehensive Course in Analysis* is what it's called. I have one other book that I've published since then, and one I'm working on, but I've slowed down a little. As I said, you get older…

**ZIERLER:** In those most voluminous periods of productivity, 30 or 40 years ago, in what ways do you ascribe theoretical physics and mathematics, the productivity, as a source of mental energy and as a source of physical energy?

**SIMON:** It's not physical. It's really mental energy. I could juggle lots of balls in the air and think about lots of different things. One of my strengths is I'm very fast. One of my weaknesses is I'm not often patient enough. If I can't solve a problem, I usually give it up. That's why one of the papers I'm proudest of, although it's not my most significant, is a subject I've kept coming back to every year or two and finally cracked. I proved to myself I could. But I've always been quick.

**ZIERLER:** Is there a place for wisdom in mathematical physics where that serves as an asset, even if your energy wanes over time?

**SIMON:** It's not so much wisdom, it's experience. Of course, the difference between wisdom and experience is not so easy to distinguish. But one of the things I am and have always been particularly good at is finding connections between different ideas that sometimes don't look related at all. The more ideas you've been familiar with in the past, the more it can help you. There's no question, experience helps. On the other hand, it's also true that mathematicians have a reputation of doing their best work when they're young, partly because having a fresh point of view seems to be very important.

### The Meaning of Mathematical Physics

**ZIERLER:** We can now turn to mathematical physics. I got three different answers from Elliott Lieb, and Joel Lebowitz, and Albert Schwarz. First of all, are the terms mathematical physics and physical mathematics interchangeable? Have you heard of physical mathematics? Or are they different?

**SIMON:** I've heard people use it, but I've never understood how it is intended as a different term. Of course, historically, in parts of England, mathematical physics is just another name for theoretical physics. But I come from the Wightman school, and what was notable about Wightman was, he really believed in proving things. To me, that's what distinguishes theoretical physics from mathematical physics. Mathematical physicists really proved things in the sense that mathematicians use proof, and theoretical physicists demonstrate things. Mark Kac had this joke about the difference between a proof and a demonstration is, a demonstration convinces a reasonable man, and a proof convinces a stubborn one.

**ZIERLER:** [Laugh] That's a great line.

**SIMON:** It is. Mark really was a remarkable person. Lots of stories and jokes.

**ZIERLER:** For you, then, it sounds like mathematical physics is its own distinct field. It's more than simply being interdisciplinary between math and physics.

**SIMON:** Absolutely. There are certainly mathematical physicists or people who are sometimes called mathematical physicists who sometimes put their mathematical physics hat aside and write a paper that doesn't really prove things. But to me, it's a different field. Some physicists will say what we do is worrying about minutiae of things that we all know are true, and even there, Arthur Wightman would say there's a point in intellectual honesty that's important to even prove things that everyone understands must be true. But there have been new insights that have come from people who approach things from this rigorous point of view.

**ZIERLER:** From that perspective, coming from the idea that mathematical physics is a discrete field, what are some of the hallmarks that make it discrete, either by methodology, philosophy, teaching, perspective? What makes it distinct?

**SIMON:** Well, I've already said, the real thing that makes it distinct is that you go and prove things. It isn't enough just to convince other people in the field that it's true. You actually have to have a "proof". There are, of course, all these issues that the logicians like to talk about that really don't prove things because this or that axiom. But there is an understanding, at least in the mathematical community, about what a proof is, and to me, mathematical physics involves proving things.

**ZIERLER:** This is to say that if I were to try to pigeonhole you, if you're really a mathematician or a physicist, you would reject the premise of the question.

**SIMON:** No, not totally. I'd say I have the head of a mathematician and the heart of a physicist.

**ZIERLER:** [Laugh] What's some research you've done that really exemplifies that idea?

**SIMON:** If I want to emphasize the heart of the physics, I should talk about something that really has had an impact on physics. Many physicists will say Berry's phase is the most celebrated in the general physics community, and it's actually quite far, in some ways, from much of my other work. Much of my other work, mathematically, is connected with analysis, particularly functional analysis and operated theory, and Berry's phase is connected with topology.

**ZIERLER:** Physicists are aiming for a so-called grand unified theory, a theory of everything. When I ask mathematicians if they are searching for a grand unified theory, they say no. As a mathematical physicist, how do you square that circle, if math can be understood as the language of physics?

**SIMON:** Grand unified theory, at least in my understanding, is just the question of trying to put together gravity with the strong-weak interaction. Mathematicians would like to understand that, too. But in some sense, mathematical physicists, at least my kind, are really looking to make sense out of frameworks that already exist. It wasn't mathematical physics to invent quantum mechanics, but it was mathematical physics to prove that atomic Hamiltonians are self-adjoint. It would be folly to expect that you would find your first attempt to actually unify, if we ever do that, would be done on a mathematically rigorous basis. It's not going to happen. Doesn't mean if I happen to have a good idea about doing the unification, I would say, "Well, it's not going to be rigorous, so I can't do it." But it's not what I'm searching for.

**ZIERLER:** Why isn't it going to happen rigorously?

**SIMON:** It might eventually. In fact, it should. But the idea of saying, "I'm not going to worry about the details of doing things totally rigorously. I'm going to throw that away, and wave my hands, and if it's reasonable, plow on," is, in fact, the way you make progress at a certain fundamental level. It's a different kind of working to make progress. We still don't really have a mathematically rigorous formulation of electroweak, let alone strong, interactions. Quantum field theory is not mathematically rigorous in four dimensions. It's one of the big problems. It's a very interesting one.

**ZIERLER:** What accounts for this shortcoming? What explains it?

**SIMON:** It's hard. One of the areas I worked in was called constructive quantum field theory, and it was probably the hottest area in mathematical physics in the early 70s, and a significant fraction of my efforts at the time was in that area. At the time we were doing it, we knew the ideas we were working on seemed very promising in two and three dimensions, but there would have to be a very good idea to do four dimensions. Technically, it has to do with whether a theory is super renormalizable or just renormalizable. Super renormalizable means there are only finitely many counter terms, and you could, with your bare hands, do the renormalization. We were very successful in that. It was always understood you'd need some really good idea to go to the next phase. Some of those good ideas probably have to do with the renormalization group, which was invented just about that time by physicists, but really pushed through later. But no one has figured out how to do it. It was at the time clear you'd need a really good idea. It's 45 years later, and nobody's had the good idea.

**ZIERLER:** Two questions that highlight an academic divide between physics and math, first coming from physicists to math, and then vice versa. Just to take one of many examples, when certain physicists are critical of string theory because it has no basis in observation or nature, so far as we can tell, and the basis of the dismissiveness is, "Well, that's essentially just mathematics," what's your perspective on that? On physicists dismissing it because it's "just mathematics".

**SIMON:** Well, of course, from my point of view, it's not mathematics either. Because it really is speculative theoretical physics. They're still searching for a framework. To do real mathematics, you have to have a framework. There has not been a precise mathematical definition of string theory. That's one of the big issues. It's one of the hard problems that string theorists haven't solved. They've only been working on it for 20 years, but they feel they're getting closer. At least in quantum field theory, there is something very close to a precise framework, whereas in string theory, they're not quite there yet. It's, in some sense, neither physics nor mathematics.

**ZIERLER:** I wonder if you've sparred with John Schwarz over the years on these things.

**SIMON:** Absolutely not. John and I have had little contact. We have just such different views of the world. Ed Witten and I might, conceivably, but we haven't. One of the things I don't like to do, although I just did sort of, is spout off about subjects I don't feel I understand very deeply. I don't really think I understand string theory very deeply. I have seen little bits and pieces enough to know they don't really have a mathematical framework yet, although there are mathematical questions that arise in the subject that are well-defined mathematical questions that people have made progress on. But no, I've not sparred with John.

**ZIERLER:** To the extent that you have a sense or an intuition about where things might be headed, feelings about string theory have material consequences in faculty hires, in terms of funding decisions. Are you of the opinion more that string theory deserves more support, that it deserves more nurturing because it might get to where it wants to go? Or are you more of the school where you don't really have patience for this because they haven't demonstrated it in the 40 years since the early 1970s?

**SIMON:** I tend to be very suspicious of overpopulated fields. I tend to think too much money goes into these overpopulated fields. But I've never had to make funding decisions, and I'm not about to pontificate on the subject. I do share some people's unease with the current state of theoretical physics, that it seems to be focusing too much on things that are not close enough to experiment. Both parts of string theory and also parts of quantum computing.

**ZIERLER:** What, then, if not string theory, might get us closer to a theory of quantum gravity?

**SIMON:** I don't know. I understand, but the issue is, if a field isn't right, does it make sense you're sending a large fraction of your bright young people to it? I don't know. It's an important field, so you send all these soldiers. But again, I have my own relatively well-prescribed area or areas that I've worked in, and I tend my garden, and at least because my administrative responsibilities at Caltech have been more mathematical, I don't worry too much about this.

**ZIERLER:** To ask the question going the other way, for pure mathematicians who are not at all interested in relating their work to physical reality, for all of the mathematics you do, is there always some connecting point to observation or experimentation?

**SIMON:** Certainly not. In fact, in the last 15 years, I've been doing things that are not really mathematical physics. The kind of mathematical physics I do is very much connected with what's called spectral theory sometimes, which is what you would think a spectrum that has to do with light. But in fact, although it is connected to light, as far as I can tell, historically, it comes from the spectra of operators, and I don't believe that whoever invented that name, and it was probably someone in Hilbert's school, expected that it had any connection to spectra in the sense that you see when you look at light from the sun. Anyhow, it's called spectral theory.

I sort of wound up looking at problems connected with the theory of orthogonal polynomials that really are totally disconnected from physics, except to the extent that if you get some insight of one part of spectral theory, it may have some feedback to some other part of spectral theory that, because of my experience, I know is connected to mathematical physics. I've random walked – it's directed random walk - in areas of mathematics sort of towards those parts that are suggested by more the mathematics than the physics. For the last few years, most of what I do is not that connected with physics, although the current book I'm writing is going back to some things in statistical mechanics, which have much more of a connection to physics. But much of the research I've done in the last 15 or 20 years is in this spectral theory of orthogonal polynomials. There are certainly some mathematical physicists who disapprove of my path in life because I've stopped doing what they regard as important.

**ZIERLER:** Just as a snapshot in time circa November 2021, and as a way to convey to an audience of non-specialists for whom your work is rather obscure or difficult to comprehend, just on a workaday basis, what does a day look like for you? Are you on the computer? Is it a pen and pad? Is it big thoughts, staring up at the sky? How do you do your work?

**SIMON:** Now, much of what I'm doing is actually worrying about this book. I'm almost entirely on the computer. This is a sort of comprehensive look at the mathematically rigorous theory of phase transitions. There were certain results I knew were around. I never quite understood the details of the proof, so I have to first understand it and then figure out the right way of exposing it in the context of this book, fitting in with other parts of the book. It's a lot of work on the computer and TeXing, although I'm unusual in that I only learned to TeX about five or six years ago. I had the world's greatest secretary for many years, and she unfortunately passed away from cancer in 2013. Caltech actually paid someone to finish the TeXing of this five-volume work, but part of the deal was, I was going to teach myself enough TeX that in the future, I could do my own TeX. I've learned how to TeX. Part of it is that. I'm now retired, so one of the nice things about that is, I can tell people I no longer write letters of recommendation. There are a lot of tasks are important that I feel I don't have to do anymore.

**ZIERLER:** As you say, this walk that you've been on in the past 15 years, is this book project a culmination of those efforts?

**SIMON:** Not at all. If you look at what mathematical physics in a reasonable sense means, one part of it is, say, general relativity. But I've never thought about that, and most of the people I've worked with have never thought about it. There's sort of this core area that maybe goes back to Wightman of non-relativistic quantum mechanics, quantum field theory, and statistical mechanics, done mathematically rigorously. My central area has, in many ways, always been non-relativistic quantum mechanics. When I came to Caltech, much of my work focused on non-relativistic quantum mechanics and orthogonal polynomials. But when I was at Princeton in the late 70s, I gave some courses in rigorous statistical mechanics, I started writing a book that turned out to be a two-volume work. One was finally finished, that sort of more formalism and all the fun stuff isn't in it, was published about 1990, finished up just after I came to Caltech. And the second volume, I never wrote. A couple of years ago, some people began to really have a campaign that I really should go back and write this book I promised.

**ZIERLER:** What are your goals once it's published? What do you hope it'll accomplish?

**SIMON:** It's a little surprising, this is an area where the golden age was in the 70s and 80s. There's been some progress since then. There have been a couple of books that are not bad, but they're not as comprehensive as I'd like. The goal is to make this area accessible. There are a lot of people who do things connected with it, Ising model, things like that. I want them to have a decent reference.

**ZIERLER:** To take a very broad view of your contributions and impacts, particularly in light of the idea that mathematical physics is its own discrete field, in all of your major accomplishments, where have you had the most impact in physics? Where have you had the most impact in math? Where have you had the most impact within your own field, the garden that you've tended to, mathematical physics?

**SIMON:** There's no question that in physics, it's the Berry's phase stuff that has had the greatest impact. There are some things that mathematical physicists actually did first that theoretical physicists then rediscovered and sort of forgot that we'd done it. For example, lattice field theories. Everyone will say it's due to Wilson. Wilson did do it in a much broader framework, but for boson field theories, two years before Wilson's work, where Guerra, Rosen and I did it, but nobody noticed it. Did it have an impact on physics? I don't know. You're the historian of science. Historians of science, of course, have to worry about things that were in Gauss's notebook but was only rediscovered, and that's how people found out. How much credit does Gauss get? How much credit do we get? But there's no question that the biggest impact is Berry's phase. Not because Berry's phase itself is so important, but I introduced these topological ideas that have become very important, surprising I think Berry, me and many other people. That's certainly the area that's had the largest impact.

**ZIERLER:** Could you explain Berry's phase a little bit, what it is?

**SIMON:** Let me back up a little bit before that because it's part of a bigger picture. There's something called the quantum Hall effect. This is the discovery that, doesn't matter what it is, but some object is quantized that people hadn't expected to be quantized, and in fact, it turns out, the best measurement of the fine-structure constant is in terms of the measurement of this quantum Hall effect. There have been probably three or four Nobel Prizes connected with the quantum Hall effect. The first was the experimental discovery, and then there were several theoretical things. In the early 1980s, a theoretical physicist named David Thouless, who's British but spent most of his career in Washington state, computed some integrals, which he was able by hook and by crook to see were quantized.

I had a postdoc at the time, officially only a post-doc at Caltech, but he had been an assistant professor at Princeton, one of the people who came with me as part of the deal, who got very interested in the quantum Hall effect and read about Thouless's paper. He came into my office, and we talked about it some. And we realized that this was basically–in topology, there are certain things that are naturally quantized. The number of times you wind around is an integer number of times. It's a natural integer. We realized that, really, what Thouless had discovered, the integers he found were really what are called homotopy invariants. We wrote a *Physical Review* Letter–we actually first tried to say, "Once we know they're homotopy invariants, there are sometimes other homotopy invariants. Maybe there are some other homotopy invariants around that we would find a new interesting integer."

The first thing we found was that in the particular topological object that seemed to be underlying, there were no other topological invariants other than the ones Thouless had found. That was the main point of this Physical Review Letter, although in retrospect, we should've said, "Hey, this is topological," because that was the big realization. This must've been done in early 1983. In the summer of 1983, I was invited to visit a mathematical physicist at the Australian National University in Canberra, originally an Irish guy who was then in France and wound up in Australia. I'd met Michael Berry a couple of times, and he gave a lecture. I hadn't realized he was there. The lecture was in physics, and I was visiting mathematics.

But I'd heard he'd given this lecture. I missed the lecture, but I went to see him, and he was very kind and explained to me what he'd found. There's a theorem in quantum mechanics called the adiabatic theorem that goes back to the earliest days of quantum mechanics. It was found by Born and Fock in 1928. The first real mathematical understanding was by Kato in 1950. What it really says is, in quantum mechanics, if you have a time-dependent phenomena, and you start out in an eigenstate of the Hamiltonian, and your Hamiltonian varies, and you do it slowly enough you stay in an eigenstate…

**ZIERLER:** What does slowly enough mean?

**SIMON:** Mathematically, it means you put in a time scale, and slowly enough means you talk about what happens in the limit is T goes to infinity. And Berry was originally doing it in perturbation theory, not with a time-dependence, but just varying a parameter and seeing how eigenstates varied. He first made the discovery that if you're looking at real matrices, and you go around a singularity and come back, the eigenfunctions flip sign. He gave a talk somewhere, and someone said, "What if it's complex?" He said, "Oh, it's the same answer."

Then, he thought about it some more and realized, "No, no, there's a possible phase." It was more natural than to do it in perturbation theory, to do this thing adiabatically. If you do the naive calculation you might expect in the adiabatic theorem, there's some natural term that grows linearly in this time, which is going to infinity but might happen to be zero. But on top of that, there's a finite leftover piece which was unexpected. He did a calculation of what the leftover piece is, and that was what he told me. My immediate reaction was, "This could have something to do with Thouless." He said, "Oh, yeah, Bernard Souillard."

Bernard Souillard is a French mathematical physicist who actually left academics a couple of years later and became a business consultant. But he said, "Souillard, when he heard this, told me the same thing, so I asked Thouless, and Thouless said, 'No, no, no.'" I said, "Well, let me think about it." That night, I figured everything out because I'd already been thinking about it. It turns out to be incredibly connected to what Thouless had done. To try to give you the connection, let me go back and talk about a simpler thing. Let's imagine the geometry of a sphere, which is curved. One of the things that Gauss discovered that was generalized by Bonnet, called the Gauss-Bonnet theorem, there's a rather remarkable fact–there's a natural notion called curvature, the curvature of the sphere.

The more tightly curved it is, the larger the curvature is. It normally varies over the surface, but of course, for a sphere, it looks the same everywhere. If you actually take a round sphere, the curvature of the sphere is one over R-squared. You integrate that over the sphere, that's four pi R-squared times one over R-squared, you get four pi. And what Gauss eventually discovered is, if you deform the sphere, you again have a curvature. If you integrate it over the whole sphere, you always get four pi. It really just depends on the topology of the surface. If you do it for a torus, you always get zero. In fact, what you get is what's sometimes called the Euler-Poincaré characteristic of the surface. It's a topological invariant you get by integrating the curvature.

What Avron, Seiler, and I had essentially realized is that what Thouless was calculating–although my Berry's phase paper first used the term curvature, but what we'd realized in the meantime was there was a natural geometric object in the infinite dimensional set of quantum mechanical states that has a curvature. When you integrate it, just like when you do it over the sphere, you get four pi times an integer, you always get something times an integer, and that integer is this Thouless integer that describes the quantum Hall effect. Now, in terms of curvature, there's a different idea. It's called holonomy. It also actually, I think, goes back to Gauss. Suppose you take a sphere.

What I'm going to do is the following experiment. I'm going to walk on the sphere carrying a spear, and I'm going to do my best to keep the spear always pointing in the same direction. Not the direction I'm moving, but the direction it was. I imagine starting along the equator, going a quarter of the way around, up to the North Pole, and then down back to where I started. I do that, I start keeping parallel to the equator. Now, I turn, but I don't turn the spear. As I walk along towards the North Pole, the spear is pointing to my right because it started out pointing along the equator. I turned, but it doesn't. It's to my right and keeps going to my right. now, I go to the North Pole, I turn again, and if you think about it, if it's exactly 90 degrees, I'm going to be pointing down in this other direction, and when I come back, even though I've done my best to keep it parallel, it's going to have been rotated by 90 degrees, which in terms of radians, is pi over two, which is exactly the integral of the curvature over the eighth of the sphere that I've looked at.

The holonomy is also an integral of the curvature, but instead of over the whole surface, it's over part of the surface. What I realized was that Berry's phase was exactly holonomy in this topological sense, and it was the same underlying curvature. I wrote a paper where I coined the phrase Berry's phase. And I must admit that I'm a little annoyed that while Berry's phase is a great name, the underlying curvature has come to be called Berry's curvature, even though he had no idea it was a curvature. He did have a formula in his paper for what is the Berry's curvature.

**ZIERLER:** It should be Simon's curvature?

**SIMON:** Well, perhaps. Yes, it's my curvature, it's not his curvature. To finish the story, actually his paper appeared after my paper. But he published it in the Proceedings of the Royal Society, which despite its impressive name and history, people don't normally look at. But I published my paper in Physical Review Letters, and literally, there were probably 500 papers written on this within the next year. The reason has nothing to do with its intrinsic interest, I think, but to do with the fact that everybody's supposed to understand the adiabatic theorem. You learn about it in the first quantum mechanics course. But there was some new facet of it that was there, and everyone had to write a paper on how, "Oh, I understand that because it just is the adiabatic theorem."

At the time, I regarded this excitement as a bit of a curiosity, but then some condensed-matter theorists began to realize, "If there are these topological invariants here, they must be all over the place." And it's become a major part of condensed-matter physics. Different states of matter are called topological phases because they're distinguished by having different topological invariants. It really is a case where neither Berry or I understood that we had found something that was going to be really important. It was a very cute piece of mathematics, but it's been very important because it's been very useful and introduced ideas. One of the reasons I also think it caught on is, related ideas, a year or two earlier, had become very important in the study of gauge theories.

A lot of elementary particle physicists were very excited. People became interested because somehow there was, at a mathematical level, a connection between what they were doing and condensed-matter physics. It's one of the reasons I think it's become so important and natural. It was not something, I think, we realized at the time. That's certainly the piece that's had the biggest impact on physics.

**ZIERLER:** Has it gone beyond condensed-matter theory? Where else do we see it in physics now?

**SIMON:** Some of the underlying ideas were central before we did it to ideas in quantum field theory. As far as I know, it's really only in condensed-matter physics. But it really is a major part of condensed-matter physics, the study of these topological phases.

**ZIERLER:** To turn to that aspect of the question of contributions in mathematics, for mathematicians who might not have your physicist sensibilities…

**SIMON:** Probably, what I'm best known for to people outside the field of mathematical physics, along the way, I got involved in various mathematical techniques. I, for example, have, he said modestly, the definitive book on what are called trace ideals, which are certain ideals of operators that are very important in many areas of mathematics and have become very important in quantum computing. Again, not because I was doing anything related. In the couple years before I retired, I'd often have post-docs from John Preskill's group come and ask me some questions that would connect it with things.

Then, within mathematical physics, there are both specific contributions, but also I was fortunate to be one of the first people to work in some sub-area. I very much enjoyed finding an area with lots of low-hanging fruit. There are now people who do nothing but that, and there are conferences just in that area. You look at the theory of so-called almost periodic Schrödinger operators. It's a huge area lots of mathematicians have become interested in because it is such an interesting and beautiful subject. Avron and I wrote some of the basic papers in that, actually about the same time we did this work on Berry's phase. Also, Elliot Lieb and I did work on understanding the quantum mechanics of large atoms, where we realized Thomas-Fermi was exact in certain limits, which is surprising. Again, led to whole industries.

**ZIERLER:** If we can imagine a table of contents for your research career, where the rough dates for each chapter would be your graduate school years, your early faculty years, your middle faculty years, the transition to Caltech, later faculty years, and now in retirement, how many chapters would there be, if you look at the major topics you've worked on, going all the way back to your graduate school days?

**SIMON:** Well, I sent you a paper called *Twelve Tales in Mathematical Physics*. However, that stopped, in some sense, about the 2000, 2005, when I shifted to the spectral theory of orthogonal polynomials, and there would presumably be a 13th chapter. But it's a somewhat artificial way of dividing things because in some sense, you could say quantum field theory, statistical mechanics, and non-relativistic quantum mechanics. You could also say in nonrealistic quantum mechanics, there is many body, and then almost periodic and random. It's not clear.

**ZIERLER:** On that point, what have been the commonalities or research areas you've always remained close to, and where has your research taken on truly new dimensions and directions?

**SIMON:** In some ways, the 13 chapters really do represent different directions, where the beginning of that chapter is a sort of new direction. In *Twelve Tales*, the almost periodic and random are separate. They really are two facets of a half-piece. But basically, when I first came to Caltech, I told Yossi Avron, who was working with me, "A lot of the things we've been thinking about have sort of wound down. We really need to think about some new area to look at." I said, "Why don't I think about it, and we'll talk about it?" I came back and said, "There seem to be two really interesting things to think about. One is this almost periodic, where there's beginning to be a little work, and certain things about quasi classical limits, that there clearly were new mathematical directions for."

I said, "It looks like this almost periodic isn't very hard. We can probably wipe that out in six months. Why don't we do that first, and then we'll get to the other one?" In fact, the almost periodic has become a huge industry. I was working on it as my main focus for probably ten years. Wasn't six months at all. I did do some quasi-classical things, but not what I was talking about then. There's been a lot of interesting work in that area, but not by me since then. There was definitely that I regard as a new direction.

But generally, if you ask about this shift to orthogonal polynomials, it really was because there was a natural question that I was looking at with my students, and we realized that it was connected to the orthogonal polynomials, and it sort of led naturally. Most of my shifts have been really just where the research led me. I'm not one of these people who, "I'm sick and tired of doing this." It's where one piece of research leads, and in retrospect, you realize you've turned a corner. But it's more that.

**ZIERLER:** What are the feedback mechanisms you've used? As you say, when a particular field is winding down, and it's time for something new, when does that mean achieving a breakthrough? When does it mean you've intellectually tired of this area? When does it mean that the field is saturated, and you just want to go into a new area?

**SIMON:** I actually can't think of any time I've left an area because I felt it was saturated. Generally, it's because, as I said, I find the low-hanging fruit, and what's left looks really hard. You think about it for a little while, and you decide, "Eh, it's probably time to look for another orchard with low-hanging fruit." There's no question that one of the areas I'd been thinking a lot about in my career, but particularly from my late graduate student days until 1985 or so, 15, 20 years almost, is the theory of N-body quantum mechanics, particularly N-body scattering.

Someone who made some of the greatest discoveries in the understanding of two-body scattering, an Israeli mathematician named Shmuel Agmon who's actually celebrating his 100th birthday next year, said to me at one time, "Those whom the gods would drive crazy, they teach of the problem of N-body asymptotic completeness." There were several people who announced solutions, and then there were errors. This is something I wouldn't say was a major focus for me because I had so many other balls in the air, but I thought hard about it and made two contributions that turned out to be important. But it was clear it was a hard problem, I didn't have any great ideas, so I wasn't going to think about it anymore.

It was, in fact, solved shortly after I left the subject by two people, one of whom had been my post-doc and was one of my first post-docs at Caltech. After he left Caltech, he met up with someone else who had been an assistant professor at Princeton while I was there, and they solved the problem. But it's clear that it wasn't that there was nothing left, it's that the problems that were left were very hard, and I'm not someone who says, "Here's a hard problem. I'm going to beat on it until it gives way." It's just not my style.

### Eureka Moments and Proofs

**ZIERLER:** When have you had eureka moments, and how do you know you've gotten there?

**SIMON:** Well, in mathematical physics, you don't know you've gotten there until you've actually got the proof. There are two kinds of eureka moments. One is realizing what's probably true, and the other is figuring out how to actually prove it. Those can be separate eureka moments. If I go back, one of the things I mentioned before was that Elliott Lieb and I had done this work on Thomas-Fermi. We were both visiting the IHES, the Institut des Hautes Études Scientifiques. It's a small institute in Bures-sur-Yvette, which is a suburb of Paris between Orsay and Saclay, a math and a physics center. It was supposed to be the French equivalent of the Institute of Advanced Study.

David Ruelle was there, Connes was there, several math Fields medalists. David Ruelle had invited both Elliott and me who didn't know each other well. Elliott became convinced that somehow, this Thomas-Fermi theory, there should be some way of making real sense out of it. It was somehow an uncontrolled approximation. He said to me, "It's something we should think about." It just happened that I had taken as a graduate student with Arthur Wightman an "intermediate quantum mechanics" course that was unlike any intermediate quantum mechanics course anyplace else in the world because Arthur actually proved things. And he talked about some work that had been done.

He did Thomas-Fermi. There wasn't much that was mathematical, but he discussed it. He talked about something called Teller's theorem that says molecules don't bind in Thomas-Fermi theory. There was a paper Teller wrote in the issue of Reviews of Modern Physics dedicated to Wigner's 60th birthday in 1962. After, Elliott and I talked for a few days. I came to him and said, "The fact is that this can't be right because molecules don't bind in Thomas Fermi theory." Elliott walks in the next day and says, "Mr. Dalton's hooks are in the outer shell." He had the idea that this quasi-classical limit, which is what Thomas-Fermi is, should only be true when there are lots of electrons. If it's a description, it should be a description of the core of atoms.

And it could be a totally accurate picture of the core of atoms, and since chemistry happens in the outer shell, Mr. Dalton's hooks, it's not inconsistent that molecules don't bind. The first eureka moment was somehow realizing that maybe there was a real field here to look at. The first thing we had to realize is, there was essentially no literature even that these equations, which people could formally write down, actually had solutions, particularly in the molecular case. And I'd had just the right functional analytic background that we could do it. And not only that, I taught Elliott an enormous amount of techniques that he then became the great world expert on eventually. These minimization techniques that we needed, he's now the world leader on.

And then, we realized that we could sort of do this classical limit–there had been an earlier paper by André Martin that we knew about that did a WKB-type approximation with single particles, and we realized using these techniques, we could do things, except there was a problem with the fact that the Coulomb potential had a singularity. He was actually at IHES for the whole year. I was three months in Paris, three months in Marseille, three months in Zurich. I left, for Marseille and we had left what we call pulling the poison Coulomb tooth. We didn't have a result. We had an interesting result if it was cut off, but it wasn't the result one really wanted. I came back for a long weekend to Paris, stayed for Shabbos with Haïm Brezis and then Elliott and I worked for a few days and figured out what we needed.

That was a eureka moment, too. Nowadays, one would, in fact, use the Lieb-Thirring inequalities to do it even more easily. It was a special case of Lieb-Thirring, but we didn't understand it in those terms. Of course, Lieb-Thirring didn't exist then. There was a eureka moment there, when we realized we had the full result. I guess the punchline of this whole–there are two punchlines. One is, we wrote a Physical Review Letter, which we sent in, and we got a referee's report back that clearly had been written by someone who'd worked on Thomas-Fermi in the 1930s that read, "This is the worst paper I have ever seen. It is a sequence of unproven assertions," which is correct, it was an announcement, "many of which are obviously false. For example, the authors assert that the Thomas-Fermi density is C-super infinity, which would make the density identically zero, one, or infinity, depending on the value of C."

It was a total misunderstanding of the notation of C super infinity. Elliott and I were at a conference that next summer in Copenhagen, and we got the report. I wanted to make a big deal about the guy not understanding notation, but Elliott wanted to focus on some physical things. We demanded a second referee. I'd heard Freeman Dyson was the second referee, and he got a big kick out of the referee's report. And the second punchline is that this fact that molecules don't bind in Thomas-Fermi turned out to be the key to Elliott's work with Thirring on stability of matter.

The idea that when you have lots of electrons and protons, matter doesn't collapse is connected with the fact that they were able to control quantum mechanics rigorously (using what were essentially the first Lieb-Thirring inequalities) by Thomas-Fermi, and then used the fact that in Thomas-Fermi, you had stability of matter because molecules didn't bind. I was really wrong when I said Thomas-Fermi couldn't make sense because of Teller's theorem.

**ZIERLER:** In the way that physics has such well-defined grand mysteries or puzzles, whatever you want to call them, as we talked about, merging relativity and quantum mechanics, looking for physics beyond the standard model, understanding the conditions at the Big Bang, does mathematical physics have its own distinct and well-defined grand mysteries or puzzles?

**SIMON:** I wouldn't say they're necessarily grand, but because they've been open for a long time, they've become important open problems. I have several famous lists of open problems. If you look on Wikipedia, you will find an entry called "Simon's Problems". There, they don't have anything like the grandness of merging quantum mechanics and relativity, but they're puzzles. One of the most interesting open problems, to me, involves the work that Fröhlich, Spencer and I did in classical Heisenberg, and then Lieb, Dyson, and I did in quantum Heisenberg. One of the most important ideas in physics is the idea of spontaneously broken continuous symmetries. It's responsible for Higgs bosons, and it's an absolutely central element. If you asked if it'd been rigorously proven, obviously not in quantum field theory because I said earlier that four-dimensional quantum field theory we don't even know makes sense, although in lower-dimensional quantum field theory, there is an analog, and there are results.

Fröhlich, Spencer, and I found a way of proving that continuous symmetries are broken in three-dimensional discrete lattice models (the only way known of proving a non-abelian continuous symmetry is broken), of classical models, where you have spins on spheres. And then, Dyson, Lieb, and I, as a follow-up, asked, "What about the corresponding quantum models?" There, there's the ferromagnet and the anti-ferromagnet. Everyone believed that the anti-ferromagnet was much harder because its ground states are not exactly known. The ferromagnet was supposed to be easier. Even though classically, they're equivalent, but quantum mechanically, they're not. Dyson, Lieb, and I thought we found a proof for both the quantum ferromagnet and quantum anti-ferromagnet, wrote a Physical Review letter, and fortunately, before the full-scale paper was published in Advances in Mathematics, Fröhlich was teaching a course out of our preprint with the details and came to Elliott's office and said, "I don't understand why such-and-such is true."

I looked at it and said, "That's because it's not." Basically, we have a proof that works for the anti-ferromagnet, but the quantum ferromagnet, which we announced, was open, and 35 years later, it's still an open problem. It's an "important open problem". It's true in other parts of mathematics, there are usually well-defined problems that become important sometimes because they're really important, but often because they're interesting, and lots of smart people have worked on and haven't solved them, they become important open problems. There are lots of things like that in mathematical physics as there are in mathematics. Sometimes, they're really, really, really central, and sometimes, they're just interesting.

You'll see in *Quanta* Magazine, somebody's conjecture has been solved. The Riemann hypothesis really is important because it will tell us about structure of primes, but often, these conjectures that have been around for 50 years are interesting, fascinating problems, but not of great depth, except that they've been around and are known to be hard. There are lots of things like that.

**ZIERLER:** For these puzzles that have been and remain hard, what role can computers play in solving them?

**SIMON:** Again, it depends on the particular problems. The problems I would think about, like this quantum Heisenberg ferromagnet model that I just mentioned, computers are useless.

**ZIERLER:** Because they lack what? What makes them useless? They lack imagination?

**SIMON:** The real problem is, you know what you expect to be true, but you don't understand why it's true. A computer does an algorithm. You call tell a computer to compute something. But the issue here is not that you don't know what to compute, it's that something you expect to be true, you don't know the mechanism that forces it to be true. On the other hand, there are certain kinds of problems in combinatorics where computers can sometimes be very useful and have been useful. But for most of these problems, at least in their current state, computers are useless.

**ZIERLER:** Of course, all of these comments are rooted in classical computing. I wonder if you are interested in following developments in quantum computing, and that may lead to new possibilities.

**SIMON:** Again, there are lots of interesting things I think quantum computers can do. But like I said, the real problem is, computers aren't useful because they're algorithmic, and you don't know the right computational questions to ask. The same thing is going to be true with the quantum computer. It can go much further than computers on certain kinds of problems, but it doesn't mean that it isn't basically an algorithmic machine. Lots of problems in mathematics, and many of the problems I talk about in mathematical physics, are really mathematical problems. They're not problems in physics exactly, although you need some physical insight, perhaps, to understand what to do. Again, computers are not going to be, at least as we currently think about them now–I don't really understand enough about AI and other such things to tell you that I won't be wrong. I'm an old guy, but in terms of computers as they currently exist, including how a quantum computer might exist, no, but AI has certain other kinds of algorithms that maybe they can do it. I don't know. But not currently.

**ZIERLER:** Switching topics, with over 40 years of service to Caltech, some institutional history questions. The first, and perhaps most fundamental, for you, your research, your colleagues, with Caltech's age-old insistence to stay as small as it is, when has that been an asset to you, and when has that been a liability?

**SIMON:** You have to understand, from my point of view, in areas I'm interested in–in physics, Caltech is not small. Caltech's physics department is as big as, I think, any of the competing private schools. You look at Harvard, Princeton, Chicago, major physics departments are roughly the same size as Caltech. One of the things I noticed when I first came to Caltech is, you look at all the schools I just mentioned, Harvard, Princeton, Chicago, mathematics is, if anything, slightly bigger than physics in terms of number of faculty. At Caltech, we have a third the number of mathematicians as the physics faculty. Now, that's not totally fair because of course, some people who are officially in physics here could be in astrophysics. Maybe it's only twice as large. But it's still much larger. We are a tiny Mathematics Department compared to our competitors.

**ZIERLER:** And you're excluding applied math from this, I assume.

**SIMON:** Correct, because applied math now has become, particularly if you now take CMS–when I came to Caltech, there were four applied mathematicians. It was a very small group. I gave up eventually, but I was very interested in convincing people to allow mathematics to grow, with no success. There were two times it was at least taken a little seriously. PMA, Engineering, and Applied Science are by far the largest divisions at Caltech. They're three times the size almost of any other division. Both of them are a little unwieldy. There were some people in engineering who felt that it might make sense to split engineering in two. There was some discussion that we should take pure mathematics and some part of EAS and form a Division of Mathematical Sciences.

At least twice, it was at least taken seriously enough that it went beyond just some faculty talking among themselves. One time, it was shot down by the provost who said, "Gee, if I thought about doing that, I'd have to rediagonalize the whole matrix." That's not something you'd hear from administrators at most places, but essentially he said, "Maybe chemistry and chemical engineering should be split apart. I don't want to think about it." The other time, it sort of fell over by its own weight because in fact, there are traditionally some tensions between applied math and pure math that always come up.

I had colleagues who were convinced, perhaps correctly, that, "Yes, it's true that dealing with physicists can be a pain, but it would be worse dealing with applied mathematicians." It never went anywhere. I don't think of Caltech as being small in physics, but it's small in mathematics. And it matters. It's also meant that we tend to be a little unstable. In the year 2000, the combination of several retirements and Tom Wolff's untimely death meant we suddenly were from our usual size of 17 down to, I think, 11, and we were in a crisis.

**ZIERLER:** When has that smallness in math been a problem for recruitment, both of faculty and graduate students, post-docs?

**SIMON:** It's always a problem in recruiting faculty. Well, almost always. Because unless you have someone who says, "I do my thing. I don't want to talk to anyone"–I faced it when I came to Caltech. At Princeton, there were traditionally three joint appointments in math and physics. Actually, technically, right now, there are four people at Caltech, I think, with joint appointments in math and physics, although the math appointments are a courtesy because the string theorists and Alexei Kitaev have joint appointments. When I say joint appointments, I mean, really, people doing mathematical physics. Over many years, we made many faculty offers that were turned down, but I knew I'd have enough resources that I could make a viable group.

But it was a major decision that I knew I was going to an institution where I wouldn't have the same kind of resources that I had at Princeton. I also realized it probably would mean that I would mainly be able to focus on instead of quantum field theory, and statistical mechanics, and non-relativistic quantum mechanics, I mainly did things connected with non-relativistic quantum mechanics because of what would be around. I knew that was going to be [my focus]. On the other hand, my wife loves Southern California, and I love the idea of raising my kids here. I made the change. But recruiting me was an issue, and it's always an issue when you're trying to recruit people.

**ZIERLER:** Is that to say that, in looking around you, where the numbers are, who to collaborate with, that when you came to Caltech, you had more of a collaboration, more work in physics and less in math just as a result of who was around?

**SIMON:** No, because almost all my collaborations, at least when I was at Princeton, were with people who were specifically doing mathematical physics. Since then, in terms of joint papers, although there were some mathematical questions I would consult someone on, at Caltech, it's again true that almost everyone I've collaborated with is in "mathematical physics," except there were a couple of times there were mathematical questions that there happened to be people I could consult with. I have a joint paper with Wolff, a joint paper with Makarov. It would've been as easy to have such papers at Princeton, but the problems that brought them in didn't happen to be around. But in each case, I had a well-defined mathematical problem that I was sure they might be able to help me with. In each case, we found something very nice.

**ZIERLER:** One of the great transitions at Caltech over the course of your career, in terms of the interests of the undergraduates, has been, in the early 1980s, of course, physics was the dominant major, and today, it's computer science. Where has math, specifically mathematical physics, been impacted over the course of this transition?

**SIMON:** Let's talk about mathematical physics first because there are no undergraduates doing mathematical physics.

**ZIERLER:** There's too much foundational stuff to learn first, right?

**SIMON:** Correct. I've had maybe two or three SURF students over the years where I've been able to give them some well-defined problem, and they could understand what the problem was without understanding the real background behind it. But it's very hard. There's too much to know for an undergraduate to do mathematical physics, and that's true throughout the country. But you don't major in mathematical physics, you major in mathematics or physics. Mathematics has always had, as far as I know–I haven't kept track since 2014–has always had between 15 and 25 majors, which is a very small number overall, but in terms of the size of the faculty, we probably have the smallest faculty-to-student ratio because we're 16 or so faculty.

Computer science probably, too, because there are so many in computer science majors. I don't think there's been much impact on mathematics. Undergraduate teaching is both very important and not very important in terms of Caltech deciding where it puts its resources. It doesn't care what undergraduates major in. It's looking at where the important scientific discoveries are being made. It's only important to the extent that if some area's small, and it winds up with a huge number of students, we have to do something. And that has happened, probably. There's probably been a growth in some parts of computer science because they need extra faculty to handle the number of students.

But I suspect it's not affected PMA a whit. PMA is the same size, in terms of faculty, it's been my entire time here. The rough ratio of number of astronomers and number of mathematicians is about the same. Again, most of our teaching hours are, in fact, required core courses, which everyone has to take. That's, in one sense, shrunk, and in a different sense, hasn't shrunk. It's shrunk in the sense that there used to be two years required, and there's now only one year required. My impression is that the second year, which used to be required of all students but isn't anymore, almost all students take anyway. I don't think there's been a huge impact in terms of undergraduate teaching on mathematics at all, and certainly not mathematical physics.

### Caltech Undergraduates are Very Special

**ZIERLER:** You were an undergraduate at Harvard, graduate student at Princeton, professor at Princeton, professor at Caltech. To the extent that you can compare in these very different aspects or timelines in your career, where do you put the strength of Caltech students relative to these competing institutions?

**SIMON:** There was a period from about 1995 to 2002 I taught Math 1A. I gave a pep talk on the first day to the students, and one of the things I told them was, "I have bad news for you. Half of this class is going to be in the bottom half of the class." Then, I said, "And I won't claim that Caltech's top students are better than the top students at Harvard, or Princeton, or Stanford. But our 50th percentile is quite a bit better, and our 20th percentile is infinitely better." Caltech's undergraduates, in terms of being fantastic all the way down to very near the bottom, there's no place close in the US.

**ZIERLER:** What accounts for that? Is it the selectivity in admissions? The kind of student who wants to be at Caltech?

**SIMON:** It's a combination of two factors. The kind of student who wants to be at Caltech, and the kind of student Caltech wants. Caltech picks students based almost entirely on whether they're burning to be scientists. Two of my classmates at Harvard in my year, one was eventually Governor of Massachusetts, and one, because of family he was in, was the publisher of the *Washington Post*. Caltech doesn't look for students like that. Harvard wants to look for students like that. When I say comparable, I don't mean in terms some sense of what they're going to accomplish, I mean in terms of academics. Harvard searches for a very different kind of students from Caltech, and it winds up with a very different kind of student.

**ZIERLER:** What about MIT?

**SIMON:** MIT is probably comparable in many ways. I haven't as much experience with MIT.

**ZIERLER:** Of course, it's much larger. It's huge.

**SIMON:** My impression is, because it's so much larger, it doesn't quite have as good a student body. But MIT might be the one place that my statement about 20th percentile isn't quite correct.

**ZIERLER:** Between how small Caltech is and because of how idiosyncratically it's organized with the divisional structure, for professors, what is the most impactful position? Division chair, provost, president? Over the course of your years, in terms of a new person coming into those roles, what has made the most difference day-to-day?

**SIMON:** Presidents are irrelevant. They raise funds. They're irrelevant, except they run the institution. I talked about this crisis in 2000. One of the things we wanted to do was to hire a fresh PhD as a full professor. It's a long story. In fact, it was a brilliant choice. We unfortunately eventually lost him to MIT, but he's really good. Even Michael Aschbacher, who's probably the toughest judge, said, "The only way of thinking about this is, this guy wrote such a spectacular undergraduate thesis in Russia that the only way to think about him is that was his PhD. And so, in graduate school, he's been like a post-doc and done some very good things, so it's time to give him tenure."

The one time that the president almost shot us down, David Baltimore decided that it made us look desperate to make this offer. Because it was such an unusual offer, while it sailed through the division, at the IACC, it was a three-three vote, and officially, it was the provost's decision because that's how Caltech works. But Baltimore was really pushing hard not to do it. And Tombrello, who was the division chair, and I had a critical meeting with the Steve Koonin, who was the provost, and convinced the provost. Of course, the president, in the end, could've said, "Yeah, it's officially your choice, but I order you"–the president does run the institution. The provost officially reports to the president.

But basically, the president is almost irrelevant. Provost is very important because he controls all the resources. Division chair is also very important because within the division, he controls the resources. As an individual professor, probably, the division chair is the most important. As an administrator in mathematics, where I have to worry about money for various things, the provost becomes a little more important. When I was in mathematics, the attitude of the provost–not that I ever got to deal with the provost. It really is true to the first approximation that the provost deals with the division chair, not with individual faculty, in the level of making decisions on what's going to happen with resources. Of course, that's true at the small scale that someone like me works. It wasn't true, for example, with LIGO. There, the attitude of the provost was very important, and individual professors were involved.

**ZIERLER:** Did you mostly manage to escape from high-level administrative responsibilities?

**SIMON:** Of course. I came in 1981. The EO at the time in mathematics was Wim Luxemburg, who I had thought had had the job forever. It must've only been a few years before I came because I served ten years eventually as EO, and Gary Lorden claimed that it was longer than Luxemburg. I don't know what the details were, it had something to do with he couldn't keep within budget, but at some point, Ed Stone, who was division chair, decided to fire him, called me, and then said, "I want you to be EO." At the time, I was 42, and I said, "I'm too young to die. I won't take the job."

And he couldn't believe it. Eventually, in 1998, when I was 50-something, I agreed to take the job. I had it on and off for a period of ten years. It's a long story about what happened, but in some sense, I was virtual EO, even for the short period I wasn't because the person who was then EO was not very good, and Tombrello, who was used to dealing with me, dealt with me anyways. I was EO for quite a while. But it wasn't so bad. I was never more than EO. Never a dean. EO is not like a department chair. For example, as EO, I didn't know what anyone's salary was. I had nothing to do with salaries. I had relatively little to do with recruiting. That's all done by the division chair, not by the EOs.

It's not that onerous a job, and I had the world's best secretary, which helped a lot. I still remember when I was at Princeton, we tried successfully to convince the chair, who was very good, to take another term. I went to see him, and I said, "The problem is the following. This is only a half-time job. The problem is, it's every other five minutes." And the issue with EO is that it's not every other five minutes, it's every third five minutes. It really is a quarter of your time. But when something comes up, it really has to be dealt with, and often now. You're writing a paper? Well, postpone it for a week, or something comes up, there's not a big deal. But there's some administrative crisis that happens, and it needs to be dealt with now.

### Science and Torah

**ZIERLER:** The last topic I'd like to engage with you on for this first session is the way you see connections or lack of connections between your science and your Torah. At a very basic level, scientifically, not spiritually, do you tend to separate out those worlds in terms of your thinking, your sensibility, your intuition? Are they different? Or is that impossible?

**SIMON:** No, I think they're very different. Judaism structures how I deal with my everyday life. The science is what I do. And I don't try to avoid, with one exception, the famous Torah Codes controversy, getting involved in some of the controversies that have occurred in the religious world between science and Torah because it's basically usually on such a low scientific level. And there are, if you look at the deep intellectual Jewish history, usually pretty good answers to a lot of the issues. But there's no point in arguing. I'm not someone who likes to get into arguments.

**ZIERLER:** I mean at a much more personal level, not in terms of politics.

**SIMON:** I read the Torah a portion of the week, and I don't say to myself, "That couldn't have happened. It's not scientific." Basically, I'm of the opinion that there are parts of the Torah that you are not intended to take literally, so I don't take them literally.

**ZIERLER:** I'll give you a very specific example. If you wrestle with the concepts of *echad* and *yachid* [Ed. *Hebrew, referring to different concepts of oneness*] do you feel like you have a deeper understanding because of your mathematical background? Or in wrestling with *echad* and *yachid*, does that yield insights into your scholarly world that might not be available to your secular colleagues?

**SIMON:** I'm schizophrenic. No. I've separated them. They're not integrated.

**ZIERLER:** I'll flip the question around. As you well know, so many physicists delight in their atheism because of how they understand how the universe works. Do you see yourself as a specific counter to that, that you have insights to both Torah and in math and physics, for which it's entirely plausible why the universe has a creator or even has a creator that's involved in our existence?

**SIMON:** I don't spend a lot of time worrying about this, but at some times in my life, I thought about it and came to a peaceful "whatever." One of the people who most delighted in this because his father was so anti-religious was Dick Feynman. Dick and I actually had a number of interactions that we can talk about at some point. But at tea one day, we were going up to the colloquium, someone turned the light on and off. Dick looked at me and said, "You know, there are people who say that causes a fire, so you can't do it on Shabbos."

**ZIERLER:** Did he really grossly misunderstand Shabbos?

**SIMON:** Yes. I said, "Dick, we could argue about this, but we wouldn't agree, so why do it?" He looked at me and said, "You're right!" I wasn't going to argue with him.

**ZIERLER:** Operating in a secular environment, do people think you're a rabbi because you look like one?

**SIMON:** Not at Caltech, certainly.

**ZIERLER:** Are you regarded as one?

**SIMON:** No. Again, you'd have to ask them. I don't feel like people treat me any differently from anyone else. Now, that may be because I'm not terribly observant of other people's reactions. I'm interested in my research and my interactions with people tend to be at a scientific level. I'm not tuned in on how they're necessarily thinking about me. But I don't really think I'm treated very differently by my colleagues here. To the extent that I'm treated differently elsewhere, it's because I'm the big-shot, people want to be nice to me, and so they're worried about kosher food and other such things. I have not personally felt this, but you'd have to ask other people if they think of me differently.

I know the Chabad rabbi here thinks I'm whatever because I'm a symbol of something, and maybe I am to some people, but I don't think of myself that way. The few times there have been students on campus who have religious interest–there was one period when there were four students on campus who had some real interest, and we would have them for Shabbos. We would have them for many Shabbosim. It was a bit of a pain for them because we live 20 miles from campus and I didn't usually come to campus on Fridays, and they had to get to us on Friday, which would be a bit of a pain for them.

**ZIERLER:** Because you are undeniably a symbol, in the United States at least, are there other eminent kippah-wearing mathematicians or physicists you know of?

**SIMON:** Oh, absolutely. There was a point when Harvard had three religious mathematicians on senior faculty. Even now, there are two kippah-wearing mathematicians on the faculty at the Coursant Institute, both of whom I know. The ones at Harvard, it's not that I didn't know them, but I didn't know them well. One at the Courant Institute is my former student, who was not religious when he was my student, and the other is someone I've known since we were graduate students together.

**ZIERLER:** In operating in a secular environment, have you ever been challenged like, "Oh, come on, Barry. You don't really believe this stuff"?

**SIMON:** The only time was this interaction with Dick. Otherwise, nobody. Oh, there was a different story, I'd forgotten about this. Caltech was run by physicists for many, many years. The president was always a physicist. And at some point in the middle of the 1990s, the biologists decided they really wanted more respect. They arranged a lecture series that was early Friday afternoon because I remember had to stop going because it was running too late when sundown was nearing and so Shabbos was starting. But they had a lecture series they called biology 101 or something like that, and you had to be a faculty member to go to these lectures.

Most of them were given by Caltech faculty members, but they had one where a guy came from Berkeley, and this was long before the human genome was totally understood. But there was a bacteriophage with 160-some-odd genes that had been totally understood. The lecturer was talking about this, and I was sitting next to a distinguished theoretical physicist who, without thinking about it, turned to me and said, "It's really hard to believe something like that could rise spontaneously." I said to him, "Precisely." He got all red in the face.

**ZIERLER:** [Laugh] That's great. I asked you questions of spirituality from a very sort of highfalutin level. What about on a more mundane level, in the value that Yiddishkeit plays in your scholarly career? Anything from *mussar*, ethics, or even *menuchah*, or rest, from having Shabbat and having the ability to turn off for a day?

**SIMON:** I'll tell you another story about Shabbat. I really was very energetic in my youth, doing all this work. I was spending some time in Israel then, too, although less than now, and I came to the Weizmann Institute. There was a nonreligious but nevertheless very Jewish professor there, old-fashioned physicist. I had heard his name because he'd done some of the early calculations that were necessary to understand the Lamb shift in helium in the late 40s. I came to see him, and he said, "I have the most amazing story to tell you. Freeman Dyson came to get the Wolf Prize. He visited us, and it was amazing. He was a goy, and he praised Shabbos. He said to me, 'Thank goodness for Shabbos, because without Shabbos, we couldn't keep up with Barry Simon.'" And my immediate response was, "He has it completely wrong. It's because I recharge my batteries on Shabbos that I'm so productive the other six days." But in that sense, it gives me a certain kind of perspective that's very useful.

**ZIERLER:** Last question, just so I understand, you don't concern yourself with the unknowability of Torah, about *olam ha emes* [lit. "world of truth" fig. "heaven"] or *nissim* [miracles] These are all un-knowables, and as a scientist, it's not concerning to you?

**SIMON:** They're unknown to science also. Torah and science are dealing with different aspects of the world, of life. But I've, successfully or not, separated them. I'm also not a deep philosophical thinker. Either that's a problem with my science or virtue, I'm not sure which. But it impacts this question.

**ZIERLER:** It probably keeps you from running around in circles any more than you do.

**SIMON:** It's in a different way, but I've met some people who just go crazy over the Torah Codes.

**ZIERLER:** Well, I'm glad you don't. On that note, in our next session, we'll take it all the way back to the beginning, to New York and even before in Europe. We'll pick up then.

[End of Recording]

**ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It's Friday, November 26, 2021. It's my great pleasure to be back with Professor Barry Simon. Barry, once again, great to be with you.

**SIMON:** Likewise.

**ZIERLER:** In our first talk, it centered around your academic title at Caltech. Now, let's start with your name, Barry Simon. Is your birth name Barry?

**SIMON:** Yes. Well, yes, that's my birth name, that's what it says on my birth certificate, which I have a copy of, and I can send you if you want it for some reason. But I was named after my father's mother, who passed away less than a year before I was born, whose English name was Bessie, but her Hebrew name was Bracha. My Hebrew name became Baruch. I gave all my kids secular names identical to their Hebrew names, but in those days–and they weren't as Jewishly identified–they, of course, gave me an English name. Baruch became Barry. Just as my brother, who was named after my father's father, whose name was Yitzchak, Ike was his English name, but they decided it was Richard for him. I don't know why they didn't make it Isaac. They liked the sound better, I guess.

**ZIERLER:** And Simon, I assume, is an Anglicized name?

**SIMON:** No. What I was told by my parents is it was an Ellis Island name. I'll get back to that in a second. The original name was essentially Slopak. I've actually seen a copy of my grandfather's ship registry that he came on, and it has the spelling S-L-O-P-A-K. The story was, he was met by a landsman, someone from his town, at Ellis Island. When the clerk asked for his name, the landsman, who didn't speak English very well either, thought he was asking for the landsman's name, which was Simon, although as my father likes to say, that probably also was an Ellis Island name. That's how it became Simon. At least, that's what I was always told by my father. I've learned a bit more. I've thought more about my grandparents in the past few years for two reasons. One is Donald Trump.

I always took for granted, "Yeah, there were immigrants." I knew that. But I didn't appreciate, first of all, that of course, there had been periods when America had been welcoming to immigrants and periods they weren't. And I appreciated what it was for them, all of them roughly at age 20 when they arrived, to come to this totally foreign country and acclimate themselves. The other reason I became interested is, I have a daughter-in-law who got very much into genealogy. She has this elaborate family tree on Ancestry.com, and she's gotten lots of records and other things. She informs me there was no such thing as an Ellis Island name, that names were not given at Ellis Island, but that you had to register a short time after you arrived in an immigration office on the mainland.

She actually, at one point, believed that his brother, who also had the name Simon–to me, the most likely explanation is brother came slightly later. It isn't totally clear. On the other hand, my father says he actually went on a date with the daughter of the Simon who's supposed to have named us. However we got it, it's certainly not our ancestral name. It's a name that either my grandfather, or his brother, or someone got when they came to America. Interestingly enough, Mike Reed's name should be Rosen. So Reed-Simon should be Rosen-Slopak. His father was the one who came in 1938. He was a chemist. He immigrated from Vienna. When he went to look for a job, he was told, "We'll only hire you if you change your name because we can't hire Jews." Rosen was too obviously a Jewish name, so he became Reed.

**ZIERLER:** It was your grandparents who were the immigrant generation?

**SIMON:** Correct. Although, my mother's father's mother came on the same boat. It's a little complicated, but he came, I think, in 1904 or '05. By the time of the 1910 census, his father was already here, but then disappeared. It's not totally clear, but he lived in their household. But my grandfather was 20, roughly, when he came.

**ZIERLER:** Where were your grandparents from?

**SIMON:** Basically, all I knew is they were Litvaks, so I would've said Lithuanian, but I now know much more. I know where my grandfathers are from. I don't know where my grandmothers are from. My daughter-in-law has not located papers that list that. Census forms, in those days, tended to ask for the birthplace of the head of household, not the wife. My mother's father was born in Odessa in I think a not very religious family. He was extremely left-wing. I don't know if you know what the Bund is. He was a member of the Bund, he's buried in the Bund section of the cemetery in Queens. I have a son who's a real *Talmud* *chacham* [Torah scholar] not like my background, and my grandfather would be absolutely aghast at the thought that he had a great grandson who was–and he was the only one alive when I was born. He passed away when I was about 6, so I had very vague memories. All the others passed away before then.

He was in the dressing trade, I think a cutter or something. But very active politically his entire life. My father's father comes from Grodno, which is a town in the northwest corner of Belarus, very close to the Polish border and also the Lithuanian border. In fact, I suspect that's where there were all these Turkish immigrants a few weeks ago when there was this crisis in that area. It's a town where the Jewish population was essentially totally wiped out by the Nazis. There were two famous pogroms, and those that survived, I think, were less than 10% of the population. Which makes me appreciate that my grandparents came to this country.

**ZIERLER:** Did you have family who were wiped out by the Nazis? Or was everybody here at that point?

**SIMON:** I presumably did, but you have to remember, this is my grandparents' generation. Moreover, my father's parents, everyone described as two saints. My mother's parents, not so much. One of the things my grandfather was known for was essentially spending all his money bringing over his relatives. Many of them came to this country. There probably were some that were left, but my father had essentially no contact with the old country. There was a cousins' club, but it was all local. It's possible my parents knew something. You have to remember, I was a little kid in the 50s. I had no knowledge that I had any relatives wiped out in the holocaust, although presumably, there must've been some. My daughter-in-law, if she looked at the family tree may actually know there are some who have. I could ask her, but not that I'm aware of.

### Brooklyn Roots

**ZIERLER:** Which grandparents did you know growing up?

**SIMON:** My father's father and my mother's mother both passed away even before they were married, around 1930. My parents were married in '34, and I think one of them died in 1928, one 1931. My father's mother, as I told you, passed away about a year before I was born. The only grandparent who was alive when I was born was my mother's father. He actually lived with us for the last two years of his life. He wasn't that old. But I remember him as a chain smoker, and he died of lung cancer. That's the only thing I really remember, that he was always smoking. I was maybe 6. I can check the exact dates, but I think I was 6 when he passed away, and I don't think he was a particularly warm individual.

**ZIERLER:** Everyone was in Brooklyn?

**SIMON:** Or Queens. New York City. They all came to New York City. I know my mother's parents got married in New York in the new country and met here. I'll tell you a story about that and the dates that I know in a second because there's an interesting story there. It's not quite clear yet, according to my daughter-in-law's research, whether my father's parents were married already or shortly after they arrived. Certainly, there was some kind of survey that my daughter-in-law has a copy of that shows them as married about three years after my grandfather came. He was alone on the boat, but I don't know. Every three years, the apartment had to be painted because that was the rule, and my mother's father's policy was, it was too disruptive, so they moved.

She spent part of the time in Brooklyn, but I think more in Queens. My father's parents lived in Brooklyn their entire lives after they arrived. My parents lived in Brooklyn from when they were married until about 1968, I think, when they retired to Florida. I should tell you the story about my grandmother. My grandmother worked at the Triangle Shirtwaist Factory, but she was out sick the day of the fire. This was March of 1911. She was married in May of 1911, and my mother was born in March of 1912. If you go to the Triangle Shirtwaist website, my brother is interviewed there, and there's a picture of my grandparents.

**ZIERLER:** She could've been one of those doomed women.

**SIMON:** My impression is there were very few people who survived. Because there not only weren't fire escapes, but they were locked in to prevent them from goofing off. It was terrible.

**ZIERLER:** To get a sense of her worldview and that of her family, would the phrase *hashgacha pratis* [divine will] have been in effect for something like this?

**SIMON:** I don't know about her, but her husband was the one who was anti-religious, so absolutely not. On the other hand, my father's parents were quite religious. Unfortunately, the chain was broken by immigration. My father has two brothers and one sister. My aunt essentially was observant, kept kosher, but none of the other kids really did. My mother once complained to me that, "I spent the first part of my marriage, and my mother-in-law wouldn't eat in my house, and now my son won't eat in my house." But certainly, they would not have said *hashgacha pratis*, no way, no how. It's possible my grandmother was religious before she married my grandfather. I doubt it, but who knows?

**ZIERLER:** Tell me about your parents. Let's start, first, with your mom, Minnie.

**SIMON:** Both my parents benefitted from the fact that City University was free in those days. My mother went to Hunter College, my father went to CCNY. They both entered the job market in the Depression, so my father got a degree in accounting, but the only job he could get was in the post office as a postal clerk. It was a civil service exam, and he was a smart guy, so he could pass the civil service exam. He was basically someone who sorted mail, but very quickly, he moved to working in the office. For most of his career, he worked in the office at the Postal Concentration Center, PCC, which is very near the big New York Public Library. I've always wondered why he didn't strike out after the War when there were more opportunities, but he was a very responsible guy, and he had a family to support, so I think he decided to not take a chance.

They finally opened up the civil service exam for supervisor. Before that, postal supervisor was totally a patronage job. In the early 1950s, he took the first exam, passed it, became a supervisor, stopped being in the office. Essentially, he had to go around and make sure the clerks weren't goofing off. He hated it. As soon as he could take early retirement, he did and worked as an accountant for roughly ten years, and then they moved down to Florida. It was a tough life because of the Depression. He always had lots of intellectual pursuits. He was a bridge player. He and I played duplicate bridge when I was in my high school. Did fairly well. There were these puzzles he always entered and I know he was very serious about, was going to make money on them. I think he never made a lot. He was a very interesting guy. Clearly, I get a lot of my smarts from him, but he was not dealt a kind hand.

**ZIERLER:** With different circumstances, he could have had an academic career?

**SIMON:** He certainly was smart enough. That's not really clear because it would've had to have been very different circumstances. He got a degree in accounting. He wouldn't have gone to an academic career from that. But he would have presumably been a serious accountant. He did people's taxes for years. TurboTax didn't exist then. People paid whatever it was, and he made some extra money doing people's taxes. Then, as I said, when he retired, he had the job as the accountant for a small catering company. I think he had the smarts is my impression, but it would've had to have been very different circumstances.

**ZIERLER:** What about your mom? Was she academically inclined at all?

**SIMON:** She was even smarter than my father in many ways. She always lorded it over me. I couldn't talk to her until I was in Junior Phi Beta, which I was. She did very well academically at Hunter. She got a job, actually, as an assistant buyer at Macy's. She worked for the woman who became famous as the author of the book *Cheaper by the Dozen*, about a woman who had a dozen kids. She used to talk about that. Then, of course, there was the Depression. My brother was born in 1942, in fact on December 7. Whether they decided they could afford it because the economy was turning up, or my father didn't want to be drafted–although he was already in his 30s. Anyhow, they did not have kids. Once they had kids, she stayed at home until I was probably in 3rd or 4th grade, and then she became a schoolteacher.

**ZIERLER:** What neighborhood were they in when you were born?

**SIMON:** From the time they were married until they moved out, we lived in what I guess would be called Flatbush. It's between Flatbush, and Midwood, and Sheepshead Bay. It was around the corner from Madison High School, which we'll talk about in a few minutes, presumably. My mother was a 4th grade teacher. She had kindergarten for a while. But she loved that. She just loved it.

**ZIERLER:** The neighborhood where you grew up, was it diverse? Was it, like, Italians and Irish? Who was there?

**SIMON:** I can think about my neighborhood by my high school. I would say 90% of the kids in my high school were Jewish.

**ZIERLER:** But secular.

**SIMON:** At the time, secular. It's actually become fairly religious since, that neighborhood. Particularly a little bit north, the so-called Avenue J area. There was one Orthodox synagogue five blocks from us, but it was small. But at the time, the neighborhood was very Jewish and mainly, I think, for the children or grandchildren of immigrants. Because my parents felt we needed to be bar mitzvahed–before then, I think they were not–we joined a local Reform synagogue that I think in its height probably had 1,000 members. For Rosh Hashanah, Yom Kippur, probably had 1,000 people in shul and probably had trouble getting minyanim other times. I even went to Hebrew school, although my parents did not keep many other than customs as Jews.

**ZIERLER:** How provincial was your Jewish world? Were you aware of Borough Park? Were you exposed to any Talmud, Torah when you were a kid?

**SIMON:** Well, I went to Hebrew school; even Reform Hebrew school, you learn Shema [a Jewish prayer] and the books of the Torah so I was exposed to a little, but it was basically very simple, background. I did not know of Chasidim, or Borough Park, or anything like that. I knew there was this Orthodox shul, which my mother, from her father, picked up–they weren't really pejorative, but they clearly didn't approve of these ideas. And my mother had an uncle who was, in fact–for Pesach [Passover], we would go for the Seder. We'd all drive there and drive back. But he knew what was supposed to be in the seder, and we went through it, so I had some exposure.

**ZIERLER:** Did Torah study, preparing for your bar mitzvah, light a spark?

**SIMON:** No. Although, it was quite clear my parents expected us to only marry within the tribe. That was understood. But my interest in Judaism came when I was in graduate school, and it was impacted by my wife.

**ZIERLER:** And growing up, you were in an apartment, a house?

**SIMON:** An apartment on the third floor. Two bedrooms. Well, it had a kitchen, a fairly large living room, which had a foldout sofa, which is where my parents slept, and a bedroom where the boys slept. I'm not sure what my parents would have done, if we'd been opposite sex, when we became older. It was not a terribly big apartment.

**ZIERLER:** Were you into sports as a kid?

**SIMON:** Not at all. Absolutely not. I was more pudgy than now and didn't really have any friends to speak of until I got to high school, and my friends were mainly in the class ahead of me because I got to know them when I bumped up and took calculus a year early. It was a very much scientific-oriented in-crowd that I was in, the year ahead of me, in some sense.

**ZIERLER:** When you were younger, before high school, did you exhibit any particular aptitude in math and science that made you stand out?

**SIMON:** My memory, and it's a little vague, is that somehow, around the 4th grade, I was moved to the honors class, and the New York City schools then, probably still now, although given current attitudes, I'm not sure it'll last long, had something called the SP program. You did the 7th, 8th, and 9th grade in two years. Although both the high school and elementary school I went to were about a block from my house, to go to the SPs, even though my elementary school went to grade eight, you had to go a junior high, and that was about half a mile away. And that's where I went for 7th and 9th grade. I certainly was already this obnoxious loud student that I was for most of my student career. Always answered questions in class. I got a math medal from my junior high.

**ZIERLER:** Was James Madison in the same category as a Stuyvesant, a Bronx School of Science?

**SIMON:** Not in terms of being selective. It was a local high school. Partly because of the clientele–there were a lot of smart kids there. In those days, there were a lot of good teachers. There were a huge number of really good teachers, and it made for a very good education. We have a distinguished set of alumni, as you may have read about. We actually have the third most Nobel laureates of any high school in the world. More than Stuyvesant. Bronx Science and a selective Lycée in Paris are the only high schools with more. We have five Nobel laureates. Even though, if you look at their Nobel prizes, I think between the earliest and the latest was close to 50 years, they were all students within a seven- or eight-year period around 1940.

There must've been some very special teachers then, but who knows? They all are long before my time, in terms of when they were students. One of them only got the Nobel Prize three or four years ago. Arthur Ashkin, who was 95 when he got his Nobel Prize, the oldest Nobel Prize winner. In addition, Ruth Bader Ginsburg was an alumna of Madison. At one point, we had three senators from three different parties. We had a Republican, Norm Coleman from Minnesota. We had a Democrat who's still there, Chuck Schumer from New York. And we had an independent, Bernie Sanders, who I think was in my brother's class, although my brother says he didn't know him.

**ZIERLER:** What about Brooklyn Tech? Did you consider that?

**SIMON:** We thought about it. Stuyvesant and Bronx Science were too big a trip, although eventually I did take trips on the subway to go to a special one day a week program. I decided I didn't want to go to Brooklyn Tech because it was not science-oriented, it was engineering-oriented, and you had to take two or three years of technical drawing, and I had no interest in doing that. My brother had gone to Madison, I knew it was a good school. He worked in the math office, and he somehow discovered that I had not been put in the math honors class, even though, as I said, I had gotten the medal in junior high as the best–and he talked to them, and they fixed that. But I got a fantastic education. Amazing teachers.

**ZIERLER:** As you say, you came into your own socially in high school. Were math and science part of that?

**SIMON:** Absolutely. What I remember is, about the second week of my sophomore math class, my teacher asked me to stay after class so she could talk to me. She said, "I would like you to bring a book to class to read and to not take part in class because it is too discouraging for the other students that before I've asked the question, you have your hand up." I was, of course, someone who probably not only had my hand up, but shouted out the answer. She said, "I understand you'll know it. You can study it. But I really don't want you to disrupt the class by answering questions all the time."

It was clear I was a "problem", so it was decided that trigonometry was something I could learn in a week or two, and I should just skip into the–there was a double-period senior math class, which did calculus, and solid geometry, and advanced algebra. But mainly calculus. I skipped into that. It was mainly seniors, but I was a junior. Normally, you took biology in your sophomore year, which I did, chemistry in your junior year, and physics in your senior year, but it was decided I should probably take physics in my junior year. I had an amazing teacher named Sam Marantz in that physics class. He said to me, "You don't want to take high school physics. It's junk." While he was teaching physics, he'd actually had a career in industry. He then taught for about ten years, including the time I was at Madison. Then, he retired.

And to give you an idea of the kind of person he was, he retired down to Florida, discovered there wasn't a decent public radio station, got involved, and within five years, he was the head of science for National Public Broadcasting. He was quite an amazing individual. He said, "Let's put you in the AP Physics class." There was a physics book that was very popular in those days called Sears and Zemansky. And they had two books, College Physics and University Physics. The difference was, college physics did essentially advanced placement but without calculus, and university physics did it with calculus. Mr. Marantz said, "We're going to do the college, but we'll get you a copy of the university. You're learning a little calculus."

I just breezed through this. He was just fantastic. I had these two classes, physics and math, which were three hours a day, with this one group of also very bright people interested in math and physics who were a year ahead of me. They became friends, good friends.

**ZIERLER:** Was taking courses at Brooklyn College, for, example, available to you?

**SIMON:** It might've been, but it never came up, and I never did it. I did a lot of advanced reading after that. I don't remember the exact books, but on my own in my senior year, I did some advanced reading. It probably would've been available, but no one raised it, and I never considered it but I did do something else. I think it was the middle half of my sophomore year, but my father, who was very ambitious for me, learned about something called the Saturday Science Honors Program at Columbia, which was run by someone who had founded it named Donald Barr, interesting guy, who later became the head of the Dalton School. You may have heard of his son, who was our last Attorney General.

He interviewed me, and I was accepted. I probably had to take some kind of test. Every Saturday, I'd get up really early, go to the subway, and go to Columbia. They had these amazing classes, which were really, in some sense, college-level, although one day a week. But we had a famous population biologist named Richard Lewontin who came down to give us a course in population genetics for one of my years. We had access to a very early essentially mainframe computer. But to give you an idea of what computers were like then, we learned how to do some assembly language programming on it, but one of the things you learned was how to structure your program–you could essentially tell the program where on the drum to put the data.

You structured the program so that the data was such–you didn't want the drum to make too many revolutions when it was recovering the data because it made the program much slower. This was in the days when computers were so slow that you really had to take into account this physical property of–the processes were much faster than the hardware.

### From Math Competitions to Harvard

**ZIERLER:** Were you involved in math or science competitions in New York City?

**SIMON:** Absolutely. We had something called the Math Team, which all the high schools in the city had. Two high schools would meet, they'd provide all high schools with the same problem, there'd be three team members, I think there were six problems, and if the whole team out of 18 got five right, that was considered very good. Because of my reputation. I was invited to come to the meets in my sophomore year, and very quickly, my teammates, who were watching, saw that I was getting everything right, much more than the people on the team. They convinced the teacher who was in charge of the team, "Put Simon in, put Simon in."

He put me in, and of course, I got more right than all the rest of the team, so I became a permanent member of the math team. I was normally in the top five in all of New York City every week for two and a half years. Some of the other people in the top five were people who were my classmates at Harvard.

Now, there's a much more organized thing. But there was something called the Pi Mu Epsilon competition. Maybe you could only do it as a senior. I don't remember doing it before then. But I think there were 60 questions. I took the exam and thought I did very well. It was graded locally with an answer key that teachers had. "Oh, you did really well. You only got one wrong."

"Which one did I get wrong?" "Number such-and-such." I said, "No, I know I got that one right." It was an interesting question. It was to find all the integer solutions of a certain algebraic equation. The way it was phrased was, "Find the number of pairs of solutions of this equation in X and Y." It was not phrased well. It said pairs of solutions, and not solution pairs.

**ZIERLER:** What's the difference?

**SIMON:** The thought was, "Oh, well, it's X and Y. They want the number of pairs, (X, Y), that fit in. But immediately, the first thing I realized was, there was a symmetry. All the solutions came in pairs. I found one pair because there was a plus-minus Y symmetry. Y only occurred as Y-squared. I quickly realized, "Oh, what they're asking is how many solutions are there where"–there were two solutions that were the same X plus or minus Y, one pair. I wrote down one. It was multiple choice. The correct answer, they thought, was two. I appealed. It was a particularly dramatic appeal because someone else had gotten a perfect score on the exam.

**ZIERLER:** But they did that by misinterpreting the question as you saw it?

**SIMON:** Well, I misinterpreted it from my point of view, or he got the wrong answer. We don't know for sure. He was the fourth person to get a perfect score in the history of the exam. But the fact that there were two of us who did so well says it was probably an easy exam that year. Anyhow, the guy in charge of the exam essentially accepted my appeal, so I wound up coming in tied for first. Of course, this made a bit of a splash. There was a section of the New York Times that was "human interest", and I was on the front page of that. I can send you the article that my brother found. The only thing I remember about the article–they sent a reporter and a photographer. Before this, I had probably met the principal once or twice. Of course, they had to go through the principal's office.

He expected the photographer to take pictures of the principal and me. The reporter said, "Well, he wants that, so we're going to do that, because we're not going to use those pictures. We'd like to take a picture of you with some mathematics in the background." They wanted me to work out the problem. Well, one of the friends I had from the previous year had gone off to MIT, and he and I would do the problems from the American Math Monthly. This was long before email, we'd sent letters back and forth. The night before this, I had figured out the solution to one of the things we'd been corresponding about. I put that on the blackboard. Of course, as I wanted, I got a letter from him, "Oh, I see you solved the problem." I was also later in the Putnam Exam, but we can talk about that later.

**ZIERLER:** As an 18-year-old, were you aware, yourself, that places like…

**SIMON:** Where did you get 18? When I was a senior, I was 16. There were two things. First of all, the SPs meant I skipped a year. Second, the cutoff was such that I was one of the youngest people in my grade before I skipped a grade. I had my 16th birthday in April of my senior year.

**ZIERLER:** Even more so, as a 16-year-old, were you aware, yourself, that a place like Harvard was in range for you? Or it was only your teachers telling you?

**SIMON:** It wasn't a question of in range because I was not a modest kid. I did a little research of my own. There were catalogues at the local public library. I decided the two schools that made sense for me were MIT and Caltech. And I very quickly decided Caltech was my first choice. At some point, Mr. Marantz, probably late in my junior year, said, "Where are you going to college?" I said, "Caltech." He said, "You should go to Harvard." I go back home, tell my mother, who was more interested in college-type things, "Mr. Marantz says I should go to Harvard." "Oh, that's a rich man's school." I go back to Mr. Marantz. "My mother says it's a rich man's school." He says, "That's a bubbe meise. Tell your mother that's a bubbe meise." Which I know you know means old wives' tale. I decided I would apply to Harvard.

**ZIERLER:** What was it about Caltech for you?

**SIMON:** Caltech's catalogue is very interesting because it actually has the educational background of all the professors. It wasn't that I'd heard a lot about it, but just by looking and hearing what people talked about–I applied to five places. Harvard, Caltech, MIT, Columbia because I figured that was a relatively safe school, and Brooklyn College, which was a sure safe school, where it wasn't that much to apply. And I assumed I would not get into Harvard because it was well-known that Madison got, at most, one person into Harvard. And in terms of academic average, I was only ranked fourth in my class. The guy who was number one was really good in everything. Not that I got bad grades in English and French. I was always very interested in history, so I got particularly good grades in that. I assumed he would get in, and I wouldn't.

**ZIERLER:** Only one kid from Madison, being such a Jewish school, were admission restricted at all at that point?

**SIMON:** I don't know. I'm willing to bet there was a quota. It wasn't that there was an informal quota because I know there was one at Princeton, even when I was on the faculty in my early days, because at one point, we heard that they became very interested in students who'd gone to Yeshiva because they knew they had a Jewish quota. They didn't want to go over it, but it didn't look good if they went under. But they knew that many of the secular Jews tended to come and become troublemakers. This was in the anti-war era. I'd heard they'd gotten interested in Yeshiva students because they had a quota.

I'm willing to bet there was some kind of quota. But generally, they do pay attention to numbers. From what I heard, it had never happened Madison had gotten two students into Harvard. And I assumed I had a good chance at Columbia. I still remember the interview there. There was an interview, I think it was probably an alumnus, but it might've been someone from the admissions office. The interviewer was very indiscreet. After he interviewed people, he dictated into a dictaphone–I could hear his opinion of the guy before me. And to say it was negative would be an understatement. He ripped into this guy. I sat there, and I was getting nervous. I walked in, the first thing he asked was, "Where have you decided?" At this point, I was too young to know the right answer to that question. I was honest. Columbia was number four on my list.

He spent the hour not interviewing me but trying to convince me to put Columbia higher on the list. I knew I was going to get into Columbia. I got into MIT, I got into Caltech. It took about a week between when I'd heard from the other places and heard from Harvard. I was expecting to not get in. My mother did not want me to go to Caltech because it was so far away. MIT, I could come home for vacations. Caltech–in those days, cross-country was very different. She lobbied me for a week about why I should go to MIT rather than Caltech, but then I got into Harvard.

**ZIERLER:** Were you thinking math and physics together, even that early?

**SIMON:** I knew that's what I wanted to do, but I didn't know whether it could be done. Somewhere, I wrote this poem about–because I knew they were different fields, and I didn't know there existed anything like mathematical physics. None of the physicists at Harvard at the time were at all friendly to mathematics. The great guru of theoretical physics was Julian Schwinger, and he was disdainful of most physicists, and mathematicians were beneath him.

**ZIERLER:** What were your early impressions when you first arrived at Harvard?

**SIMON:** You meet people, and you talk to people. I met some really smart people. I was this brash, obnoxious young guy. I went to the 50th reunion. Two people came up to me at the reunion who I didn't really know. One of them was in fact a Radcliffe graduate, and she told me the story about her husband. But they both she talking about her husband and the other guy said to me, "I came to Harvard wanting to be a math major. I met you my first day and decided I should major in something else." Because I'd not only taken this calculus, but I'd done extra reading and so forth. I was this rather brash young guy. There were some impressive people in my class. Three of my classmates included me inducted into the math section of the National Academy.

**ZIERLER:** It was math for you if you had to choose one?

**SIMON:** It was physics. I really took a lot of math, but I knew I wanted to be a physicist. That was the impact of Mr. Marantz. If it hadn't been for him, I'm sure I wouldn't have been a mathematical physicist, let alone a physicist. But I was a physics major. But I was "in competition", I took all the same advanced math classes as the top math majors. There was a two-year honors sequence for which the second year did calculus on Banach spaces and differentiable manifolds. Famous Math 55. About ten people a year managed to place into that directly as Freshman, and I was one of those ten. It had two very interesting teachers who clearly knew much more math than me–in high school, I quickly learned I knew more math than my teachers. It was very interesting.

**ZIERLER:** Who were some of the most memorable professors at Harvard for you, both in physics and math?

**SIMON:** One guy who had the biggest influence on me was a guy named Lynn Loomis, who you probably have not heard of. It's funny, the Crimson always described him as the Prince of Mathematicians. He was a fantastic teacher. Among the undergraduates, he was their most famous mathematician because we didn't know anything. This was the mid-60s, so he was certainly in his 50s. He had, 20 years before, done some notable work in analysis, and he has a book on Banach algebras and did some other things. But he was probably the least famous of the math faculty in the outside world, but what did I know? My first year, I took 55A, which was calculus on Banach spaces, with him. In my sophomore year, I took the graduate real analysis class from him. He was a very sensitive guy.

After the Putnam Exam, my father apparently wrote him a letter suggesting that the team members should get a Harvard H like the athletes got. I have in my file a letter Loomis sent to my father. It was really quite sweet. "Don't worry, he'll have a stellar career." But in my senior year, I'd heard he needed a grader for this Math 212, the real analysis class. I went to see him and said, "I hear you need a grader. I'd like to do that." He said, "No, I can't do that." He saw I looked crestfallen. He said, "No, no, I know you can do it. The problem is, that class is half graduate students. It's difficult enough for them. They have all these bright undergraduates, some even sophomores. I can't have them have an undergraduate grader also." Two days later, he came back to me, "I can't find another grader who's qualified," so I did grade for him.

Another one who was memorable, more because of contact I had later with him because he was a religious Jew, is Shlomo Sternberg, who taught, in fact, the second half of this Math 55. He did the calculus on manifolds part of the course. I took a reading course with him in my sophomore year, and then after I got my PhD. I actually spent a summer at Weizmann in 1971 because he invited me. Anyhow, I had contact with him later. The other one who had a great deal of impact on me for a special reason is George Mackey. I'll talk about physics in a second. Mackey was probably the closest thing to someone who was interested in mathematical physics at Harvard, not in the sense that he mainly did things connected with physics. He did group representations, primarily harmonic analysis. But he became interested in the mathematical foundations of quantum mechanics. He wrote a book eventually on it, and he gave a course in my junior year.

But he gave a talk at the math club in my junior year. At that point, I knew I wanted to go for a PhD in physics, and the places on my serious list were Harvard, which I assumed I could get into, but it didn't make sense to me to stay in the same place, although Harvard did not discourage people from doing that, MIT, and Berkeley. Those were the three places I was serious about. But I knew that what I wanted to do was this rigorous mathematical physics, which I didn't know existed. Mackey gave his talk and immediately ran out the door because Harvard math professors made a point of not having a lot to do with their students. They were not a friendly bunch as far as student interaction.

But I ran after him, and I blurted out this question. He said, "Oh, you should look into Wightman at Princeton." And Princeton was not on my radar then. I just didn't know enough. Even though, arguably then and now, it's the top physics department in the country, certainly up there in the world, but it was not on my radar. It just wasn't. I looked into it, and I quickly decided what I really wanted to do was go to Princeton for graduate school, which was all because of George Mackey. I presumably would not have heard about Arthur Wightman.

**ZIERLER:** Did you take a class with Schwinger or interact with him at all?

**SIMON:** My mother had two things that she–first of all, she said, "You can't be fresh with me until you make Junior Phi Beta," which I did, and we had a bet that I was going to get all As in my math and physics classes, and I was sure I'd win that bet. My senior year, I took the quantum field theory class that Schwinger taught. He taught quantum field theory unlike anyone else. Everybody else in the world would use Feynman diagrams. But he didn't believe in Feynman diagrams, although rumors were, in his office, he would use them secretly. It was a very abstract course. I understood most of it, but there were no exams. There was a writing project, and you had to pick your own project. I wrote something that I thought was pretty good, but it was rather mathematical. The grade was entirely based on what Schwinger thought of this paper, and he gave me a B+. That was my interaction with Schwinger. That was the year, by the way, he got the Nobel Prize, so there was a lot of excitement about that. He had no interaction with most of his students to speak of, except he was this oracle.

**ZIERLER:** On the social side, out of your parents' home, for yourself, were you Jewishly connected at all as an undergraduate? Did you go to Hillel?

**SIMON:** Yes. Look, I needed to find a Jewish girl because that was the expectation. I was not very connected, but I certainly went to Hillel, I went to the Hillel mixers, I dated and eventually married my first wife, who was an undergraduate of Tufts I met at one of these Hillel mixers.

**ZIERLER:** And by the mid-1960s, as the 60s were ramping up, Civil Rights, Women's Lib, the anti-war movement, were you political at all at Harvard?

**SIMON:** At Harvard, no, but at Princeton, yes. The dean of the college at Harvard, essentially the dean of students, ran a summer program at Mills College, which was a totally Black college in or near Birmingham. Basically, he had recent undergraduates come and teach special classes with his students. I was interested enough in Civil Rights that after my first wife and I got married at the end of my first year in graduate school, essentially honeymooned at Mills College, teaching. I gave a math class for students who were supposed to be teaching elementary school. I still remember being shocked at how little understanding these students had. To me, the idea that there was a problem about computing–sales tax is 3% and your bill is $1.50, how much is your tax? And someone says $.45.

To me, it wasn't a question of numbers, it was a question of having a sense of what the order of magnitude of the answer should be. I remember at the time, and it's something that in terms of math education has always struck me, I said to the chair of the math department at Mills, "These people are going to be teaching mathematics." He said, "You don't understand. The people who want to be teachers and have any sense of mathematics, teach high school math. The ones who wind up teaching elementary school are the ones who are afraid of math." I've understood since then that the biggest problem with math education in this country is elementary school teachers who are frightened of mathematics.

**ZIERLER:** When you graduated, was the draft something you needed to deal with?

**SIMON:** No, not when I was a graduate student, but when I was an early faculty member, so I'll get to that in a second. I also became very politically involved in the famous 1968 Democratic campaign when I was already a graduate student at Princeton. That was the one where Johnson bowed out, and there was a real race among Eugene McCarthy, who was the first one in, Bobby Kennedy, and Hubert Humphrey. And I was big for McCarthy. I actually went out. I remember I was handing out leaflets for McCarthy at the polls near Perth Amboy for the NJ Democratic primary. I was hassled by the police because the local machine was pro-Humphrey. The police were, "You're too close to the polling place." They kept coming back and hassling me because that's what they were told to do by the local machine. I remember being shocked, of course, by Kennedy's assassination which was that night. But yes, I was very anti-war.

**ZIERLER:** To go back to Mackey's formative advice, when you started to learn about who Wightman was, did he square the circle for you in terms of your dual interest in math and physics?

**SIMON:** Again, I knew he existed, but it didn't occur to me to go read his papers. I should've. If I had a student like me then, I would've said, "Go and read his papers." I could've understood his papers, but I didn't go and read his papers. It never occurred to me. I wouldn't say he squared the circle until I got to Princeton. Then, he squared it.

**ZIERLER:** Did you consider math programs also for the PhD? Or it was always going to be physics?

**SIMON:** No, it was always going to be physics. There was never any question. Although, it's interesting, one of the things I took as a senior was a graduate class in algebraic topology taught by an instructor named Poénaru, who actually got quite a reputation eventually, although it was not at Harvard. He was Romanian originally, visited Harvard for a few years, and wound up somewhere in France. Again, I was a rather loud student. He actually spent a number of meetings with me trying to convince me to give up on this physics stuff and do topology. But I'd made up my mind, I wanted to do physics. I owed it to Mr. Marantz.

**ZIERLER:** Last question on Harvard, tell me about the Putnam competition.

**SIMON:** Before I do that, on the physics side, besides Schwinger, there was someone I took a sophomore physics class as a freshman with Daniel Kleppner which was the physics that I really enjoyed. And the first time I took a class that really turned me on was the first quantum mechanics class which I took as a sophomore, which was taught by Ed Purcell, who was a fantastic teacher.

In my junior year, I took the graduate quantum mechanics class from Paul Martin, and it was a very interesting class, although he used the Schwinger-Martin Green's function technique that was obscure enough that it was only in the very last few weeks that I realized why he was getting imaginary numbers out when I thought he couldn't, because he actually had moved the contour off the real axis by a small amount. The other thing I should mention, I read Landau and Lifshitz's mechanics book as a freshman, on my own because I was taking some mechanics class. They have a discussion of what they don't call it that but we call Noether's theorem, and I just fell in love with it. It says, basically, that there's a connection between symmetry and conserved quantities. It's amazing.

And I went around telling everybody about it. It was when I knew that was what I wanted to do, this kind of physics. It had an enormous impact on me. It's interesting. It's Emmy Noether, who invented Noether's theorem. I probably learned the next year it was called Noether's theorem. I'd also heard about Noetherian rings in my algebra class, and it didn't occur to me that this abstract algebra person could possibly have done this, and her father was a mathematician. I assumed that this was Max Noether's theorem. I'm a little embarrassed that eventually I learned it was his daughter's theorem.

**ZIERLER:** Back to the Putnam competition.

**SIMON:** The Putnam competition, I probably took every year at Harvard. And it's an exam given on Saturday that's three hours in the morning, three hours in the afternoon. One of the things that schools have to do is pick their official team. At least at Harvard, it was not traditional to tell people who was on the team. My senior year, it turned out that whoever picked the team decided that since I wasn't a math major, I shouldn't be on the team, but I was the first alternate. But one of the team members had his head in the air so much that he spent the morning wandering around Harvard Yard, trying to find where the exam was. He was disqualified, so I wound up on the team.

At that time, and it's still true now, they don't rank the people in the top five, they just say top five. Then, the next group is usually five or six. In those days, I think, again, they didn't rank them. But we had two in the top five and one in the next group. That was a record for many, many years until it was broken a couple of years ago when somebody had three in the top five. It's considered a big deal. It's decided long after the graduate admissions are decided on, but I'm sure I didn't have any trouble getting into graduate school. My number was very strong.

**ZIERLER:** Once again, did you consider Caltech for graduate school?

**SIMON:** No. I applied to Harvard, MIT, Berkeley, and Princeton. Never thought about Caltech. I'm not sure why.

**ZIERLER:** Was the Schwinger-Feynman rivalry on your radar at all?

**SIMON:** No. I knew he'd shared the Nobel Prize, but no, not at all. At this point, even though I'd taken his course in quantum field theory, I probably had not heard of Feynman diagrams at the time. I don't think I applied to Caltech. Could be wrong, but I don't think so. Once I learned enough about Wightman, Princeton was number one on my list, and I expected I'd get in. There was someone at Berkeley who did mathematical physics who really worked hard to try to get me to come to Berkeley. He'd written some notable notes in general relativity. I asked for a copy of his notes. He said, "Well, if you'd have come to Berkeley, I would've sent them to you, but since you didn't, I'm not going to." It left a bitter taste in my mouth.

**ZIERLER:** How well-formed were your ideas about physics graduate programs in terms of what you wanted to pursue? It's such an exciting time in physics and theoretical physics.

**SIMON:** I would say that my physics undergraduate education at Harvard was incredibly formal. We never mentioned very much about experiment. It was all formalism, and there was no particular excitement about all the exciting times in physics at Harvard. I came to Princeton, and it was totally different. I can say I probably took seven or eight classes. I didn't officially take that many my first year at Princeton. They were all a breeze for me, and the reason was, I had all this formalism. The other students were tripping on formalism. The formalism was easy for me, so I picked up an enormous amount of real physics in my first year at Princeton and the excitement. Although, the really exciting stuff you're thinking about in particle physics was later. I was a graduate student from '66 to '70, and the exciting stuff began to start in the 70s. The golden era of the standard model was really the 70s, so there wasn't that kind of excitement. But there was clearly a lot of stuff going on. Dicke was doing his famous experiment about some general relativity test. A lot of people who were later my colleagues had a huge impact on me.

**ZIERLER:** When you get to Princeton, Jewish boy from Brooklyn, does it feel like a WASP-ier place than Harvard?

**SIMON:** No. I don't think it is particularly WASP-ier than Harvard. I didn't feel that at all. In fact, one of my fellow graduate students was a Lubavitch chassid, who eventually dropped out. It didn't feel particularly WASP-y because I was focused on doing my thing. I probably didn't talk to anyone who wasn't in math or physics.

### Arthur Wightman

**ZIERLER:** Do you have a clear memory of first meeting Wightman?

**SIMON:** Before I decided to make a formal decision, I was home for Easter vacation, spring break, and Princeton was within driving distance, so my father drove me down to Princeton and insisted that he was not going to come and meet Wightman, but he would stay out in the car, which I didn't fight with and appreciate. And I went in to meet Arthur Wightman. Arthur was a charming guy, clearly wanted me to come. He was very interesting, remarkable. The standard joke was, the only thing more frightening than the books in Wightman's office is that he knows what's in all of them.

**ZIERLER:** What was he working on when you first met him?

**SIMON:** Everything. That was always Arthur. Arthur's published research is almost all in quantum field theory, although he had an interesting paper in foundational quantum mechanics, and he has some not exactly recent review papers in other areas, but his focus was always quantum field theory. His goal was to understand what quantum field theory really was. He once told me, "Some people will say that you're cleaning up what other people have done, but there's such a thing as intellectual rigor, and one really should do it right." He understood that quantum field theory was not well-defined, and it wasn't clear what a quantum field really was. And so, his big contribution was this thing that's called axiomatic field theory, which wrote down what the properties were, and the big surprise was, from these axioms, you could actually derive several basic things, two in particular - the relation between spin and statistics and the so-called PCT theorem.

He wrote a famous book on that subject. He was still thinking about that, but by the time I was at Princeton, he was probably close to 50. He was more a cheerleader than anything else with incredible breadth in interest. He was most interested in the subject that was hottest and what came to be called, which he probably named, constructive field theory, the idea of actually constructing mathematically rigorous things that obey the axioms. He had a lot of influence on Ed Nelson, who was in the Math Department at Princeton, who also was one of my two mentors. He led Nelson to become interested in this, and Nelson had two huge breakthroughs in his career in constructive quantum field theory.

Arthur did a lot of his research by having graduate students do things. Oscar Lanford and Arthur Jaffe did their PhD theses on the first steps towards constructive field theory, Arthur on Boson and Oscar on Fermion field theories. Even though he had lots of ideas and led people in the right directions, his sole paper on constructive field theory was a *Physical Review* Letter he, Lanford, and Jaffe wrote essentially on their theses, and he later organized a famous summer school, where he made a contribution to it summarizing various things. But that was absolutely typical of graduate students. He was interested in C*-algebras. He had a student named Bob Powers who was at Penn for his career. And again, he had a spectacular thesis under Arthur, probably an approach that Arthur had suggested to him.

There's another thing that's sometimes called dimensional renormalization that has to do with regularizing Feynman integrals by analytically continuing in dimension. Basically, this is an idea of Wightman–it wasn't dimension, that was later rephrased that made it much hotter in physics. He thought of it as analytically continuing in some parameters that occur in the Feynman integrals that are, in fact, just the dimension. He had learned when he was young about regularizing singularities and distributions from Marcel Riesz, and he decided maybe this was what renormalization was about. And he had this idea. It's a great idea. What did he do? He had a senior at Princeton do a thesis on a simple example, show it could work, and Arthur then gave it to a graduate student.

The graduate student wrote the first paper on the subject. It's absolutely typical. Arthur had an incredibly broad view of statistical mechanics, classical mechanics, quantum mechanics, quantum field theory. Didn't have as much published research as he might have been because he was so generous with his ideas.

**ZIERLER:** Was it at Princeton that you came across the term mathematical physics?

**SIMON:** I have no idea. Certainly, it was a phrase that was very much coming into vogue. I remind you *The Journal of Mathematical Physics* was probably started in 1964, so it was in the air, but it wouldn't have been in the air at Harvard. I might have heard about it then, but I certainly heard about it at Princeton.

**ZIERLER:** Would Wightman have called himself a mathematical physicist?

**SIMON:** Certainly, by the time I was there, he would've. Well, he might've. He probably would've said he was a theoretical physicist.

**ZIERLER:** How much interface did you have with the math department at Princeton?

**SIMON:** When I said I took these seven courses, probably half were in math. I knew all of them, and I was, again, noisy in my classes. I knew all the math graduate students. I don't know if you've been to Princeton, but there's this huge tower that's Fine Hall. That opened in 1970, my first year on the faculty. Before that, we were in Palmer Lab and the original Fine Hall, and they were really one building. You just walked down the hall to go to math.

**ZIERLER:** On the personal side, was it in graduate school that you started to become frum?

**SIMON:** No, I was already a faculty member.

**ZIERLER:** It was a gradual process, or it happened suddenly?

**SIMON:** Gradual process because I was really introduced by my now wife, my second wife.

**ZIERLER:** Where did you meet your wife?

**SIMON:** In the math common room at Princeton. We did not hit it off at all.

**ZIERLER:** Were there any other women graduate students at that point?

**SIMON:** When I applied to Princeton, there was a section of the catalogue called rules for graduate students. The first rule, the only one in all capital letters, read, "WOMEN ARE NOT NORMALLY ACCEPTED TO GRADUATE STUDIES AT PRINCETON." There was a decision made to open the graduate school to women, must've been starting in the fall of 1968. I came 1966. There were no women there when I came. Of course, the joke then, and I suspect it was a factor in the decision, was, graduate students had lost automatic draft deferment. The then-president of Harvard said, "This is terrible. It will make the graduate school the purview of the lame, the halt, the blind, and the woman." This was the phrase used by the president of Harvard. I believe it comes from the King James version of Luke: *Then the master of the house being angry said to his servant, Go out quickly into the streets and lanes of the city, and bring in hither the poor, and the maimed, and the halt, and the blind*. I believe halt means poor.

My suspicion always was that one factor in Princeton's decision was that because of draft issues, they decided they should accept women because they were going to have trouble getting as good males. The Math Department made the decision that they were going to try to accept not just one, but more than one. My wife to be was an undergrad at UCLA, and one of the people who was there in her junior year as a visitor was Norman Steenrod from Princeton. He made a point of coming up to her and saying, "There's some talk we may start accepting women. You should certainly apply to Princeton." The faculty was clearly recruiting, and in her class, I can't remember whether there were four, five, or six women. I think there were five women. In fact, the interesting thing is, the AMS had a cover on Women in Math Month on the Notices of AMS.

It was a foldout, or maybe a front and back cover, I can't remember now. But it had pictures of about 40 female mathematicians, and they made a point to take from that entering graduate class, the heads of six women. My wife appeared on the cover of the Notices about three or four months after I was on the cover of the notices. We may be the only couple to have both appear on the cover of the Notices of the AMS.

**ZIERLER:** In terms of Wightman's style as a graduate mentor, how closely was he involved in the development of what would become your thesis?

**SIMON:** In what would become my thesis, in some sense, not at all. Let me talk about my three first serious research projects. First year at Princeton, often second, too, one mainly takes courses–I had an NSF fellowship, so I didn't have to do teaching. You do have to do a lab project. I did one in nuclear physics, and I know the guy who was my supervisor. I had a friend named Kai Lee who was an experimentalist. Later, when I was on the faculty, I'd heard that the guy who supervised my experiment told someone, "Kai Lee and I had to work really hard to get Simon through his experiment." At the end of the year, most first-year students take just the first day–it used to be this general exam was this grueling three-day exam.

There were three hours of exams morning and afternoon on Monday, Tuesday, and I think Wednesday morning. Maybe it's two days. I can't remember now. But there were oral exams on the last afternoon. The first-year students only took the prelims normally, which was the first day, but if you wanted, you could take the whole general exam. Usually, one or two did, and I did. I passed that, so I started already research in my second year. Wightman would give people problems, so I went to see Wightman, and he gave me a problem. By the way, Sam Treiman, who was a remarkable guy we'll probably talk about, who I got very close to both as a graduate student and later on in the faculty. At one point, I was thinking, "Well, I maybe I should at least look into high-energy physics." I went to see him, and he looked at me and said, "You think I give students problems?"

In fact, for weaker students, he did do that. But he said, "You've got to find your own problem." But that was not Wightman's style at all, so he gave me a problem that is hard to describe, but it involved some cancelations that happen with fermions that are connected with an inequality on determinants that happen in Feynman theories. You need to have determinants, which are modified by renormalization. My original thesis problem was to, in fact, try to extend this earlier result that one of Wightman's friends named Caianiello had found to the case when they were simple mass renormalizations. Which I did. I wrote a paper for *Nuovo Cimento*, an Italian physics journal then popular among theoretical particle physicists, and Wightman said, "Well, you're only a second-year student. We'll wait and see."

That's one of the problems I got from him. On the side, I was writing several other not important but still nontrivial papers on questions that had occurred to me. My biggest research project in many ways–one of kings of the mathematics of non-relativistic quantum mechanics is a man named Tosio Kato. Very interesting guy and was born, I guess, in 1917 since we had the 100th anniversary celebration. He died in his 80s. We'll talk about that a different time. But one of the things he did as a graduate student, he became very interested in results on making mathematical sense of Rayleigh-Schrödinger perturbation theory, and then perturbation theory in general, and he wrote a big, thick book on the subject.

There are some very interesting results. It's called *Regular Perturbation Theory*. I won't say I read his book quite cover to cover because it's encyclopedic, but I became an expert. I was the local expert on the subject. One of the things Wightman had, again, in typical fashion, became interested in was what happens when the perturbation is not regular. Turns out most of the perturbations that really occur in physics are not these regular perturbations, they're more singular. The simplest example of this is the so-called anharmonic oscillator. The thing everyone learns about in basic quantum mechanics is the oscillator where the underlying potential is X^{4}, and the anharmonic oscillator is when you add an perturbation. Small βX^{4} perturbation.

This was of particular interest to Wightman because it's the analog of the simplest quantum field theory, which is where you take a free field, which is like the harmonic oscillator, and you add a ϕ^{4} interaction. That's the simplest example of a quantum field–so he was very interested in what was the meaning of perturbation theory. It was widely believed that the Feynman perturbation series diverged. The question was, if the series diverges, what does it have to do with the right answer? Wightman was very interested in this, and thought you should study it in the simplest example, which is this harmonic oscillator. And in typical fashion, he gave it as a problem to a graduate student of his named Arnie Dicke. Arnie was not the strongest student Arthur had.

He got some results–it turned out even existence of solutions, if you looked at it right, it was sort of in the literature, but there were various questions he could analyze that he did, but when it came to actually understanding perturbation theory, they really ran into a big roadblock. It was a very simple scaling idea that formally Kurt Symanzik had had in the quantum field theory, and they were sure it should work here, and couldn't make sense out of it. Since I was the expert on regular perturbation theory, because this had to do with the region where they thought things were regular, I was brought in, and I got involved in this anharmonic oscillator problem. In my third year at Princeton, Wightman went on leave, and we corresponded, again, not through email because it didn't really exist then, but by letters back and forth. It was understood that Dickey was going to focus on the part he could make progress on, and I could play around with the rest of it.

I had lots of results. I'd proven various things. Arthur was very excited about this. He talked to people, sent ideas back and forth, and it really did have some interesting results. I then got a rather remarkable letter from him that read, "The specter of Padé is haunting Europe. S-matricists of the world, unite. You have nothing to lose…" It happened that in particle physics, people were taking all kinds of Feynman perturbation theory, and there was a summability method called Padé approximates. He suggested that I try to use this Padé approximate method to see how it did with this anharmonic oscillator. Now, when he left, the anharmonic oscillator was expected to be my thesis, and it would've been a very good thesis.

But in the meantime, a different subject came up which was my thesis. The anharmonic oscillator did not wind up being the thesis, but it was a very important paper that made a bigger splash than my thesis. It turned out there was also an interest in this anharmonic oscillator by a guy named T. T. Wu, who was an applied mathematician and interested in physics at Harvard, who had a graduate student named Carl Bender. They also were working on this, not from a rigorous point of view, but they had a number of interesting results. Normally, I wouldn't have heard about them, but Bender was a very good friend of Arnie Dickey. In those days, people wrote preprints, but they were sent to maybe 20 people because you couldn't just Xerox things because it was too expensive. You had to mimeograph them, and then you sent them out by postage, you didn't email them.

Very few people got preprints, but Arnie got a preprint of this paper, and one of the things that Bender and Wu had done is, there was a recursion formula for the perturbation coefficients, and they could use it to actually compute the first 75 terms in the power series. I had all the power series. I could plug it into this Padé formula. I have only done one piece of serious scientific computing in my life, and that was this calculation. In those days, that meant you wrote a program, you punched it into punch cards, you handed in your punch cards to the computing center, and a day later, you got the output. I figured out how to program things to do this calculation of Padé, handed in my punch cards, got things back, absolute nonsense.

I stared at it for a while and realized I'd left out a minus one to the n. Went back, did Padé, it was miraculous. It converged incredibly rapidly fast. Several years later, people using a slight variant of Padé and these 75 coefficients computed the first 22 decimal places in this energy using the summability method. It seemed to be miraculously convergent. I was really excited. This was my first "big result", except, of course, there was no proof. There was a standard way of proving that this Padé converged that only worked sometimes. Padé seems to converge in many cases when we don't understand why. But there's something called Stieltjes' theorem. And I quickly realized that it might apply in this case.

One of the things it implies is that not only did things converge for Padé, but they do it monotonically. I looked at my numbers, and they seemed to be monotonic. That was a good sign. And I very quickly realized that except for one very important issue, I had already determined you could analytically continue things in a certain direction, but there could be singularities on a first sheet. Anyhow, I told Arthur, "If there are no singularities, then I can prove this thing is a series of Stieltjes." He was still in Europe. He actually talked to André Martin who was a very interesting, talented theoretical physicist at CERN. There are some people who maybe aren't exactly mathematical physicists, don't always do things rigorously, but they're in between, and he was very much in that framework.

He was a very interesting guy. Earlier, he'd sent me some other suggestion I'd used in looking at this problem. Martin, with a buddy of his named Loeffel, was able to prove the missing step in my argument. I had to work hard to convince Arthur to coauthor the joint announcement with the two of them that we actually could prove that this perturbation series was summable. There's one postscript to this. At the time, the world's great expert on Padé approximates, made his whole career, was a guy named George Baker, who had books on the subject. There was a physicist at Rockefeller University, Nick Khuri, who I'd met at summer school the year before, who got very interested in me, and he was really interested in this Padé stuff. He had me talk to George Baker.

If you look at my numbers, I was doing the calculation to ten decimal places. And for the largest value of the coupling constant, for the last three items, the last three decimal places, it was not monotone in the sense that the numbers went slightly down. I assumed, and I still assume, this is roundoff error. We did have a proof, but Baker was adamant, "The numbers show you're wrong. You must have a mistake in your proof." There was no mistake. That was one of the things that, in some sense, is a thesis problem I got from Arthur.

But I didn't use it for my thesis because in the meantime, while Arthur was on leave, there was a post-doc, maybe he was an assistant professor, but untenured theoretical physics faculty who was somewhat mathematical named George Tiktopoulos, who gave a course on, essentially, potential scattering and other things, where he had some basic integral that the potential needed to obey for it to work, and I was in the class, and I kept insisting he needed extra assumptions because he needed to be sure that the Hamiltonian was self-adjoint, and you couldn't use Kato's self-adjointness theorem, and he needed an extra condition.

In fact, one of the papers he was exposing was by the same T. T. Wu. and Alex Grossmann had done some work on scattering theory, and they had made this additional assumption because probably not Wu, but Grossmann knew to get self-adjointness they had to make an extra assumption. And he said, "No, no, you don't need that. I can make sense out of it. Perturbation series converges. You're wrong." Eventually, I figured out that by using what are called quadratic form techniques, you could, in fact, make sense out of Tiktopoulos was right, you could define self-adjointness by a method that went beyond Kato's ideas. I decided, "Well, you could probably do all the rigorous mathematics in this quadratic form framework," and I was writing back and forth to Wightman also by mail about this, and we decided I should do that for my thesis.

The thesis was actually this problem Arthur had not given me, although I'd learned about Kato's theorem and many of the things I talked about in my thesis from a course I took from Wightman in my first year. But this is not a problem he gave me, it's one I came up with, in some sense, by trying to prove Tictopoulous wrong and proving him right. That's what my thesis was about. Since then, in fact, quadratic forms have become a standard technique, and Kato and I actually had an interesting interaction some years later, which we can talk about, that resulted in something called Kato's inequality. There are lots of things that came out of my thesis, and the quadratic form techniques are now sort of a standard thing. In some ways, the thesis is probably as important as this paper that made a bigger splash. But that's what the thesis was on.

**ZIERLER:** Besides Wightman, who else was on your committee?

**SIMON:** Presumably, Tiktopoulos, and I'm pretty sure Ed Nelson. But at least in those days, the committee was just something you set up at the last minute, when you had to have the final exam. Everything was just the advisor before then. Nowadays, I don't know about Princeton, but at many places, there's a committee that–because some advisors have been abusive to students and various other things, most institutions, and certainly Caltech, now set up a thesis committee that oversees the graduate student's progress much earlier than that. There was nothing like that in those days. But I took courses from Ed Nelson, and he had an enormous impact on me.

He was certainly on my committee. We're getting ahead of ourselves, but Nelson was responsible for my first job as an instructor. It was clear the basics of my thesis was done, and I was going to be finished with it by the end of the year. It was probably January too late to think to apply for jobs, but in those days, things were more low key. Murph Goldberger, who I knew well, even then–I'd taken courses from him, he knew me and what I was doing–had been a graduate student at Chicago. He'd been on the faculty as Fermi's assistant before he'd come to Princeton. The Chicago physicists were complaining to him that Princeton wasn't sending them any graduate students as post-docs, and it was really not right.

Being Murph, he decided, "Well, you nudge me about this, what I'm going to do is send you someone who's good but not really in what you want, which is a theoretical particle physicist." I went out to them and gave a talk, and it was actually a very interesting talk because I talked about this summability and related things. I don't know if I'd done the Padé stuff, but I had all this analytics stuff, and some of the ideas were related to this Bender-Wu work. Their work was not rigorous and had used, essentially, formal WKB methods. In my talk, I mentioned their work and said, "They used notoriously unreliable WKB methods." Afterwards, this elderly gentleman comes up to me and says, "I should introduce myself. I'm the W in WKB."

He was a very friendly guy. I got an offer from Chicago, and I may have gotten an offer, or at least asked if I was interested, from Rockefeller, where Nick Khuri was. It was complicated because my then-wife–we only separated in my first year as an instructor–was by then a graduate student in the history of science. She had started out as a math graduate student at Harvard. She'd left Harvard, decided she wanted to do history of science, and when she married me, she moved to Princeton and got accepted in history of science. There was clearly a two-body problem, and at one point, we had a hard decision to make. Ed Nelson comes up to me and says, "I heard you might be leaving next year because you're finishing up. How would you like an instructorship in mathematics at Princeton?" My first job was actually in the Math Department at Princeton, even though I had a PhD in physics.

### From Grad Student to Princeton Professor

**ZIERLER:** Did you see this as a soft landing to a tenure-line position at Princeton?

**SIMON:** No, it was a post-doc. Princeton's very different. You have to remember, Princeton has a lot of post-docs, a lot of assistant professors. When they hire assistant professors, at least in the old days, they'd tell them, "While it's officially tenure-track, almost no one gets tenure." It happened in my day, a significant fraction of the people who did get appointed as tenured faculty were, in fact, Princeton assistant professors. That's less true these days. But it still was true that assistant professor, and certainly post-docs, were not regarded as the first step in a tenured position. I assumed I'd get tenured, but I wasn't thinking about that. I knew I was going to do good work and wasn't worried about tenure, per se. But it seemed to me I could stay in Princeton, and I knew it was a great environment, and I had personal reasons for wanting to stay. I accepted the job at Princeton.

**ZIERLER:** And you were married at this point?

**SIMON:** I was married at this point. There were already some difficulties, and essentially, we separated in the fall of 1969. I was a graduate student '66 through '69, and then I was an instructor in '69-'70, and we separated in the early part of 1970. We decided early on for lots of reasons we should get divorced. We had no kids, but divorce was highly nontrivial in those days. But one of the grounds for divorce in New York at least–we'd actually been married in New Jersey–was desertion. We found a lawyer in New York, and eventually wound up getting divorced in June of 1970. My first year as an instructor. One of the things that happened in that first year was, the Padé paper I mentioned had made a big splash, and it was clear that I was going to be an interesting commodity on the market.

Wightman and I guess Nelson decided they should probably try to promote me to assistant professor jointly in math and physics. They said they wanted to do that, and I said that would be great. Wightman was the editor of a book series, *Lectures in Theoretical Physics*, and he had decided that my thesis should be published there, which it did eventually. He said, "Look, you have a job. I really need to go through the thesis carefully, not just look it over. I will look it over. We don't have to worry about it because you have a job. You'll finish up and take your final exam, but don't worry about it." I wasn't worried about it, and he wasn't worried about it.

The departments voted to make this appointment, and the chair of the Physics Department, who was handling it, took it to the Dean of the Faculty, who said, "He doesn't have a PhD?" They'd gone through this, and he'd explained. And the Dean of the Faculty said, "This is not acceptable." Bob Dicke, who was the chair, went back and told Arthur Wightman, "What's holding it up?" He said, "I haven't had a chance to read it." "You're going to spend all weekend reading it, Arthur Wightman." There was this big hustle. We were laid back. They put together the committee very fast, and I had my final oral two weeks later.

**ZIERLER:** Now, did the book benefit from Wightman's weekend read?

**SIMON:** Absolutely.

**ZIERLER:** Were there any other joint appointments at that point between math and physics?

**SIMON:** Princeton has had joint appointments for many, many years. But sporadically. Actually, as far as I can tell, the first joint appointment at Princeton was Sir James Jeans in the first decade of the 1900s for a few years. I believe, and I could be wrong, that von Neumann, before the Institute, was at the University for a few years. He might've been a joint appointment. I don't know when Wigner was made a joint appointment. And then, Valya Bargmann, who had been Einstein's assistant at the Institute. When he left the Institute, he came as a joint appointment. Arthur, who originally was promoted to tenure in physics, eventually it was decided it made sense to make his a joint appointment.

When I came to Princeton, there were three joint appointments in the senior faculty. Since we're talking about these joint appointments, in a certain sense, when I was promoted to tenure, I think I was viewed as taking Wigner's slot. Not Wigner's place. No one could take Wigner's place, but Wigner's slot because he had retired. I was promoted to tenure in '72. Wigner probably retired in '70. And then, Elliott Lieb was replacing Bargmann, who retired. He may have been actually appointed before Bargmann retired, but it was understood he was taking Bargmann's slot. When I left, Aizenman was appointed to my slot, as it were. When Wightman left, he was never replaced. I think there were only two joint appointments at this point. In fact, Elliott has retired, and Aizenman may now be the only joint appointment at Princeton.

**ZIERLER:** At what point between 1970 and '72 do you get the message that you're going to be the exception, that as an assistant professor, you are on the path to promotion?

**SIMON:** You have to realize, in my year, I was not the biggest exception. One of the people who entered math, who was a good friend of mine then, and still is to some extent, although we haven't had that much contact since I left Princeton, is Charlie Fefferman. Charlie entered graduate school in math the same year, 1966, as I entered, but we were different. I was 20, he was 16. He had skipped high school. He and I were both appointed to instructorships at Princeton in that first year. I may be wrong. Anyhow, he did such spectacular things, for which he got the Fields Medal in his first year out, that by the end of the year, when he was 21, one year out of graduate school, he had full professor offers from Chicago and Princeton.

I was not on the fast track like he was, but it was quite clear that I was doing very well. By the way, I think their hand may have been forced. I didn't have any idea about this at the time, but at the same time I was promoted at Princeton, I also had an offer from Berkeley, and while I didn't know that Berkeley was going to make me an offer, I'm sure that the people at Princeton knew I was going to be made a tenure offer. They understood they had to fish or cut bait. I probably would've had a third tenure offer if I wasn't so naive and rude. One of the things I did at the point where I already had in-hand tenure offers from Berkeley and Princeton is, I visited Stony Brook.

**ZIERLER:** Was Jim Simons a draw?

**SIMON:** No, I didn't know who Jim Simons was. I'd never heard of Jim Simons. He was an unknown to me. But he was the chair of the department. I was actually probably invited to give a joint colloquium. The big draw was the big muck-a-muck in physics there, Frank Yang. There was a party afterwards, and at the party, they took me aside. In retrospect, I think they were making me an offer. It was not quite explicit, but I can't believe how naive I was. I was also naive because I was ready to accept Princeton even before this, but I was ordered by the chair in math at Princeton that I couldn't accept Princeton until I got the formal offer in writing from Berkeley because he wanted to use the offer from Berkeley to see if he could get me a higher salary. I was a naive young guy.

I didn't understand how these things worked. I just on-the-spot said, "I can't think about it. No, I'm not interested." In retrospect, I'm pretty sure they were making me an offer. They had the power to do that. And I was rude to both of them. I've never had any run-in with Jim Simons since then. Although, I have a good buddy of mine who's his *mechuten* [Yiddish; in-law]. He's a mathematician who was a graduate student at Princeton when I was there. But I've never had anything to do with Jim. But I really insulted him terribly. In retrospect, it's one of the embarrassing memories I have.

**ZIERLER:** Last topic for today, when do you start wearing a yarmulke at work? Or when are you outwardly visible with your *Yiddishkeit* [Jewishness]?

**SIMON:** It was a bit of a process. My wife and I, it was more sandpaper than anything else when we first met. Somehow, after I was already separated and about to be divorced, we were at a party together, we interacted a little more positively just before I went off in 1970 to the famous Les Houches summer school. I came back in the fall, we ran into each other, and we essentially had a whirlwind courtship, as it were, during which, I'd gotten interested in Yiddishkeit. But at the time we got married, it was, "I'm going to have a kosher home." Probably the last *treif* [Yiddish; non-kosher] food I had was at an Oberwolfach conference that next summer. Flying back to Israel, the thing I remember most dramatically is, there was a flight delay, it was on a Friday going back from Zurich, and my wife had given up on my getting back before Shabbos. Anyhow, I got back just in time, and it was at that point I decided that consistency is important, "I'm going whole-hog." I don't remember whether whole-hog meant wearing a kippah all the time. It probably may have even been earlier, but certainly then.

**ZIERLER:** And who was there in Princeton? Was there Chabad? Young Israel? What community did you have at that point?

**SIMON:** When I went to Hillel, the Hillel rabbi was anti-orthodox is the way to put it. But some group of graduate students, I think, the year before, maybe even two years before my wife came, had opened up a kosher dining co-op off campus. We would barely be able to get a minyan on Shabbos, and that was what there was at Princeton for some number of years. In the mid-70s, there was an eating club, which was not doing that well, so the university took it over, and there was a faculty member who became its housemaster or whatever you want to call it. Stevenson Hall. He was worried that they were going to close it, it was marginal, and he figured out that if he provided a unique service, it would be much more difficult to close.

He decided they should have a kosher option. They brought in Young Israel, and that's how Stevenson Hall started. After I left Princeton, probably 25 to 30 years ago, somebody found an alumnus who was really interested in setting up what's now the Center for Jewish Learning, which is its own separate building, only kosher food, and there is a whole chevrah [Hebrew; friendly community]. There now are lots of Yeshiva students who want to go.

### Becoming Religious

**ZIERLER:** Last question, just at the time when your career is really kicking into high gear–50 years ago is a long time–when you start to put on the yarmulke, operating in this secular scientific environment, are you ever concerned that's going to be a problem for your career, people aren't going to take you seriously? Did anybody give you *chizuk* [Hebrew; strength] that it was OK, that you'd be already? How did all of that work?

**SIMON:** Never occurred to me it was an issue. Never, ever, ever. The one decision I made that I was–I had a beard from when I was a graduate student. I decided to shave it off to see what it was like. I had surprised my wife just before we went down to Rio de Janeiro for a month in the summer of ‘72, She took one look at me, and she said, "Grow it back." She didn't like it. I used to have an academic beard, a little bit like what you have. You probably have to shave every day.

**ZIERLER:** I only shave here. This is clippers.

**SIMON:** You don't have to shave up there?

**ZIERLER:** No. I'm lucky.

**SIMON:** I used to have to shave here. And I made a decision, "I don't want to have an academic beard, I want to have a Rebbe beard. To make a statement." I let it grow in some. And of course, when it turned white, I really [let it grow]. But at that point, I was already so established that it never occurred to me people would have any reaction to it. Never occurred.

**ZIERLER:** Maybe the lesson here is that if you're comfortable in your own skin, people will be comfortable around you, regardless of what you look like.

**SIMON:** I've had a couple of interactions that we could go into if you want at some point, but I wouldn't say they were negative, just questioning. But it's very rare. Two or three of them.

**ZIERLER:** Well, that's good to hear. Next time we'll pick up when you're a fully tenured member of the Princeton faculty. We'll go from there.

[End of Recording]

**ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It's Thursday, December 2, 2021. Once again, it's my great pleasure to be back with Professor Barry Simon. Barry, good to be with you again.

**SIMON:** Likewise.

**ZIERLER:** I'd like to pick up on one point from our previous discussion where I might have asked the question in a way that assumed something that might not have been the case. In asking you about how you felt when you first wore a kippah publicly, I might have assumed that there was no one else around in your world who was doing that. Was that, in fact, true? Or were there other outwardly observant Jews in your milieu?

**SIMON:** It's not only in my milieu. You have to remember, one of my professors I mentioned earlier at Harvard was Shlomo Sternberg. He always wore a beret, not a kippah. I think I've seen him once without the beret. On the other hand, there were two other senior mathematicians at the time, Hillel Furstenberg, who got the Abel Prize last year, and Leon Ehrenpreis who were religious and who, as far as I know–I've never seen them except in a kippah. Now, I didn't meet them until probably five years after the time we're talking about. In any event, it was not unusual. Even at Princeton, my wife and I moved into Hibben Magie, which were junior faculty housing, and there were five couples that were religious that every Friday night, got together to sort of schmooze with each other.

One of the others was an assistant professor in mathematics at Princeton. One of them was an instructor in mathematics at Princeton, one of them was a post-doc in physics. It was not unusual. It's one of the reasons probably it didn't even occur to me that it was an issue. But it's not unusual. What's interesting is there are lots of observant mathematicians. It's not that they're not in physics, but it's rarer than in mathematics. But in mathematics, you see them a lot. There was a point where Harvard had something like 20 senior faculty and three were observant Jews. Since, two have gone to Israel, and one's retired. But there was a point when there were three out of 20, so it's not an unusual phenomenon.

**ZIERLER:** As you were making this transition, all of the *shailas* [Hebrew; questions of Jewish law] that might come up, did you have a rav in your life at this point? Who was your spiritual advisor?

**SIMON:** No. Not really. We did have some *shailas*. We had one *shaila* we went and asked a rabbi my wife knew who was connected with academics, but he was in New York, and it was a very special issue. No, not at that point. After my daughter was born, we felt we needed to be closer to an observant community. We moved to New Jersey, to Edison/Highland Park, and there was a rabbi there in the local shul. I remember one *shaila* I had is, I was going to Japan, and the question was when one kept Shabbos because of the date line.

**ZIERLER:** Classic question.

**SIMON:** And at the time, I had an observant graduate student who was actually also taking rabbinic classes at Yeshiva University, with, in fact, Rav Soloveichik, the junior, who was also for many years a rosh yeshiva at the University. He told him, "It's a very complicated question where the date line is. He should ask his local rabbi." I asked my local rabbi, and he looked at me as if I was crazy and said, "On Saturday. What's the question?" Once we moved to Los Angeles, we had many more *shailas*, and we have a very good local *rav* [rabbi] who's very learned, but often, on the questions we asked, would bring it up the tree and have someone in New York he would consult. That's who I consulted for most questions, and then there's a fellow named Rabbi Adlerstein who I regard as my rebbe, although he normally said, "Well, you have your communal rav. You should ask him your *shailas"* but occasionally I would ask him a *shaila*. But certainly, when this process began, we were in Princeton, which was *midbar* [lit. "wilderness"; fig. place with "place with few Jews] as far as…

**ZIERLER:** Religiously, you were out in the wilderness.

**SIMON:** In those days. It's a little more serious now, but even now, I don't know what the situation is at Princeton.

**ZIERLER:** I know you said you're not overly philosophical, but as you were becoming frum, thinking about your family's history back in Europe, do you feel like you reactivated some latent observance that goes back in generations?

**SIMON:** It's certainly true that I did. On the other hand, I'm not sure that at the time, I thought about it so much. As I got older, I became more reflective about such things, and it's certainly clear that my father's parents were observant, and I'm sure going back many, many generations. On my mother's side, it's not clear. As I mentioned, her father was anti-religious. I'm not quite sure about her grandfather. I have a son, as I mentioned, who's a Talmud *chacham* [Jewish scholar]. I'm sure my maternal grandfather would be turning over in his grave at that thought. On the other hand, my father's father, I'm sure, would *shep* *nachas* [Yiddish; feel pride].

**ZIERLER:** Let's return to the research. There are two other items I want to bring up that I know happened before you achieved tenure. Let's start, first, with complex scaling. Tell me a little bit about your work in complex scaling and particularly why it was of such interest in quantum chemistry and quantum field theory.

**SIMON:** Actually, not quantum field theory. I'm not really aware it's been used much there. In atomic physics as well as quantum chemistry. I partly think of it–I'm not sure anybody else does–as, for me, a missed opportunity, not that I didn't get involved later. I mentioned last time that Arnie Dickey and Arthur Wightman had come to me on this question about anharmonic oscillators. That's what got me into that subject. The whole issue involved–under real scaling, things are implemented by unitaries. Is there some way of analytically continuing in a complex parameter? I came up with a very simple argument that essentially said, "Yeah, in fact, the eigenvalues are not only invariant under real parameters, but also under complex parameters."

I never asked myself, even though you have the same kind of underlying analyticity, what happens in, say, the case of an atomic system with decaying potentials where you don't have discrete spectra. If I had asked that, I would've discovered what's called complex scaling. I probably should've asked it. But again, missed opportunities. About a year later, a French mathematical physicist named Jean-Michel Combes, who was based in Marseille/Toulon for his entire career, essentially didn't exactly ask this question, but he wrote a paper on a technical issue. But in an appendix, he developed what we would now call complex scaling.

And he had the good idea–I may have been involved and told him that the appendix was much more interesting than the paper, but he did an appendectomy and turned the appendix into a full-fledged paper. The original paper was with a student, then there was a more important paper that did it for N-body scattering. But they realized it's really much more fascinating that continuous spectrum actually shifts away from the real axis to expose potential bounds states and resonances. I realized immediately that this gave one a tool one could use to understand what's called time-dependent perturbation theory.

When I talked about Rayleigh-Schrödinger perturbation theory, in quantum mechanics classes, it's called time-independent. It has to do with what happens to eigenvalues that remain discrete. When you have an embedded eigenvalue, it has a finite lifetime. It was normally studied by what looked like a different ad hoc method. The miracle is that when you have complex scaling, what I found is, this embedded eigenvalue becomes an isolated eigenvalue. You can apply the same methods that Kato and Rellich derived, and suddenly, it wasn't a new perturbation theory, the same ideas that would let you understand the so-called time-independent case would also work in the time-dependent case, and you could actually get a convergent series, and you got lots of beautiful results.

The quantum chemists became very interested in this technique because they could use it for numerically computing resonant widths, which was a very interesting problem. Further, one of the post-docs working in our group understood what happened in electric field. I did work with him. This was something I began probably about a year before I got tenure, and I'm sure it was a factor in my tenure case. But I continued to work on it for 10 or 12 years. Quantum chemists were very interested. In fact, the name complex scaling was invented by the quantum chemists. Combes actually called it dilatation analyticity, and I shortened that to dilation analyticity, which is a much more awkward name.

Complex scaling became the standard name, and it caught on. It was actually quite interesting and clearly made enough of a splash that at one point, I was getting NSF funding half for math and half for physics, and my physics program officer said the quantum chemistry officer had approached him, and they wanted part of my grant.

**ZIERLER:** Were you flattered?

**SIMON:** I was flattered, although the interesting thing is, it resulted, on one of the renewals I had, in the most negative review I've ever gotten because it went to some quantum chemist who regarded all of mathematical physics as junk. But yeah, I was flattered I was not shocked because there was a quantum chemist who ran regular schools and had a whole school on it in Florida. It was actually quite a big deal among quantum chemists. Remains so, to some extent.

**ZIERLER:** On the quantum field theory work, where does the name hypercontractivity come in?

**SIMON:** Ed Nelson, actually just before I was a graduate student, did some very important work long before him, mathematicians had studied what are called contraction semigroups. That's a semigroup or group for which norms decrease. They're contractions. And often, you have a situation where they act on all the L^{p} spaces, and it's a contraction on all the L^{p} spaces. What Ed realized was, in the particular case of the harmonic oscillator in a certain representation for it, you actually were, after at least a large enough time, bounded from L^{2} spaces to L^{4} spaces, and this was very useful.

You were better than being just contracted. Irving Segal, then, did some important work. In my first year as an instructor, there was a visitor named Raphael Høegh-Krohn, and he and I sort of got interested in understanding what Segal had done and rephrased everything. We decided there needed to be a name for this property that Ed had discovered. We decided to call it hypercontractivity. The funny thing is, at some point, Ed complained to me that it shouldn't be called hypercontractivity, it should've been called hyper-bounded because it wasn't a contraction from L^{2} to L^{4}, it was only a bound. I said, "You're right, except hypercontractivity sounds much better." In fact, it became widely used - the last time I looked, if you search on Google, you'll get thousands of hits for hypercontractivity.

I had a graduate student named Jay Rosen who proved that for a slightly different class of objects that enter in non-relativistic quantum mechanics, you actually had something that was more contracted. If you waited for a large enough time, they were bounded instantly. For any positive time, you were actually bounded from L^{2} spaces to L^{4} spaces, and I suggested he call this supercontractivity, which doesn't have much literature, but then about ten years after this original work with Høegh-Krohn, at the same time I was in Australia doing my Berry's phase work, a British mathematician I know named Brian Davies was there, and he discovered that in some context that was particularly interesting, you went instantly from L^{2} spaces to L∞ spaces, which was even better.

I remember he and Derek Robinson, who was our host, and I had a meeting. We were trying to figure out what to call it, what was better than supercontractivity. Derek suggested jokingly, "Oh, you can call it super-duper contractivity." We eventually came up with the name ultracontractivity. Again, it became very popular. You'll find, again, thousands of hits for ultracontractivity. In fact, I'm sort of proud, there are many names I've invented that have stuck. Hypercontractivity is one. Kato's inequality, CLR inequality, HVZ theorem, diamagnetic inequality, and Berry's phase. I guess I have a good sense of naming.

**ZIERLER:** Finally, to round out the quantum field theory work, in 1972, prior to 1972, what was your work connecting lattice approximations to the statistical mechanical models?

**SIMON:** Let me step back because I should give some background. Ed Nelson was a really innovative person in quantum field theory. He not only did this work that led to the term hypercontractivity, he was the first person to understand this new thing, but he also understood there was some earlier work trying to look at what's called Euclidian field theory. Normal field theory is done in, of course, Minkowski space. Space time with the Lorentzian metric, where the natural objects are hyperbolas because time and space have a different setting. One of the things Wightman had realized, and I think others before Wightman, was that correlation functions in quantum field theory could be analytically continued in the space and time parameters.

If you analytically continued from real time to imaginary time, then the Minkowski metric became a Euclidian metric, so space and time had the same setting. Schwinger, at first, suggested that you might even be able to formulate fields in a Euclidian framework, and Symanzik went further, but Nelson actually realized there was a full framework for this that really could be viewed as an extension of the Feynman-Kac formula to a quantum field theoretic setting. It was sort of interesting because this really was revolutionary work, which Ed began talking about probably early in 1971. It didn't make much of a splash at all. One of the reasons was, Ed very much thinks like a probabilist.

It was a language that was so strange to the people who were doing the functional analytic approach that it wasn't really appreciated. Ed didn't really have any striking new applications of the ideas to technical issues. Things changed remarkably in January of 1972 when Francesco Guerra–he may have done it a little earlier–announced or talked about some applications he'd done. Guerra was a very quiet guy, a visitor from Naples, probably had Italian money, was visiting Princeton. He'd heard Nelson's lectures, and I literally had probably talked to him very briefly twice in the year and a half that he was in Princeton before January of '72. In December, when Arthur Wightman and I were at a conference, he said, "Just before I left, Guerra told me he had some interesting results in constructive field theory he really wanted to tell you about."

We decided that Arthur, Lon Rosen, and I should meet together with Guerra, and he could explain to us what he'd done. He began by writing down on the blackboard three statements he was going to prove. And afterwards, Lon and I compared notes, and we both had the same reaction. This was so much beyond what anyone could do that we both thought to ourselves, "Yeah, sure, you're going to do that." Literally 15 minutes later, he'd done it by starting out with a result that Nelson had mentioned in his talks. He just had a few steps. Eventually, we actually found a version that takes about three minutes that uses some convex function theory. It suddenly became clear that these Euclidian field theory ideas were incredibly powerful, not only conceptually but on a technical level.

You could prove lots of interesting things with it. Guerra agreed that it made sense that the three of us, Lon Rosen, Guerra, and I, should work together in exploiting these ideas further. Within a short period, we had improved these three results Guerra had written down. We had found, about a week later, a very quick, simple proof using these Euclidian ideas of a result that Glimm and Jaffe had announced that seemed to have a very complicated proof. I still remember that about a month later, Glimm came to Princeton and gave a talk on this work of Glimm and Jaffe. Afterwards, Lon and I took him aside and showed him this simple proof. And just as we were in shock after Guerra had shown us, he was in total shock. I would say that after that, within a few weeks, everyone had stopped thinking about quantum field theory in any way except using these Euclidian ideas.

There was this huge revolution that the heroes to me are Nelson and Guerra, although Lon and I had something to do with it. We, then, extended it further, and we realized it was quite natural in understanding what was going on to shift to a lattice approximation. That is, to take this Euclidian space and replace it by a lattice version. We essentially invented what is called lattice field theory, at least for these Boson models, which is all that Nelson had considered at the time. About a year and a half later, Ken Wilson, without knowing about our work reinvented or rediscovered it, but in a much more general context that also included lattice gauge theory.

But we essentially, before Wilson, even though it's become a standard tool in high-energy physics, developed this lattice approximation, and we realized that really, what quantum field theory in this lattice approximation became was a model that looked a lot like the classical Ising model, where at each site, you have a plus or minus spin, except instead of taking plus or minus values, the spin took arbitrary real values, and the technical results involving, say, correlation inequalities that had been developed in understanding Ising-type models could then be applied to quantum field theory. Guerra, Rosen and I wrote this long paper–in fact, it was so long, the Annals, which was the most prestigious journal at least at the time in mathematics, there are now some competitors, took it, but they insisted we break it in two because it would've taken a whole issue otherwise.

They said, "We can't have an article that takes the whole issue. You have to break it in two." It appeared in two parts. Then, the next year, Robert Giffiths and I found a further thing that allowed you to prove a Lee-Yang theorem for quantum field theory. This was very important work. Much of it was done before I was officially promoted to tenure, but most was done just at the period that my tenure was being approved, so I don't think this had a big factor in the tenure decision. But it made a big impact and continues to be important in quantum field theory and statistical mechanics, and the fact that they're regarded as two sides of a subject.

**ZIERLER:** A general Princeton question around this time. With people like John Wheeler, Bob Dicke, and Jim Peebles, I've heard it said that black holes were more real at Princeton than they were elsewhere. For you, with your mathematical sensibilities, were black holes more on your radar than they might otherwise have been?

**SIMON:** No. I sort of knew about their work, but in general, general relativity was regarded somehow as a very different discipline. It's hard for me to think of any mathematical physicist who has done sort of significant, rigorous mathematical work both in general relativity and other parts of–while it's true that someone like me has worked in non-relativistic quantum mechanics, statistical mechanics, and quantum field theory, not general relativity–there are incredibly close mathematical links between quantum field theory and statistical mechanics, as I just discussed, and certainly quantum field theory and non-relativistic quantum mechanics.

In some sense, quantum field theory is just non-relativistic quantum mechanics in an infinite number of degrees of freedom. But general relativity is a very different subject, and it's one of the reasons why we still don't have a theory of quantum gravity, because it's really a very different framework. That doesn't mean someone can't work in both. Someone like Steve Weinberg is in the non-mathematical side has done work in both areas. You could in principle do it, but I'm not aware of anyone who has. I certainly have never done anything serious in relativity.

**ZIERLER:** Which is kind of counterintuitive because long before black holes were observed, they existed only as mathematical concepts.

**SIMON:** That's correct. But again, the people who were doing that kind of mathematics were Hawking, who did both mathematically rigorous things and not, and Penrose, and there are other people like Bob Geroch. They're different people. The mathematics they do and use is very different from the mathematics that my side of the field does. In some sense, they're basically using ideas from differential geometry and to first approximation people doing field theory, statistical mechanics, and non-relativistic quantum mechanics are using methods from functional analysis. They're just mathematically very different.

**ZIERLER:** When it came up for your tenure decision, by the time that was on the horizon, was there any drama? Was it a foregone conclusion that you would be awarded tenure at Princeton?

**SIMON:** It wasn't a question that I would be awarded tenure in the sense that it wasn't natural for me to come up with tenure. I didn't realize this at the time, but I'm sure what precipitated it was that Berkeley decided I was worthy of tenure, and they were going to steal me. This is probably due to Kato's influence, I'm guessing. I think what precipitated it, and I was totally unaware of this, was that some of the people at Princeton, probably Nelson and Wightman, got requests for letters of recommendation, and they assumed and it was probably correct, although there is the famous example 15 years before me of Don Spencer, who had tenure at Harvard and returned to Princeton as an untenured assistant professor because he liked Princeton so much. He was eventually promoted to tenure. But they presumed, probably correctly, that if I'd gotten a tenure offer from Berkeley, and they hadn't matched it, I would leave. They realized it was time to fish or cut bait and realized they'd better cut bait. Again, I was not aware that this was the reason. I was just told, "We've decided we're going to promote you to tenure."

**ZIERLER:** To foreshadow to Caltech, was the possibility of moving to Northern California particularly attractive to your wife at the time?

**SIMON:** No, she's really a Los Angeles person. Not general California. Her parents grew up in Los Angeles. As you may know, we're in the same state, but we're in different worlds. Again, one of the other issues that is a big factor, it is true that people with academic careers who are observant Jews will go to places where there's very little choice for their kids to go to school and not many shuls. They make that choice. I might've made that choice if I had no other choice. But if you had options–there wasn't much for us in that view in Princeton, but there was not far away in the New Brunswick, Highland Park area.

It might not have been so attractive. My wife might not have been very thrilled about the idea of moving to northern California because it doesn't have the same possibilities then. Even now, not much. That was always a restriction in the sense that we would prefer a place that had more Jewish services available, if you will, had more of a Jewish community. Given that I had that as an option, I would pick that. It wasn't a very hard choice between Berkeley and Princeton.

**ZIERLER:** Was tenure finalized before you took the leave to go to France and Switzerland?

**SIMON:** I don't know what finalized means.

**ZIERLER:** The offer letter.

**SIMON:** There's no offer letter because this was an internal promotion. At some point, you do get a letter saying you've been promoted. But the way things work is, the departments vote–it's presumably never happened in history that the Math or Physics Department has made a promotion to tenure that has not gone through eventually. The process is that it then takes time because it needs to be approved by the central administration, and then eventually, it has to get approved by the trustees. That's true of every place in the world, except there's this famous recent case in the University of North Carolina, I think it was. Presumably, the formal promotion only happened in June.

The trustees have these meetings once a year. But I was already told, "We voted to promote you to tenure," probably in December of 1971 would be my guess. I was probably told the central administration had approved it in February. Certainly, there had been some discussion of my going on leave the year before, but before December. It was probably formalized at the same time this was happening. The actual formalities of going on leave were long before I got the letter.

**ZIERLER:** If I could reframe the question, when you're going to Europe, it's with the assurance that tenure is in-hand?

**SIMON:** Well, at the time we actually left for Europe, which was–that was the year we went off to Brazil for the summer. Again, I didn't worry about the fact that the trustees hadn't officially approved it. Certainly, before we left to Brazil for the summer, I knew I had been promoted to tenure. There wasn't a question. Whether I had the formal letter, I have no idea.

**ZIERLER:** Specifically, where did you go in Europe? What institutions did you visit?

**SIMON:** At the time, there were sort of three big centers in mathematical physics in Europe. We spent a third of the year, essentially, in each of them. We spent roughly three months each near Paris at the IHES, Marseille at the CNRS, and then in Zurich at the Eidgenössische Technische Hochschule, if you'll pardon my bastardized Deutsche.

**ZIERLER:** You took the whole family with you?

**SIMON:** This was '72, '73. My oldest daughter was only born in '74. We had no kids at the time. However, we tended to go away in the summer, for much of my career, and when we had five kids, we traveled with five kids.

**ZIERLER:** Primary question, how was *kashrus* [Yiddish, familiarly; keeping Kosher] in Europe?

**SIMON:** All three places I mentioned had thriving Jewish communities. There wasn't anything to speak of at IHES. That's outside Paris. They had very nice housing. At the time, we did not have a place to go for Shabbos. We were there, actually, for Rosh Hashanah, Yom Kippur, and we stayed at a hotel in Paris. There were restaurants open in the area up near the opera, and we stayed at a hotel there. There was a shul we went to for davening on Rosh Hashanah, Yom Kippur. There was no place for Shabbos. In Marseille, we lived in a little fishing village outside of the city.

Again, there was no place for Shabbos. There were kosher butchers, so my wife would go into this area near the opera, and I probably went with her. There were essentially two religious areas in Paris, and we happened to go to one of them. We'd go to the butcher to get meat and anything else we needed. Similarly, in Marseille, there were kosher butchers. They were actually near the Institute in Marseille, but nobody in the Institute lived in Marseille. In fact, I think that part of Marseille, while it had its Jewish community, was not regarded as very high class, and perhaps not even very safe. There were these two villages further along the coast where all the senior faculty stayed.

We stayed in one of them, a little fishing village called Cassis that was very nice. When we were in Zurich, we lived in the housing of the ETH. The ETH split into two parts, and the physics section, which I was visiting–the mathematical physics there has always been centered in primarily in physics because that's where Res Jost was. We had housing there. It was probably an hour-walk into the area where the shuls were. The first Shabbos we were there, we walked in not knowing whether we'd find any place to eat. Somehow, "Oh, hello, stranger." It's the usual thing that happens. There was a very nice family where the wife was English, but the husband was a very proper Schwyzerdütsch gentleman, who essentially adopted us.

After that, there was a waiting list of people who wanted to put us up for Shabbos, so Zurich was very different from our time in Paris and Marseille because every Shabbos, we were actually staying with the local community. We didn't really make contact with the communities in Paris.

**ZIERLER:** This being a very long time ago in Europe, you felt safe walking around with a kippah?

**SIMON:** Absolutely. The first time I became nervous about this and shifted to a beret was at the time of I think the first Lebanese War, and there was some very nasty anti- Semitic graffiti when I was visiting Zurich. That was at the point where I decided I probably would be safer to shift to a beret.

**ZIERLER:** I'll just point out the irony of history that chronologically, in 1972, you were closer in years to the Holocaust than to 2021, and you felt absolutely safe in Europe. It's amazing.

**SIMON:** Absolutely. But the Holocaust was such a shock to people who had any sensitivity that it tended to suppress antisemitic thoughts. As it gets further away, it's less of a suppression, and that's why it comes back.

**ZIERLER:** Just generally, there's always value in the sabbaticals. Culturally, were there new approaches in mathematical physics you were exposed to in Europe? New ideas, new areas of research that you might not have considered otherwise?

**SIMON:** Yes, and no. Yes, particularly the fall was an incredibly productive time for me, and I did do new areas. But it wasn't with Europeans. One of the things I started doing–Elliott Lieb was also visiting IHES.

**ZIERLER:** By the way, mazel tov to Elliott Lieb. He just was awarded the 2022 APS Medal for Exceptional Achievement in Research.

**SIMON:** Absolutely. I was thrilled yesterday to get the email from the APS. I sent him a mazel tov instantly. Elliott had this idea that Thomas-Fermi might be an interesting subject, that there might be something there that was relevant to rigorous quantum mechanics, and it wasn't just some uncontrolled approximation. That was a totally new direction for my research, which I started in Paris, but it wasn't due to the Parisians, it was due to Elliott. And I had this idea that Bob Griffiths, who spent most of his career in Carnegie Mellon, had some ideas that he'd used studying Ising models that I thought might have interesting possibilities for quantum field theory, and I essentially wrote to him, did he have any idea about how to extend it not to quantum field theory, but to continuous spins? We exchanged some letters, and we started working together.

This was, again, a new direction in my research. I had the possibility, because I wasn't teaching, to think in new directions, but it wasn't because I had new ideas from local people I met. I was visiting places that had other visitors. Yes, I went in a new direction do to my corresponding to someone in Pittsburgh and my meeting with another American. This actually happened again when I was in Australia, where I mentioned this work on ultracontractivity. That was with a visiting Englishman. And the work on Berry's phase was because I met Berry, who was also visiting there. Other people can be very stimulating, but they don't have to be locals. Often, when you're visiting someplace, it's because they like to have lots of visitors, so you interact with other visitors.

**ZIERLER:** What work came out of this interaction, visitors with other visitors, while you were in Europe?

**SIMON:** I mentioned the work with Lieb, with Griffiths. There had been this incredible explosion connected with the Euclidian quantum field theory, and I was able to use the year in Europe to somehow package it, in a way, put together everything in a sensible way, so I gave lots of lectures, and in particular, at ETH. I gave a series of lectures that turned into the book on P(ϕ)__{2} theory. That was the first constructive field theory book. I essentially wrote this entire book in ten weeks. I was working very hard. There were lots of good students in class, and Jürg Fröhlich, who was at the time a post-doc in Geneva–I gave these lectures twice a week, and he took the train from Geneva to Zurich to come to the lectures. He was a very stimulating student.

**ZIERLER:** When you got back to Princeton, '73, '74, there was excitement in particle physics generally around this time. You have Gross and Wilczek, you have what Sam Ting is doing at Brookhaven, the November Revolution at SLAC, Georgi and Glashow in grand unification at Harvard. Were you aware in real time of how formative all of these events were? And how, if at all, did you slot into what was happening in particle physics?

**SIMON:** The November Revolution, everyone was talking about. I knew about it. The Gross-Wilczek stuff–David had an office across the hall from me. I'd interacted with him, and I knew that they were doing this, but I didn't realize quite how important it was. I suspect I was not the only person. It took a little while before what they'd done had been quite appreciated. But I did play something of a role in their work. I mentioned that there was period where it was known I was being promoted, although I'd not officially been promoted. The chair of the graduate admissions committee in physics, Val Fitch, who later got the Nobel Prize, went to see Arthur about one of the applications they had who seemed to be interested in mathematical physics.

And Arthur said to Val, "Barry's not officially even in physics yet, but he's about to become a regular member of the faculty. I hope you don't mind if I discuss this with Barry." He brought me the application of this young guy. No, this was when I was about to turn from a post-doc, so this was, in fact, early in 1970. I was about to be promoted to become an assistant professor. I had been just in math, but I was about to become an assistant professor in math and physics. He asked Fitch if he could bring the application to me.

We looked at it. It was someone who wanted to come to graduate school in physics at Princeton, had been a math major at Chicago as an undergraduate, and had taken very little physics but had absolute rave recommendations from mathematicians. He brought me this folder. He had a very strong letter, I remember, from Calderon, and we both decided he was likely to come to Princeton and work in mathematical physics if he came. We definitely wanted him, so we recommended very strongly to Fitch that he be admitted. And Fitch was a mensch, and he was not admitted. It was a close decision. It's a very hard decision. Arthur came to me. This was late morning one day. He said, "Well, they met yesterday, and they didn't accept this guy."

In mathematics, admissions was done in a very different way. In physics, a committee made the decision. In mathematics, a committee makes a preliminary cut, but the final decision was made at a meeting of the entire faculty. Again, because I was about to become professorial faculty, I was invited to it. That meeting happened to be a lunch meeting shortly after we'd learned that this guy had not been admitted. I said to Arthur, "Why don't we take him over to math? Maybe they'll admit him." We had students from both math and physics doing mathematical physics. And with these rave letters from the mathematicians, he was, in fact, admitted. I don't know what happened with his other acceptances, but he decided he liked the idea of coming to Princeton, so he came to Princeton in pure mathematics.

After he passed his qualifying exam in math, he said, "I'd really like to do a theoretical physics PhD." I will claim I'm responsible for his having been a graduate student at Princeton, this student. And he was told, "Well, if it has some mathematical component, we'll accept it. If they want to have you work with them, that's fine with us." He went over to work with David Gross. As you might have guessed, this is Frank Wilczek. And his thesis was the work they got the Nobel Prize for.

It was so impressive that they insisted he transfer to physics and actually get his PhD in physics. They didn't want him to get a PhD in math. But that was my connection to Gross and Wilczek. From a point of view of mathematical rigor, the ideas connected that I needed to do this are so far with anything we can do, even 40 years later, mathematically rigorously. There's no connection. I understand something of what they did, I very much appreciate it, but it's not something I did research on.

The connection between at least the work that was being done in mathematically rigorous quantum field theory we were doing and what particle physicists are doing is still quite distant. They, it turns out, and string theorists, too, have separate mathematical questions that are very interesting, and you can answer mathematically. It's a very different style of mathematics from what mathematical physicists are doing.

**ZIERLER:** When did you start collaborating with Joel Lebowitz?

**SIMON:** I actually do not think I have any joint papers with Joel.

**ZIERLER:** I'm looking at your publication list. You have something with him and Lieb, operator theory needed in quantum statistical mechanics.

**SIMON:** Yes, and no. That's not a collaboration. They wrote a very important paper, and they realized there were some technical issues that they weren't quite sure how to do, but they figured were right up my alley. Elliott, I think, probably came to me and persuaded me to write an appendix to their paper. If I had a different personality, I might've insisted I be a joint author on the full paper, but it wasn't right. They had this important piece of work, and I had this little caboose. Fine, I wrote an appendix. Elliott, by the way, did this a second time on a paper with he and Ruskai, where I have an appendix. Joel and I never really worked together. That said, he had a tremendous influence in statistical mechanics.

I mentioned that Guerra, Rosen and I had found these connections. I was the one who knew all this rigorous statistical mechanics because Arthur and Joel knew each other well. Every half-year, Joel had and still has, even at close to 90, this statistical mechanics meeting. It's different from when he was at Yeshiva. When he was at Yeshiva University, the meeting was not one day, it was two or three days. But one day was just on rigorous results and had in-depth meetings, and I went to those from probably when I was a graduate student, and it's where I learned a lot of the rigorous statistical mechanics. I knew Joel well.

My second leave after being in France in '76, '77 was actually at Yeshiva University, so I could commute there from Princeton, at Joel's invitation. It was such a successful year that they decided to close the Belfer Graduate School at the end of the year, which eventually convinced Joel to leave Yeshiva University. Going on leave is very useful because you don't have as many responsibilities, and you can focus on research.

**ZIERLER:** What about your work on convergence theorems for entropy? This is an appendix to Lieb and Ruskai.

**SIMON:** Again, similar thing. What happened was, they'd proven some important inequalities, the so-called strong sub-additivity of entropy. Their formal proof was only for finite matrices, and they wanted to know it for operators, for infinite dimensions. To me, this is an exercise that you could've even given to a good graduate student. Doesn't have the depth of the strong sub-additivity of entropy. It's important that they get it all right. Elliott said, "Let's ask Barry. I'm sure he can do it." Of course, I very quickly did it, and they asked me to write an appendix. That's where that came in. Basically, I was a piecemeal worker. You make a suit, and you might have someone do a little sewing for you on the side. On these two papers, I was the guy they hired to do a little bit of fixing the cuffs.

**ZIERLER:** What was the draw for you to take leave at Yeshiva University in '76, '77?

**SIMON:** Well, the biggest draw was commuting from Princeton. It just made sense to stay at Princeton. We had, at that point, a 1-year-old. My wife was pregnant at the start of that year. It just made sense not to leave Princeton. I could've gone to Columbia or NYU, but I knew Joel.

**ZIERLER:** And the Physics Department at Yeshiva was strong at that point.

**SIMON:** Absolutely. It had Susskind. The reason it was strong was because it had a really strong chairman, Joel Lebowitz. Actually, he was responsible for there being strong people in math. That was Joel's influence. It's a real crime that they closed down Belfer.

**ZIERLER:** Did you interact much with Susskind while you were there?

**SIMON:** Again, no more than I interacted with Sam Treiman or David Gross. We would occasionally discuss things. But other than sort of talking, I've never had strong mathematical interactions–well, that's not quite true. Certainly, the big names, I haven't. There's occasionally been a post-doc in high-energy physics that would come to me with some technical issue that would lead to a paper.

**ZIERLER:** I know it's a different world, but just being around Susskind, were you aware of the early waves being made in string theory at this point in '76? There's the Veneziano model.

**SIMON:** The Veneziano model, I was certainly aware of. The Veneziano model is connected to Regge poles, and I was aware of that because it's more closely connected to the non-relativistic quantum mechanics I've worked on. I was certainly aware of the work on the Veneziano model. I certainly did not discuss it with Susskind. I didn't have a lot of interaction with him.

**ZIERLER:** Tell me about your work on the Yukawa model.

**SIMON:** With these Nelson ideas–in constructive field theory, the biggest heroes, in many ways, were Glimm and Jaffe, and there was competition, and sometimes not always good relations between them and us. I'm sure they think that's due to me, I think it's due to them. But it was quite clear the next model after P(ϕ)__{2} that's natural is Yukawa. It has slightly more complicated renormalizations than P(ϕ)__{2} As I mentioned in the last interview, there was this work on bubblessian on this work of Caianiello that actually already was Yukawa. I'd done, as this graduate student, this work that was not within the framework of constructive field theory, but just understanding something connected with Yukawa-like ideas, and there was a post-doc at the Institute named Erhard Seiler, who was visiting, who began to realize there was a natural way of understanding Euclidian Yukawa theory in terms of regularizing determinants. This fit exactly in with the earlier work I'd done, and he and I started working together, proved some interesting results in operative theory and regularizing determinants, and led to these papers on Yukawa. It's interesting work, but not of the significance of the earlier work in the Bose field theory.

### Phase Transitions and Symmetry Breaking

**ZIERLER:** What about your work on phase transitions and symmetry-breaking?

**SIMON:** Ah, that's certainly among the top – most important. That actually had interesting roots. This must've begun in the fall of '75. This is the year before I was on leave at Yeshiva. Tom Spencer was, at the time, at Rutgers. Jürg Fröhlich was an assistant professor at Princeton. We had this incredible group of young assistant professors I heard, I don't remember from who, not from them, but I heard they had discovered a way of proving breaking of continuous symmetry in three-dimensional quantum field theories. It was known that two-dimensional theories do not normally have continuous symmetry-breaking. They'd found a very simple argument, although it wasn't they who explained it to me, and there was a rumor going around about it.

I immediately realized it was very important to understand what would happen in the corresponding discrete lattice models, the purely statistical mechanic models, the so-called classical Heisenberg model. It was not obvious how to extend their argument, but I sort of understood and realized that one of the things they used that didn't obviously extend, I understood where it came from and was therefore able to prove this result in the classical Heisenberg model. People doing statistical mechanics couldn't care less about quantum field theory, but they were very excited about this. At some point, the three of us got together at the AMS meeting in San Antonio and decided what really made sense was to join forces and do this as a joint paper.

Shortly after, we found a really streamlined, elegant way of doing what I had done for this classical Heisenberg, and this led to this Fröhlich, Spencer, Simon paper that, in fact, still remains the only proof of continuous symmetry-breaking in any physical model with non-Abelian symmetry groups. There are some with pure 2D rotation, very specialized. But this very general argument. Jürg went off to leave in Europe. Tom and I, at that point, had not had much interaction with each other. I decided the next natural step was to do quantum models. Elliott was very interested.

When Elliott had heard that I'd done the classical Heisenberg model, he said to me, "This is not known. This is very interesting." I said, "Yeah, I know." He said, "Congratulations." We talked about it. We decided we should look at the quantum model. I don't remember quite how we got Dyson involved, but it was one of the most fun things. Elliott, Freeman, and I would get together–whenever we were at the university, there were too many people who wanted to see me, so the only way we'd get anything done was, the three of us would meet in Dyson's office at the Institute. We agreed we'd set, I think, three hours once a week on the same day, and we'd just sit there. We were working on this, but we'd talk about all sorts of other things.

We couldn't quite get things to work. Freeman went off to give a talk somewhere, and Elliott and I figured out this last step. Not entirely correctly, as it would turn out. But we thought we'd finally done it. This was long before email and other things. We were so excited, we sent a telegram to Dyson that read, "Mr. Heisenberg has arrived." That was the whole telegram. We, then, wrote an announcement. One of the things we realized early is, in the classical case, the ferromagnetic and anti-ferromagnetic are exactly the same thing. There's a symmetry that takes one into the other. But in quantum mechanics, you can't realize the symmetry. It's an anti-unitary, so the quantum Heisenberg ferromagnet and the quantum Heisenberg anti-ferromagnet are quite different, and the anti-ferromagnet has frustration and other things.

Before our work, it was regarded as a much harder problem. We had these ideas that worked we thought both for the quantum Heisenberg and the quantum anti-Heisenberg. We wrote a Physical Review Letter, and we then wrote the full paper and submitted it. It was accepted. The next year, Jürg Fröhlich was back in Princeton and decided to give a course on our paper. We got the galley proofs of the whole paper and put it in the department mailbox, not a US mailbox. And Jürg walks into Elliott's office and says to Elliott, "I don't understand how such-and-such is proven." Elliott says, "I don't know, let's go ask Barry." I took one look at it, and I really hit my head. I realized instantly that something wasn't right.

For the anti-ferromagnet, everything worked fine, but for the ferromagnet, we used a trick that was just wrong. We were sure we could fix it, and we never fixed it. 35 years later, nobody's fixed it. It's still true that it's only for the quantum anti-ferromagnet that one has proven continuous symmetry-breaking for the quantum Heisenberg model. We didn't, and it's an embarrassment that we have this announcement that's wrong. I joke, "Well, it's a good thing we weren't three unknowns."

**ZIERLER:** What was Freeman Dyson like?

**SIMON:** He was a very funny guy, very different from most people I've dealt with. Very oracular in the sense that he would think about something and sound like an oracle almost. But very clever, very sweet temperament, had lots of funny jokes. It was a pleasure to deal with him. Except this one piece of work, we somehow didn't interact that often. We had these famous brown-bag lunches he would come to, and it was very interesting. But I didn't really have as much interaction with him as I might've.

**ZIERLER:** Was he mostly at the Institute or on campus?

**SIMON:** Except when he came to the brown-bags, and he'd sometimes come to the seminar, he rarely was on campus. He was almost always at the Institute. Until he started coming to the brown-bag, I don't think I'd ever seen him on campus.

**ZIERLER:** How much time did you spend at the Institute?

**SIMON:** Except when people are working together–they're both in Princeton, but it's probably a 40-minute walk. It's a 10- or 15-minute drive. People don't spend as much time as you might guess they might spend together.

**ZIERLER:** But in terms of where the most exciting talks would be for you, would they be more likely in the department?

**SIMON:** I would rarely go to the Institute. Certainly, there was a mathematical physics seminar at the University I would go to every week. There were math and physics colloquia many weeks I'd go to. There might be two or three others at the University. If I went to a dozen talks of any kind at the Institute in a year, it would be a lot. Because it's a shlep. If there's someone you're working with there, you go there to work with them. Otherwise, it's making a trip. It's not just walking down to the seminar and walking up afterwards. There would be announcements, but there isn't as much interaction between the University and the Institute as you might expect.

### Ed Witten Enters the Scene

**ZIERLER:** One last question before we break for lighting Chanukah candles. When did Ed Witten enter the scene?

**SIMON:** That's not a three-minute answer.

**ZIERLER:** Chronologically, at least.

**SIMON:** He first came as a graduate student to Princeton in the fall of 1973.

**ZIERLER:** When does it first become apparent that he has these abilities?

**SIMON:** I need to tell the whole story. It's not a three-minute story. I need to give two pieces of background before I get to the punchline. First of all, I returned from leave in '72, '73 to become Director of Graduate Studies in the Physics Department. I had a joint appointment, but this was an administrative position that rotated. Since we had slightly over 90 graduate students in physics, it was quite a load. Not anything close to being department chair. My predecessor had, in fact, been David Gross. The other background piece I should mention is that in addition to the regular programs in math, physics, etc., there was a very strange program in applied mathematics.

There was no applied mathematics department, no real "applied mathematicians" at the time at Princeton. Martin Kruskal had started out with an appointment in the plasma physics group that was off-campus, not a regular faculty appointment. But while there, he had done some famous work in general relatively involving the Schwarzschild solution. The Schwarzschild solution these days has probably studied what are called Kruskal coordinates that make the horizon sort of clear. On the basis of this work, he was, in fact, given an appointment in astrophysics on campus. He was not really an astrophysicist in the usual sense, and early on, in the period of this appointment, he actually did this work that eventually became very famous on solitons, a series of five or six papers.

But he was always interested in mathematics more generally and in applied mathematics. He convinced someone, presumably the dean of the graduate school, to allow him to set up a so-called program in applied mathematics. There were graduate students in this program, but since there wasn't a real department, they had to have a home department. They still took their qualifying exams and other exams in applied mathematics, that is, not in their regular department. There was a seminar or course that Kruskal gave that all the applied math students had to go to.

But it was not a real program in the usual sense, and it didn't have any faculty, so the decision on who to admit was basically Kruskal's, except, of course, when he decided he wanted to admit a student, he had to find a home department that agreed to take them. It both had some great successes and some awful failures. I remember being dragooned by Kruskal into serving on committees for oral exams, and I remember several oral exams of students that terribly, awfully failed. It was just awful. He, of course, had some very great successes. My own student, Percy Deift could not have gotten into either math or physics because he was a graduate student in South Africa, had a master's from a South African university in chemical engineering.

He came to Princeton originally in applied math with his home department being chemical engineering. It's a long story. Eventually, he came to work with me and is now probably my best-known student. I was just beginning to settle in as Director of Graduate Studies in the fall of 1973. The classes had not quite started. Most of the supports had been arranged by Gross, but there were small changes that needed to be made, and I sort of figured out how things were working. This young man walked into my office and said, "I'm a new graduate student in the applied math program with physics as my home department, and I don't have any support at all. I have to even pay full tuition. Is there anything you can do to help me change that?"

I said, "I'll have to take a look at your file and get back to you." I arranged to get his file, and I couldn't believe it. It was a disaster. It was someone who majored as an undergraduate at Brandeis, I believe, in history, went to graduate school in economics, and maybe had even changed major once as an undergraduate, and had decided in Wisconsin that he wanted to come and study physics. He at least knew enough that there was no chance he could've gotten in in physics. He applied to the applied math program and had been admitted. It meant that my predecessor, David Gross, had had to approve his being admitted. I went across the hall with the folder and said to David, "You admitted this guy. He's a disaster. It makes no sense. How could you have done it?"

He looked at the folder and said, "Yeah, I remember this folder. You're right. It didn't meet our criteria. He didn't seem to be good enough. But Kruskal was really keen to admit him, so I said to Kruskal, 'Do we have to support him?' And Kruskal said, 'You don't have to support him. I can admit him without support.'" David said, "I figured, well, Kruskal wanted him, it didn't cost us anything, what do I care? 'Sure, you can do it.'" He had a laid back personality. I went home, and I began to think to myself. There were, at the time, 92 students to my memory, most of whom were officially in physics, but a few of them were affiliated in some program where physics was their home department. 91 of those 92 had full support, both tuition paid and a stipend.

One student did not. He should never have been admitted in my opinion, but it didn't seem fair, it didn't seem right that we should have this one student who was treated so differently from the other students. With 92 supports, you can always do some rearranging. I found two guys who I said, "Can you support another half-student?" And I was able to scrape together one more support, so I found support for this student. Then, forgot about him. It was not my problem. I'd found a support. He, in fact, didn't have an advisor in physics. Kruskal was his advisor. He was Kruskal's problem. A couple months later, near the end of the term, he comes back to me and says, "I'd like to transfer full-time to physics."

I thought to myself, "Yeah, right. It makes no sense." But I said, "I've got to look into it." At least in this case, I was wise enough not to immediately say, "Get away from me." I said, "Who are you taking courses from? I'll speak to them, and we'll make a decision," assuming that it was going to be, "Sorry, we can't do it." One of the people he was taking a course with was Sam Treiman, who I'd, of course, known as a graduate student and then for these few years on the faculty. I had a tremendous admiration for him as a person for his sense of students, his ability to deal with students. His most famous student is Steve Weinberg. He was teaching graduate first-year quantum mechanics class, so I went to Sam and said, "This guy wants to transfer into physics. What do you think?"

He looked at me and said, "He's fantastic. Do it." Sam tells me this, and I said, "Fine, you can do it." The end of the year occurs. The Physics Department had a general exam at the end of the year that was, to my memory, three days long, three hours in the morning and three hours in the afternoon, Monday, Tuesday, Wednesday. The first-year students took the Monday and Tuesday morning exams. Students taking the full general exam would take all three days. Some students, maybe one or two out of 25, would try to take the full general exam the first year. I had done that, but it was not usual. And this student not only took the exam but had the highest grade in the exam ever. It's Ed Witten. That's how I was introduced to Ed Witten.

**ZIERLER:** Did he play catchup? Given the fact that he didn't have the background, did he just absorb all of this in some supernatural feat? How did he do it?

**SIMON:** I will tell you another Sam Treiman story that shows what Ed's abilities are. This was many years later, probably before Ed came back to Princeton because I think he came back after I'd left. But it was after Ed had gotten married. Anyhow, Sam was talking to Ed's wife, Chiara Nappi. Chiara said to Sam, "There was one time that I suddenly realized Ed had learned quite a big about algebraic geometry. And I said to Ed, 'Ed, I didn't know you knew any algebraic geometry.' And Ed replied to me, 'Don't you remember when we drove out to Chicago, and you drove the whole way? I had a chance to read about it.'" Ed was very good at absorbing things very fast. Ed is very quick. Yeah, he played catchup, but he's really sharp.

**ZIERLER:** Amazing. By the end of the 1970s, what were some of the big topics in your research agenda?

**SIMON:** End of the 1970s, I'd been working on lots of different things. Many of them were sort of beginning to wind down. I continued to work in constructive field theory. We were really quite successful in two space time dimensions. Three space time dimensions was much harder. It really involved rather elaborate expansion techniques, very different from my style of doing things. Much of the progress had been made by Glimm, Jaffe, and Spencer. And it was becoming fairly clear that one would need incredibly new ideas to go beyond three space time dimensions. I had almost stopped working in constructive field theory. There were still interesting questions in statistical mechanics, but these big progress things had slowed down, the low-hanging fruit had disappeared. There'd been a very successful set of results that Avron, Herbst, and I had worked out in magnetic fields that were interesting questions that people really hadn't looked at.

**ZIERLER:** This is the work on Schrödinger operators?

**SIMON:** This is work on non-relativistic quantum mechanics, what happens when there's a magnetic field. People had sort of proven the basic self-adjointness results, but there really had not been much that involved the physics of magnetic fields per se, and in particular, the special role of gauge invariance. There was no real understanding of the perturbation series for the Zeeman effect. It turned out to have many similarities with what happened for the anharmonic oscillator. And there were some new phenomena we discovered. One of my most highly cited papers involves the reduction of the center of mass in a constant magnetic field, which turns out to have some very interesting subtleties. But we'd done that. We finished that. That was finished. When I came out to Caltech, it was clear that I had to find some new directions. There really was, in some sense–a break is too strong because I actually continued to occasionally write papers on statistical mechanics, magnetic fields, and things like that throughout my career. But it was clear that I needed to find some new area.

**ZIERLER:** Where would you put phase transitions and reflection positivity? That's new directions, or that's before?

**SIMON:** No, reflection positivity was, in fact, part of the tools–I mentioned this work with Fröhlich and Spencer in '75, '76, that was reflection positivity. We'd already done that. There was follow-up that Fröhlich, Israel, Lieb, and I did. That was the late 70s. It isn't that I didn't do anything on phase transitions. I have papers in the 80s. But I'd had all these playgrounds with low-hanging fruit, and I'd picked all the low-hanging fruit. It wasn't that there weren't occasionally things to look at, but it was clear I needed to think about new directions. Yossi Avron, who had been a post-doc at Princeton, was promoted to assistant professor, and I'm not quite sure how I convinced the department, but it may have been that normally, when one goes on sabbatical, one gets half a year's salary from Princeton.

But I was going to Caltech on this fancy Fairchild program, and Caltech was paying my entire salary. I was able to convince my colleagues to also let Avron come on leave the same year. Caltech had no one in mathematical physics when I was coming out here. The reason I was coming out, in many ways–Murph Goldberger had been the department chair at Princeton, and he was now the president at Caltech. He had been the one to arrange it. I figured it would be interesting to come out. Moreover, as I explained, my wife was a big fan of Los Angeles. It would seem to be a nice thing to go out through the year to Caltech.

**ZIERLER:** How much interaction did you have with Murph at Princeton?

**SIMON:** Scientifically, not too much, except for one case. But he was department chair when I was Director of Graduate Studies. And the only way of putting it is, we were in the trenches together. There were some horror stories that I can tell as Director of Graduate Studies. There was the time that the department was closed down by a bomb threat that was due to a graduate student. Murph and I had to figure out what to do with that case. We were in the trenches together.

**ZIERLER:** Without getting into details, was somebody suffering from mental instability?

**SIMON:** Almost all these cases were due to students–these students are incredibly bright, but as often happens, many of them are a little bit unstable. This was a case of a student who was suffering. Those were the days when, if something like this happened, you would just kick the student out. There were no formalities. But for example, there was this question that came up. He had an NSF fellowship, and he tried to transfer. He actually wanted to transfer to Harvard, this student. Murph and I had to decide what we were going to do. We didn't have formal proof. Basically, by comparing handwriting of the threatening note that had closed everything down, and something the student had written, we had determined to our satisfaction that this student had been the one who'd done it, so we asked him to leave.

But now, he wants to transfer to Harvard. What did we do? By the way, we did decide, in the end, to do it. They decided since he had his own support, they'd admit him. I think he committed suicide. It's a very sad story. These cases often wind up being sad stories. We really had been in the trenches together. Murph had clearly respected my mathematical abilities. Every summer for many years, Murph worked for a project called JASON. But essentially, he and a group of theoretical physicists would meet in La Jolla in the summer to do Defense Department research. There was some problem involving sound waves that turned out to be equivalent to some one-dimensional quantum mechanical problem.

He, Dick Blankenbeckler, and Henry Abarbanel, who was an assistant professor at Princeton at the time, had figured out some formal result about what should happen. He came to me and asked if I could prove anything about it. I wrote a paper that's very highly cited. There was a follow-up that Murph and I wrote. We did a little scientific work together. But when Murph left, one of the things he said, "Caltech mathematics is not as strong as it should be. I hope you can help me on this." Murph and I knew each other well, we were friendly. While I was out at Caltech, we would have lunch probably about once a month. I would bring my own lunch, brown-bag it to the Athenaeum.

Normally, they probably wouldn't allow that, but if you're meeting with the president, they make an exception. I came out, it was clear that I told Yossi earlier in the year, "We really have to look in a different area. There are two things I've been thinking about. One is quasi"–I think we discussed this a little bit last time. I shifted into this work on what happens with almost periodic potentials, which I don't exactly recall, but I think we were just motivated by the mathematical interest, but it turned out to be very timely because that's what quasicrystals are. This is just about the point when quasicrystals became important. But I think we had begun the work before. I can't remember.

There was this very dramatic thing that happened because one of the things that happens that's very interesting is the spectrum in quasicrystals turns out to often be a Cantor set with lots of gaps. In the middle of this first year when I was on leave at Caltech, the first pictures of Saturn's rings came out. It seemed to have lots of gaps. It looked, and still looks, a little like a Cantor set. We had the idea that maybe it was the same phenomenon. In fact, periodic motion in celestial mechanics was first studied by a mathematician named Hill, who the Hill center at Rutgers is named after in the late 19th century. He had realized that the structure of periodic motions would have a band structure. He had studied the equation, he got Hill's equation, which turns out to be the exact same equation as enters for one-dimensional periodic quantum mechanics.

We had the idea, "Well, if you instead had an almost periodic phenomenon, you might get this funny Cantor spectrum, and there were obviously two periods involved in the motion of the rings around Saturn, the period at which the rings were going around Saturn and the period at which Saturn was going around the sun. There was a natural picture. We had this idea. The problem was, if you tried to figure out how important the sun was, the effect of the sun was not very big. It didn't quite fit totally. I actually asked Freeman Dyson what we should do. We had a picture of what might be true, but there was this puzzle. There had to be something we didn't understand that made the impact of the sun more important than one might at first think. Freeman said, "Publish, and be damned."

He essentially was saying, "If you're wrong, so you write something wrong and if you're right…." Peter Goldreich, who I had some interaction with, of course, had a competing theory that I think is the correct theory called shepherd moons for what caused this structure. When I told him what Freeman said, he said, "He's a remarkably silly man." We published this, and in fact, it was wrong. In the sense that no one has ever found any explanation of why the impact of the sun should be bigger than the value of the picture. It's presumably the wrong picture, but it's a different mechanism that produces it. But it was exciting. Probably the only thing of "real physics" that I was close to doing, but it was wrong.

### The Switch to Caltech

**ZIERLER:** In our next talk, we'll discuss in more detail the circumstances of your switch over to Caltech. But just for that initial year, in terms of understanding the push and pull factor, how much of it is Murph as president surveying the landscape and really recognizing a weakness in mathematical physics at Caltech?

**SIMON:** Well, it was not a weakness in mathematical physics. There was no mathematical physics. There's a weakness in mathematics. Mathematics was always the stepchild of PMA. It's still the stepchild of PMA. At the time, mathematics was ranked, I think, 15th in the US News and World Report, which is much lower than almost every other department at Caltech in the sciences. Engineering is top ten, usually top five, often top one or two. Mathematics was below that. He knew there was a weakness. That was a reason why he wanted to get me that has nothing to do with why we came.

**ZIERLER:** And that first year on the fellowship, did you see that as a soft landing, a tryout? Or you were expecting to go back?

**SIMON:** I was expecting to go back, except, and we'll presumably get into this more next time, a major factor with my leaving Princeton was my salary and my naivete in the sense that at most academic institutions–fortunately, Caltech is more sensible, it's not as true at Caltech–you really have to get outside offers to get a big salary raise normally, or some big prize. The department chair can't say, "This guy really looks very good, and if we don't treat him right, he's going to get poached." That doesn't work with convincing the administration to give someone a bigger-than-normal raise.

The only way of getting a bigger-than-normal raise is, somebody makes you an offer for enough money, and the institution has to match it. As someone said to me, "You don't understand how capitalism works." Basically, I had lots of people coming to me, wondering if I might want to leave Princeton. I would say, "No, I'm very happy. I have no desire to leave Princeton." And in about '78, Elliott and I–Elliott had only been at Princeton for a few years–realized that our salaries were just barely keeping up with inflation, if that. That was not very good. I became very unhappy. In fact, before I left, I had been approached by Rutgers, and they were essentially going to double my salary. It was clear that I was thinking about leaving, and I was known to be on the market.

That was a year I wound up with lots of offers. Or I could've had lots of offers. Berkeley was, again, very interested in me. But my wife didn't want to go to San Francisco because there was just no Jewish community. There was essentially a school with classes that had ten kids in a year. Our kids already were going to Jewish religious schools. If we had no choice, we would've taken it. But we had choices, much more vibrant religious Jewish communities. I remember Paul Cohen really wanted to lure me to Stanford, and he complained to Peter Sarnak. "We should've figured out a way of opening a shul for Simon." That was a year that, in the end, I had three or four formal offers I was juggling. But the salary was a factor. It was known I was thinking about moving. It was an interesting year.

**ZIERLER:** What does it tell us institutionally about the ethos of Princeton that they were essentially tone-deaf to concerns over salary?

**SIMON:** Once I talked to them, they weren't totally tone-deaf. They felt they had to do something, and they offered me, I think, 40%. Caltech was not only at 80% raise, but it was more complicated because the Caltech salaries are 11 months. But basically, in terms of nine months' salary, Rutgers was doubling, Caltech was an 80% raise, and Princeton offered to match it with a 40% raise. And the way the institution was set up, it was hard for Princeton to do more than that. That's actually often the case. The idea of doubling a salary is unheard of. But it's not just Princeton, it's very, very common. Once I began at Caltech, I was very much involved in recruiting.

We sometimes would get approached by people who indicated they might want to move, and it became clear that some of them were just trying to generate offers, not because they wanted to move, but because that's how capitalism works, they wanted to get a raise. I remember one guy we approached. "Would you be interested?" His response was always, "I've never responded to an offer I haven't been given." That's the way you generate offers that you can then use to get raises. It's just the way the system works. But when I came to Caltech, the division chair then told me, "I can't give you more of a raise than I did," but very quickly, my salary went up quite a bit.

**ZIERLER:** You're engaged in these formal negotiations during the visiting year? Or this takes place after the visiting year?

**SIMON:** No, it was all during the visiting year.

**ZIERLER:** The 80% bump, that's sort of stratospheric. How much is that about it's the president of Caltech who's driving the recruitment?

**SIMON:** It's not. It's the division chair. It helps the presidents there because then, the division chair can get what he wants. But the way Caltech works, there's no way the president–the division chair also realized I could help Caltech and Caltech mathematics. But there's an additional factor, you have to realize. I should tell you that after I had the Caltech offer, people asked me, "Are you going to accept?" We were certainly leaning, and my response was always, "That depends on Dave Morrisroe."

**ZIERLER:** That's a new name for me.

**SIMON:** He's an historic figure. For many, many years, he was the Vice President for Business Affairs. I think that's what he's called now. I don't know if that's what he was called then. He essentially ran the business side of Caltech. Why did it depend on Dave Morrisroe? You have to realize that real estate prices in Los Angeles were very high. This was 1981. Mortgage rates were 15%. I couldn't afford to move, except that Caltech had special mortgage plans. This was, again, the "good, old days." Now, there are so many rules that the federal government places on programs like this because otherwise, they're going to say, "This is not just some way of helping them, this is actually extra compensation that's taxable."

But there wasn't any such concern in those days. The question was, what kind of program could Caltech set up so that I could get a mortgage I could afford? Now, the situation is such that Caltech has absolutely rigid rules because if they don't, they run afoul of federal regulations. But in those days, Dave Morrisroe, consulting with various other people, would figure out what to do to help lure you there. I still remember one point when I had almost decided, because I'd been told I was going to get such-and-such, I met with one of Morrisroe's assistants, who was actually very helpful for me because Caltech was my mortgage holder, looked at the real estate and helped a lot.

He, at some point, said something to me that made it clear to me, what I thought Morrisroe had told me they were going to do, they weren't going to do. I was shocked, and I decided there was no way if what he told me was going to happen was going to happen I could afford it. I went to see the division chair all upset and said, "I told you last week that I thought I was going to accept, but that was when I understand, and I don't"–and he looked at me and said, "So-and-so is Morrisroe's errand boy. He doesn't know what he's talking about. Don't worry about it." But financial considerations were a major factor in the move, as they often are.

**ZIERLER:** Substantively, talking about looking for new directions in the research, if you strip away the financial considerations, your wife's excitement at the prospect of settling in Los Angeles, did you see setting up shop in Caltech as a fertile opportunity to see those new directions that became apparent to you at the end of your time at Princeton?

**SIMON:** Yes, and no. You have to realize that Princeton, in terms of resources that were available to me, was almost infinitely better than Caltech. There were three senior people in mathematical physics, and during those golden years, we would have six, eight, ten junior people around. I knew there was no way I was going to get that kind of resources at Caltech. Caltech, in mathematics, is much smaller. Physics at Caltech is about the same size, and I was going to get some resources from physics. Moreover, one of the things I couldn't negotiate was an absolute promise that there would be another senior appointment in mathematical physics. The response was, "You bring us a strong candidate, we'll seriously consider them."

And indeed, over my years here, we've made many senior offers to mathematical physicists. But I wasn't going to have the same size, the same resources. The one decision I did make is that Caltech had enough resources that I could get enough in the way of other people to work with that I could continue to have a good research program. I determined that it met a minimum threshold, but it certainly was not an improvement on what was true at Princeton, and I expected that was true, but that I would probably have to focus on fewer areas than I'd worked on at Princeton.

**ZIERLER:** For next time, we'll pick up on when you get to Caltech and what the scene is like at that point.

[End of Recording]

**ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It's Thursday, December 9, 2021. Once again, it's my great pleasure to be back with Professor Barry Simon. Barry, as always, it's great to be with you.

**SIMON:** Likewise.

**ZIERLER:** Today, I'd like to start on a specific point as you were considering whether or not to make Caltech a permanent move or whether you would go back to Princeton during that initial year that you had the fellowship. Let's start, first, with your post-doc, Avron. Tell me how the story there, how he was with you at Princeton and what you negotiated to make sure he would join you for the long term at Caltech.

**SIMON:** As Yossi is very fond of saying, he first met me in 1971, and I first met him in 1973. Because basically, he did introduce himself to me at a conference in 1971, but I didn't remember him. I met lots of people. He knew who I was, so he made a point of introducing himself to me. He was, then, a graduate student at the Technion. And then, in '73, we talked some. It's sort of a little strange, Eugene Wigner left Germany in '31, before Hitler came in, but he didn't resign his position from Berlin. Somehow, they then kicked him out, even though he wasn't there.

After the War, they decided they owned him some reparations. After some negotiation, the money they were supposed to give him would be available for a post-doc to come to Princeton. Wigner had visited the Technion, he already knew Yossi's thesis advisor, Yehoshua Zak. Between Zak and Wigner, they decided that if Avron, who was very interested in coming to work with me, wanted to use the money to come to Princeton, he could use that money. He originally came to Princeton on that money. We talked a lot. Probably during that year or two, we worked some. He became, then, a regular post-doc, and probably a year or two before I went to Caltech, he was appointed an assistant professor at Princeton. At Princeton, all assistant professors are nominally tenure-track.

There's no such thing as a non-tenure track assistant professor. On the other hand, everyone who's hired is told, "Yeah, you're nominally tenure-track, but we don't give tenure to anyone as a first approximation." Although it is true, at least at one point, and while I was there, it was still sort of true, almost everyone at Princeton had been an assistant professor. But typically, there were at any given time, 10, 12 assistant professors, and typically, at most, one would be promoted to tenure. It was nominally tenure-track. He wasn't technically entitled to a leave, but since I was going on leave with the Fairchild money, it wasn't costing anything, I was able to convince someone, I don't remember who, to let Avron come to Caltech also that year, paid by Princeton.

He was the main person I worked with at Caltech because there was really no one in my area. I talked to a lot of people, but in terms of serious collaboration, it was Yossi. And I knew if I was going to make this move, I really wanted him to come with me to Caltech. My initial proposal was, "He was an assistant professor at Princeton, he should become an assistant professor at Caltech." But here, there's a very different culture. At Caltech, when someone's appointed as an assistant professor, to first approximation, they're told, "When we hire you, we expect we will be able to promote you to tenure. This is not a promise in any sense. You have to justify it. But it's not nearly a nominally tenure track."

And I could not argue that I expected Yossi to get promoted to tenure at Caltech. He was very good, he's very talented. But just as I couldn't have argued he wouldn't have been promoted at Princeton. The division chair said, "We can't appoint him as an assistant professor, but I'll give you money for him to be a post-doc." I don't remember now for how many years. We did this very important work on topological methods in condensed-matter physics on the work of Thouless. And he went back to the Technion as an assistant professor.

He was also back at Caltech around '87 or '88 for a year. I visited him, and we wrote lots of papers over those years. But it was great to have him around. In particular, the work I mentioned on topological phases was done during this time at Caltech. And obviously if they had said, "No, too bad," I would've said, "I can't have people to work with, I'm not accepting." It was a critical fact that they provided this money. And it's not unusual for new faculty to be provided money for a post-doc.

**ZIERLER:** Another cultural question. You coming in, knowing full-well that there wouldn't be anyone there really to work with in mathematical physics, to what extent is that par for the course at Caltech, where the institutional ethos is, they hire the best, without regard for whether there's a large group for that person to join or not?

**SIMON:** Well, if we can find the best, someone who's really good, we will hire them. On the other hand, often, searches are targeted to look in areas, and sometimes they're new areas we want to go into, but often, they're areas where we have some strength, but we want more strength. It is fairly unusual to hire someone in an area where there's no one else, but it certainly happens, probably more often than I think it happened at Princeton. As I think I mentioned last time, I was told I could bring up senior appointments, and I did, and I could suggest assistant professors, and we'd had two over the years. Each of them had a two-body problem and wound up leaving for that reason.

They're very distinguished people now. One of them, in fact, was Avron's student, Yoram Last, who was an assistant professor for a few years, and then went to Hebrew University because his wife was finishing up as a graduate student there and then had a job there. Another one was Gian Michele Graf earlier. That was a total disaster in the sense that he's Swiss, his wife had a Swiss MD, and it just turned out there was no way she could get it recognized in California, so she couldn't get a job as a medical professional. After I think two years, he went back to Switzerland. And we made probably four or five offers over the years to senior people, until finally Rupert Frank accepted, I guess around 2010. On the other hand, I always had lots of funds for post-docs, including one from physics, although the first one from physics was an indication of the way sometimes things work at Caltech.

There was, even then, the equivalent of what now is called the Prize Fellowship Committee in Theoretical Physics. And probably, it was my first year at Caltech. I didn't someone who looked pretty good who turned out not to be so great, but he wasn't terrible. But I didn't know that, and I very much wanted to have him come. And there were a limited number of slots. You should realize, at the time, I think there were five people in particle physics, high-energy physics, whatever you want to call the area. This was pre-string theory, so it's just that. But in fact, one of the problems that Caltech had was, two of those five were Feynman and Gell-Mann.

Gell-Mann essentially spent all his time in Santa Fe, came back to Caltech one day a week. Dick was Dick, he's fantastic, but he was, at the time, close to 60. It was regarded that high-energy physics really needed to search. We can talk about that, too. But when I proposed this person, the chair of the committee, who was a high-energy physicist, said, "Post-docs are a limited resource, and we have to decide whether we want to use them in a strong area like mathematical physics or a weak area like high-energy physics." This is, again, something that one would not normally do, but I was new. I asked to see the division chair, and I essentially–I won't say I quite had a tantrum, but it was close. And Robbie Vogt, who was the division chair, said to his secretary, "I want Geoffrey Fox," who was the chair of the committee "in my office" (added quotes).

Geoffrey came in, and Vogt said, "I'm very unhappy that you…" Anyhow, I got that post-doc, and since then, I've had a good experience, and I've always had lots of post-docs around. And I expected that. I was led to believe that would happen. I've really been able to run a pretty decent program, particularly for someone in mathematics. I think there was one point, counting someone who had an NSF post-doc, I had four post-docs at once, and it's unusual that anyone in math has more than one. One of those was NSF, and one of them was a theoretical physics post-doc, but still, I was given much more in the way of resources than I think anyone else in mathematics.

**ZIERLER:** Were Gell-Mann's frustrations with Caltech fully characterized at this point?

**SIMON:** No, I had been told that he liked the Santa Fe Institute, and so was coming back one day a week. It may have been in the background, but I'm somewhat oblivious of these political things. I'm not sure when the bad relations came to fruition. He still had enough influence that, for example, he pushed to get John Schwarz made a faculty appointment at a point when the big breakthrough in string theory of Schwarz and Green had happened, but I'm not sure most of my colleagues appreciated that, and I think Murray was central in that getting done. The joke around the department when I first came, because it was regarded that we had problems, particularly in theory–the problem was, Murray was too much involved, and Dick wasn't enough involved. Dick basically had the attitude, "You guys are OK. You'll do a good job. I don't need to get involved." Murray tended to downplay any area that wasn't high-energy physics. He referred to squalid-state physics and half-ass-tro physics. And I was told people were a little surprised because he actually supported my appointment.

**ZIERLER:** Because you're not high-energy physics.

**SIMON:** I'm not a high-energy physicist, and I'm a mathematician. Goldberger, also. There's this Fermi tradition, not just Fermi but particularly people who had interacted with Fermi, that any mathematics a physicist needs, they can figure out by themselves. They don't need to use mathematicians.

**ZIERLER:** Was Feynman sick at this point yet?

**SIMON:** No, not at all. I came in '81, and Dick passed away in '88. At least, he was known to me to be ill probably nine months before he passed away. I had quite a bit of interesting interaction with Dick, including in the last few months of his life. It was sort of a little sad. He had gotten very interested in what's called dimensional renormalization, in which one essentially does renormalization by analytically continuing in the dimension of a space, and it's just a formal parameter in the integrals. But Dick got into his head that somehow, one could make sense out of fractional dimensions, that there would be a set of axioms that would describe a space of dimension 4.01.

I was very skeptical about this, and he knew this was not really physics, it was mathematics. I was his in-house mathematician. He'd come up with these schemes, call me in, and normally it would take me ten minutes to figure out some reason why his scheme definitely wouldn't work. It was sad. I didn't want to do it. I started avoiding it, and Helen Tuck would come to my office. She was tough. I couldn't tell her, "I'm not coming." I would come and shoot down his idea. I knew he was very ill, and I hated to do it. We had more interesting interactions earlier.

**ZIERLER:** I want to hear about when he sort of gave you a little bit of trouble, in his own way, about being religious.

**SIMON:** Oh, that was very brief. But at tea one day, someone flicked the lights because it was time to go up to the colloquium. We had been talking. He couldn't resist talking about the fact that, "You religious guys won't turn a light on Shabbos because you say it creates a fire, and that's absurd, electricity's not fire." Now, the situation is much more complicated than that. The main issue is that you're not supposed to, on Shabbos, strike the final blow. It's the completing a circuit that's a problem because it's completing something, and one's not supposed to complete things. It's a reason why, but it's quite clear from the Torah that it's one of the commandments. I knew he was basically not even saying this because he thought deeply about it. I knew that his father was rather anti-religious, and he just sort of picked it up. I looked at him and said, "Dick, we could argue about this, but we wouldn't agree. Why don't we talk about something else?" He said, "You're right," and we just went off to the colloquium. We never discussed religion again.

**ZIERLER:** At what point did you negotiate the dual appointment in math and physics?

**SIMON:** I don't think I had to negotiate anything. Since I had a dual appointment at Princeton, I think it was assumed that I expected that at Caltech, and it was true.

**ZIERLER:** But at the divisional level, because Caltech is organized in such a unique way, with PMA as the division…

**SIMON:** Correct, so in some sense, the joint appointment just means what my title is. You are usually in some option, but that's not a formal appointment. The only way one distinguishes between a mathematician and a physicist is what your title is. We have professors of mathematics, we have professors of physics, and we sometimes have professors of astrophysics, professors of astrophysics in physics. It was decided that an appropriate title for me was professor of mathematics and theoretical physics, and I was fine with that. Although, if you'd asked my preference, I probably would've said mathematics and physics, but I didn't mind theoretical.

**ZIERLER:** But at Princeton, where it's two separate departments, doesn't that mean twice the committees, two department chairs that you're answering to? Was that streamlined at Caltech at the divisional level?

**SIMON:** It wasn't so complicated at Princeton. You can use the joint appointment to avoid being on too many committees. The one thing that was interesting at Princeton that I had to put my foot down about, the teaching load in math was two and two. Two courses each semester, at least in the old days. It's probably less now. In Princeton, in physics, it was one course in each semester. But most of the physics faculty paid half their salary from grants. Those were the days when grants were much larger in physics. I didn't really know about this, and I assumed I'd have half a load in math and half a load in physics, that is, one course each semester in math and one course one of the two semesters in physics. That was half of what the physics load was. My first year–this may have been when I already had tenure that the issue came up.

Anyhow, I was teaching two courses in physics, and I would say, "That's not really right." Murph Goldberger, who was at the time the chair, came up and said, "Well, in physics, most people pay half their salary from a grant. Your grant is in math, so you don't have money to pay half your salary. You should, therefore, teach a full load in physics because you're not buying off half the teaching." Eventually, he gave in. At Caltech, it was quite different. I taught one course in physics the first year or two. But of course, we have much less faculty in math than physics. There was much more of a teaching problem.

At some point, I started teaching courses in math. I really had no real interaction–the department chairs at Caltech are EOs. I never really had much in the way of interactions with physics EOs. I had a lot of interaction over the years with the division chair because I was the go-to guy for mathematics, even when I was not EO. The idea that you report to a department chair at either Princeton or Caltech is just crazy. I still remember when I became EO at Caltech, and I told some people, "I'm now effectively the chair of the Math Department." "Oh, you're their boss." I said, "No, I'm their servant." The fact that I "reported to two different department chairs" at Princeton–I think there was a decision made at some point that my salary would be negotiated by the math chair, but I'm not quite sure about that. That's the only case where it really matters.

**ZIERLER:** What's the timing of your acceptance of a formal offer to join Caltech? Is it within that sabbatical year?

**SIMON:** Oh, yeah. Absolutely. Because one of the things we wanted to do while we were out here was buy a house. The Fairchild scholars normally had fancy housing that Caltech had specifically for them, although I think I heard recently that were discontinuing that, and that the new Pasadena Chabad house was formerly Fairchild. But we wanted to be where the Jewish religious communities were. There was a religious math post-doc I knew vaguely at Caltech, and he helped find us something in the Pico-Robertson area. It made much more sense to search for a house, although the complication was, the mortgage rates were so high, I had to negotiate the mortgage as part of the offer, even though we wanted to search. We sort of had to do it on a time scale that we'd still have several months left. I don't remember the exact dates, but the offer already probably came in February or early March and was negotiated within a month. Near the end of that year, I visited the Soviet Union, and I actually bought the house when we were in the Soviet Union, in some sense.

**ZIERLER:** Now, the salary bump at Caltech, did that wash out because of real estate in Los Angeles?

**SIMON:** It wasn't a question of real estate in Los Angeles, it was more so the mortgage rate. If I didn't get the special mortgage from Caltech, I couldn't have afforded it. It probably was close to a washout. I probably gained a little bit of money from it because I had the special mortgage rate. Eventually, we paid a much lower rate, and we were able to pay off the mortgage fairly quickly.

**ZIERLER:** What were the circumstances of going to the Soviet Union?

**SIMON:** The Soviet Union was a major center of mathematical physics. There were in particular two absolutely major figures, Dobrushin and Sinai. They were essentially not allowed to the West. If you wanted to see these people, you had to visit. They arranged an Academy visit for me, although without my knowing that there were some incredible politics that went on in the background.

**ZIERLER:** Was one of the sensitivities at the height of the Refusenik movement, that as a religious Jew, you might be going there with a secret tefillin or anything like that?

**SIMON:** No, they were so unaware of such things, that even though I did go with secrets, that didn't worry them at all. Although antisemitism was probably a little bit of a factor. The basic thing that happened is that the 1980 International Congress of Mathematics was in Helsinki that I didn't go to, but they did not let many of the Russians go there, and I signed a protest petition that was objecting to the behavior of the Russian government. Somehow, the timing of this petition managed to embarrass some of the big mathematical muck-a-mucks, and there was a lot of, "What happened? We have to study what happened."

It was a French petition, in fact. I was told there was one guy, I don't remember his name, at the Steklov Institute, where there was a meeting about this, who I was told always had the attitude that if he could get other people in trouble, he wasn't in trouble, so things would look better for him. He didn't care about getting me in trouble, but the translator of Reed-Simon was at Steklov, and he wanted to get the translator in trouble. He got up in a meeting–I only heard this story much later–and said, "The problem is the French petition, but the American mathematician Barry Simon signed it, and some of the people at our institute push his work." While the translator was low enough ranked that he told me, "Eh, we didn't care that much," there was another guy at the Steklov Institute, who was higher ranking but had actually signed off on the recommendation to have Reed-Simon translated.

And he decided it was an attack against him, and that the proper way of handling this was to become my bitterest enemy. While I had this Academy invitation long before, in the middle of the year, it became less clear that I was actually going to be allowed to come to the Soviet Union. There was an attempt to get my visa revoked or my invitation removed. I don't remember the exact details. But they held up my invitation. When I got there, Sinai said to me, "We're really glad to see you. We weren't sure we'd see you." I did give a talk to the Moscow Math Society, but part of the deal was I could only go in a side door. Incredibly petty but typical Soviet politics, unfortunately.

The people who owned this house before us were really nice, but there was a friend of the woman next door who was a real estate agent. In any event, she made some arrangement that she bought the house from them, but on the condition that she could resell it within a certain period. She was the person I had to negotiate with, and she was almost impossible. Fortunately, my lawyer was my uncle, who was really very good and lived out here. I don't remember all the details, but we were leaving for Moscow on Sunday, and essentially, even though I'm not sure the woman knew this, she was tough as nails, and my uncle said, "You've got to just say no." We said no. An hour later, she phoned my uncle and wanted to reopen negotiations. An hour before Shabbos, he said to me, "It probably won't get settled until you're out of the country." But we'd arranged that my father-in-law, who'd also lived near, had power of attorney. "We'll take care of it." The papers were signed while we were in the Soviet Union.

**ZIERLER:** What were you working on with Avron during these years? You published so much with him. What were some of the big projects?

**SIMON:** In Princeton, the biggest project was with a third guy who was a post-doc at the time named Ira Herbst, who spent most of his career at Virginia. We wrote four papers, plus some announcements on quantum mechanics in magnetic fields. Still, it's one of my most heavily cited works, on removing center of mass in magnetic field, which turns out, because of constant magnetic fields, you could think, "Oh, translation invariance." But because of gauge phenomena, it's a very different mathematical structure when there isn't a magnetic field. Basically, the translations only commute up to a phase. It's a complicated situation to describe, but that's one of the papers, and we also did some work on atoms in large field. It was a nice set of papers.

As I mentioned last time, when we came to Caltech, we started working on this almost periodic stuff. I have this paper on the rings of Saturn, which was wrong. But in late 1983, he found this paper of Thouless. Yossi had always had a fascination with the quantum Hall effect. He told me about that in the first place. And he'd found this paper of Thouless that led to this work on topological methods. Dick had a little bit of a role in that, too, in the following sense. Several months before the paper of Thouless, Yossi and I were talking about something, and Dick bursts into my office. "Tell me all about the homotopy groups of spheres." This is something that had become fashionable in high-energy physics at the time.

He was puzzled, as most people are, about why the higher homotopic groups are nontrivial, even though the higher homology groups are trivial. This is something I'd had a course when I was a senior at Harvard in algebraic topology, and I'd always been struck by this and understood. I recalled from my memory, it was certainly not at the top of my head, and I gave him this mini-lecture on Hopf fibration, the exact sequence of a fibration, and how you could use it to commute homotopy groups. When I was done, Yosi looked at me and said, "Barry, I didn't know you knew anything about that."

Before I could answer, Dick, with his huge Dick grin on my face, swept his arm across my bookcase, and said, "What do you mean? He's a professor. Of course, he knows it." The point is that I probably would have remembered the necessary topology, but it was exactly the material that Dick had forced me to remember that was critical when we started working on the Thouless work that led to this paper we wrote. Without mentioning the name, it pointed out that these integers they'd discovered were topological invariants, what are known as Chern classes. One of my friends told me, "Oh, what you are talking about are, Chern classes?" I started using that in a later paper.

**ZIERLER:** Tell me about the conference in Birmingham, Alabama in 1983.

**SIMON:** Well, there was a whole series. Birmingham had a couple of really energetic people who tried to put them on the map. For a period of about three or four years, they had annual conferences. The only thing I think that's notable about that is this famous picture that has all sorts of mathematical physicists. That's what I remember about it.

**ZIERLER:** It's noted on your webpage as being a historic event.

**SIMON:** Oh, only historic because it had all these people. What's really historic is the picture. I put it on the webpage because it has this fantastic picture of all these people. Elliott Lieb, me, Jürg Fröhlich, looking much younger than we are now, Peter Lax, Cathleen Morawetz, Shmuel Agmon, Tosio Kato. It has all the big names in things that are connected with PDEs as applied to quantum mechanics. It really is a rather historic picture. If I said it was an historic conference, I really meant it was an historic picture.

**ZIERLER:** What kind of work actually gets done at those kinds of conferences?

**SIMON:** Depends on the conference. To first approximation, the most important thing about conferences is you learn about what other people are doing. For me, and I think for many other people, it's much easier to understand what someone's done if they get up and give a talk on it than if they write a paper. The paper, particularly for some authors–I always use the rule of thumb that even if you write a paper, certainly if you're going to write a book, you tell them what you're going to tell them, you tell them, and you tell them what you told them. But most people don't write papers that way. It's very dry, they don't explain–they just do it because they know they're going to prove a big theorem.

They don't have to tell you why it's an important theorem. It's true that if you do that, your paper's more likely to get accepted. But when you give a talk, they're not going to be able to give you all the details, so they have to explain why it's important. It's much easier to understand what someone's done. You go to the talks because there are the talks, so you hear about something that you might not have thought to read the paper. These conferences are most important for the ability to learn what other people are doing. But you also will sometimes meet new people, you will start collaboration. There was one cute little paper, not a major one, that Brian Davies and I wrote because I had written a paper on something, and this was in Gregynog, which is out in the wilds of Wales somewhere.

We went for a walk after dinner one day, and by the time the walk was done, we'd essentially figured out the details of a paper. That's also true. You sometimes will have interaction with people that you might not have. Sometimes, by talking with people, you can make real progress in a short period. Sometimes, there are even more remarkable things that happen at conference centers. There are some places that have multiple conferences. Going forward much further in the future than what we've been talking about, this was probably 2015 or '16. But around 2000, one of my then-post-docs, Rowan Killip, who'd been my graduate student–he may be the only case where I had a graduate student who was also my post-doc. He was really very good.

Anyhow, we did this paper that wound up in the Annals about sum rules–it's actually one of my better papers in the last 25 years. There are some elements of what we did that seemed rather ad hoc to us at the time and mysterious, but they worked. In 2015, I learned that some French probabilists had found a different way of understanding this using large deviations, whatever that was. But it's a method from probability theory. It was very hard, the way the paper was written, to understand what they'd really done. I started discussing it with Jonathan Breuer. Avron had a student named Yoram Last, who was an assistant professor, and he had a student named Jonathan Breuer, who was my post-doc, so I had three generations who were my post-docs.

I was visiting Hebrew University, Jonathan and I started talking about this, and we couldn't understand what any of this was. Jonathan went off to a meeting in Cambridge on, I think, periodic Schrödinger operators. But they happened to have, at the same time, two mini-conferences, one on periodic Schrödinger operators and one on probabilistic methods in geometry. One of the people there was Ofer Zeitouni, who spends half his year at the Weizmann Institute. Where else did two Israeli mathematicians meet but at Cambridge? Jonathan took Ofer aside and said, "Can you explain this paper to me?" Ofer looked at it and said, "Oh, I looked at that paper. It seems rather trivial."

He started to explain what they'd done to Jonathan. Jonathan came back and reported this to me. I said, "He doesn't understand what they've done." I convinced Ofer to come to Jerusalem, and I explained to him–it is partly true that in one sense, the paper is trivial, in the sense that they actually computed two different objects or did two different computations, each of which was in the probabilistic literature on random matrices. But they realized it was the same object, so they got this equality that Killip and I had proven by this much less natural method. I explained to Ofer, and he understood. I don't know how much Jonathan had to do with Ofer. I'd probably met him a couple of times.

But we, then, started working on this approach. And this all came out of the fact that Jonathan and Ofer were at the same conference center. You have interactions. It really allows the kinds of interactions that you can't do on Zoom. It's why I suspect conferences will still continue, even though it's much cheaper to use Zoom than to fly everyone to a conference center.

**ZIERLER:** That same year in 1983, you wrote a paper on instantons. Was that a one-off problem, or was that related to other things you were working on?

**SIMON:** The instanton part was one-off, but it was part of a bigger project that actually–the first paper in that series I always referred to as Ed Witten's homework assignment. Ed wrote this absolutely wonderful paper in which he found a very elegant and simple proof of the Morse inequalities using supersymmetry. It really is a magnificent paper. This was about ten years before Caltech made its offer to Ed. I came back, went to Robbie Vogt, and said, "This is an absolutely fantastic paper. We should hire him as a mathematician, even if the physicists don't want him." But it really was a wonderful paper. Ed knows what a proof is, and he needed a certain result that's incredibly reasonable about strong coupling perturbation theory. Well, it's actually quasi classical.

It's strong coupling, but that's the same as small h bar. He assumed something had to be true, and he knew that Reed-Simon had a proof of a related result in one dimension, but he needed it in not only higher dimensions, but on manifolds. He says, "Well, this is a result. I'm not sure it exists anywhere in the mathematical literature, but you can probably use the ideas in Reed-Simon to prove this." I knew enough to know that the ideas in Reed-Simon were one-dimensional, would not work, and so proving the theorem that Witten wanted to use was a true mathematical theorem I always called Witten's homework assignment.

I didn't publicly call it that, but that's what I thought of it as. The first paper in this series was this quasi-classical limit Witten wanted for this case. I, then, realized that a more subtle and interesting question was what happened with eigenvalue splitting. I realized that what I'd computed, which was a very pretty use of path integral techniques, what popped out was something called the Agmon metric. It was really a very pretty piece of work. I remembered I was doing this a summer I was in Israel, and David Gross's then-wife's aunt was the next-door neighbor of my wife's cousin, so I ran into David there, and I hadn't seen him for a while.

And he asked me what I'd been working on. I think he was probably the guy who said, "Oh, that's just an instanton." I probably didn't even know it was an instanton, but I'd discovered this way of looking at instantons, where you could actually prove something. And there are still interesting questions in this.

**ZIERLER:** On the service side, when did you chair the Physics Theory Hiring Committee at Caltech? Is that right after you joined proper?

**SIMON:** It probably wasn't the first year, was probably the second year. But as I told you, there was this feeling, perhaps not unjustified, that Caltech had a crisis in theory. "What happens after Feynman and Gell-Mann?" Astronomy and astrophysics have always been incredibly strong and was incredibly strong, theoretical astrophysics was incredibly strong then, and nobody thought that was a problem. And it really wasn't. But no theorists at all in squalid-state physics and high-energy had issues. The first year, Robbie Vogt and I talked a lot, and I think he decided he could trust me on various things, so he appointed me the chair of the Theoretical Physics Appointments Committee with a hunting license.

Normally, you get one or two. Two is a little unusual, but that's at most. I think we made four offers at once that year, two in particle theory and two in solid state and condensed matter. One of the condensed-matter theorists was Daniel Fisher, the other one Mike Cross. Daniel unfortunately said no, Mike came. The two on the high-energy side were Mark Wise, who's a phenomenologist, and the other was John Preskill. I must say, 15 years later, I thought the one huge success of that group of that hiring was Mark Wise. John was doing interesting things but was not really a major figure in high-energy physics.

He was smart enough to realize that that was true, and he should probably think about something else. Essentially, he became a pioneer in quantum computing, quantum information theory. That also was a tremendous success, although I'm not sure people quite viewed it that way until he did that shift. Not that he wasn't doing good work, but it wasn't as great as the work in quantum computing.

**ZIERLER:** To what extent did the wattage or star power of a person like Feynman dampen prospects for hiring a major person earlier, prior to your tenure at Caltech?

**SIMON:** I'm not sure that that was the problem. I could be wrong. You're asking me why David Gross didn't come to Caltech. On the other hand, I don't think Caltech made an offer to David Gross. I think people described it well. Dick wasn't involved at all, and Murray not only had this rather narrow view of what was important, but actually thought the people who did things fairly close to what he had done were the important figures. In fact, the appointments that were made in that era were just not as strong as some of the other people who were available. Now, I was not around then, so I don't know if we made offers to the really important people. Wilczek, Gross, Weinberg. I just have no idea. But I think it really was that Murray, in some sense, had good taste in the areas of physics he worked on, but he might not have had such good taste in the people who went after. With John Schwarz being the exception.

**ZIERLER:** In this position, being charged with hiring for theory, did you feel like you had a mandate to modernize the physics program?

**SIMON:** No. One of the other big things in which Caltech is different from many places, it's not that we'll never go after established people, but there's a big preference to go after young people who you hope will be major figures. I felt my committee was supposed to locate what seemed to be the most promising young people in these areas. Now, my memory is that Fisher and Cross were slightly further along, and we had to offer them tenure, but it was probably their first tenure offers. They may have gotten from other people. I know Fisher did. But Preskill and Wise were assistant professor offers, and that's very much the Caltech way. At Princeton, it isn't that we didn't hire assistant professors, but it wasn't a big deal. We hired lots of assistant professors, and some of them were spectacular, but at Caltech, you feel you have a weak area, you look for the best young people, and they sometimes do well. We did this in mathematics when we had a crisis in 2000. We hired, like, six people in a two-year period. Which, given that mathematics has typically 17 non-post-doctoral faculty, we'd lost a lot of people due to retirements and death and made six really strong appointments.

**ZIERLER:** In all of these hiring decisions, what did you learn about Caltech when it was going after an up-and-coming star who probably also had offers from Stanford, Harvard, MIT, Princeton? Where did Caltech win out, and where did it come up short?

**SIMON:** You have to realize that the recruiting is almost entirely done by the division chair. Although, of course, the division chair would sometimes consult me. I don't really know what was effective and what wasn't, except by stories I hear. But the hiring committees at Caltech involve figuring out who we want to hire, but the actual negotiating is never done by EOs, it's done by division chairs with usually little direct input. Not that there isn't some consultation. But it's really the division chair, so I'm the wrong person to ask. Often, it's a two-body problem. For example, these six people I mentioned, I don't think that they had offers from maybe one or two other places. We, for example, tried to hire Mirzakhani at the point when she had six offers at once, all tenure, her first tenure offer. That's the kind of offer you're talking about. There, the biggest issue was a two-body problem. But many of the things I'm talking about, these six junior hires in 2000 with Preskill and Wise, we weren't competing. We identified people relatively early. Once they were here, many of them liked it a lot until they would get stolen away. Those six people, five or ten years later, were all gone.

**ZIERLER:** Who succeeded Robbie Vogt as division chair in 1983?

**SIMON:** Ed Stone.

**ZIERLER:** This is your first look at the transition from one division chair to another. Given the unique role and power of the division chair, what did you learn from that transition? How would you compare Ed Stone's style to Robbie's?

**SIMON:** Robbie has a very forceful personality. Ed is very laid back.

**ZIERLER:** Gentle.

**SIMON:** And gentle. It was also somewhat problematic in that Ed and Robbie had come from the same research group, but Robbie decided he was division chair, and he had to be division chair full-time. Ed Stone decided he had a research program. He was a half-time division chair. You would see that in some ways, and he was not as aggressive in terms of dealing with problems. I know that I shocked him at one point because he decided to fire Luxemberg from being EO, I think it had to do with staying in the budget, and he just assumed I would take the job. I told him, "I'm 40 years old. I'm too young to die. I'm not going to do it." He was shocked. He went to David Wales next. He was the first EO in the post-Luxemberg era.

I really think that during my time here, not looking at the present division chair who still has part of her term left, Robbie and Tom Tombrello stand out as the two most outstanding division chairs by far. And it's partly their personalities. They fit the mold. I was on every division chair search from certainly the time after Ed through when I was about to retire, probably not the current division chair. One of the things you do on the Division Chair Search Committee, you have a preliminary meeting where you try to decide what you think is important in a division chair. We decided we wanted a division chair that every morning, the provost woke up and said, "Oh my God, I have to face So-And-So."

**ZIERLER:** How well did that serve Caltech when Robbie became provost?

**SIMON:** Of course, the person Robbie would deal with was Ed Stone, who he'd been working with all the years. No matter who the provost is, nobody was going to be frightened of Ed Stone. But Robbie and Tom were certainly people–in fact, both of them had lousy relations with the provost, which I think can be successful, but we also probably lost things because the provost decided, "That SOB, I'm not going to give in." It's a toss-up. Given that the job of the division chair is to get resources from the central administration–but it's also their personalities. They were very aggressive in solving problems in a way that the people in between them were not.

**ZIERLER:** I'm curious if you were paying attention when Feynman really became a national figure after the Challenger disaster.

**SIMON:** I was paying attention in that I noticed it. I actually had some interaction with Jim Gleick. There's a famous book about Feynman called, I think, *Genius*. Gleick was the science writer for the New York Times. He wrote a book about Feynman that really, I think, helped him become this national figure after–no, Gleick was after Feynman passed away, now that I think about it. He wrote it after, but it added to the Feynman aura. I had an interaction with Gleick totally independent of this. We talked about Dick some.

**ZIERLER:** When did you start collaborating with Werner Kirsch?

**SIMON:** Late 80s. He came, I think, with his own money and was a visitor. He never was a post-doc. But I would not list him among my most significant collaborators, actually.

### The Import of Schrödinger Operators

**ZIERLER:** But you were working on Schrödinger operators generally around this time?

**SIMON:** I would say that from the time I came to Caltech until I shifted a little bit into problems connected with orthogonal polynomials, which are not so different, I would say the focus of my research during 20 years was, in fact, Schrödinger operators. I'd had an occasional paper on statistical mechanics, but it was almost all things connected with Schrödinger operators, but there are many different aspects of Schrödinger operators.

**ZIERLER:** During the mid-80s, what were those aspects you were focusing on/

**SIMON:** The main focus from the time when Avron and I were visiting Caltech until probably about 1990 was this almost periodic, and to a lesser extent, random Schrödinger operators, which are two not-unrelated areas, and one of the fascination is the ways in which they're different. But it really, as a sort of formal area, almost didn't exist until Avron and I started working on it because some other people were beginning to work on it. I wrote a paper that had been widely read and is called *The Almost Periodic Flu Paper* because it was a review article, and it began by saying, "In some years, the Hong Kong Flu sweeps the globe. This year, it was the almost periodic flu."

Because there was a sudden explosion of a dozen people working on it, but it gave birth to a subject which stuck around and had lots of fascinating problems and was sort of a major focus until about 1990. There were still lots of problems. It isn't that I slowed down, but I really needed a new direction. It took about a year to find it. Particularly, given that that was the point when I started also doing some writing for PC Magazine, I'd heard there were rumors that, "Simon's slowing down. He's reached old age." And then, I had this new burst around 1990.

**ZIERLER:** I want to get to that, but before that chronologically, when Ed Witten started to get really excited about string theory in '85 and '86, wanted tons of people to work on it and, "We'll have this whole thing solved," did you not buy the hype immediately? Were you intrigued just because of who Witten was already at that point?

**SIMON:** No, I've never bought the hype. I still appreciate this idea that string theory is the only candidate we have that stands a chance of getting to a theory of quantum gravity, but I never bought the hype. In fact, I gave some talks on this Witten proof of the Morse inequality, and one of the lines in my talk, I heard at some point, got back to Witten, who was quite annoyed by this. But in the talk–and this was before string theory, this was actually supersymmetry, which I was already a little skeptical about as a piece of physics–I said, "In 50 years, it may be that physicists have totally forgotten about supersymmetry, but it will be well-known people will remember there was this supersymmetric proof of the Morse inequalities by Ed Witten. And that's what supersymmetry will be known for 50 years from now."

But I never bought the hype that much. While the problems that string theorists study have real mathematical content, there's no question about that, it's a very different kind not only mathematics, but connection of mathematics to physics to anything I've ever worked on. Everything I've worked on involved some area of physics, where the underlying physical framework is understood and accepted. There are questions about to what extent you can make mathematical sense out of them. Quantum field theory's a little different in the sense that, while it was, from a perturbation theoretic level, it sort of made sense, really, the whole point of axiomatic and then constructive field theory was constructing something that didn't exist before.

But most of what I've done has involved well-established parts of physics, not areas of physics–I know that if I do something, it's going to be a part of mathematical physics. It's not going to be a piece of physics that ten years later, people say, "Well, they were wrong, it's totally irrelevant," because I'm working on something that's a well-established part of physics. String theory is very different from that. It's amazing, it's 35 years since the first string theory revolution, and it's still not clear it has anything to do with nature.

**ZIERLER:** You mentioned supersymmetry. Were you interested at all around the excitement that if the SSC was built, supersymmetry would be observed?

**SIMON:** I was aware it was there, and I was therefore paying attention. But it was not an area that I'd ever worked. Again, I used supersymmetric ideas, but not in the context of physics. I had nothing vested in whether there are supersymmetric partners of particles. I certainly know there were people who said, "Oh, it's going to be found, and there were suddenly going to be Nobel Prizes for Schwarz and Witten." I was aware that people were therefore very interested.

**ZIERLER:** Which gets to sort of a broader question about, for you and your research, the relationship between theory and experiment. Where, if ever, have there been experiments or observations that have borne out theory that's been relevant, either for specifically what you're working on or your general approach to the kinds of things you're thinking about?

**SIMON:** At the time I do the work, never, in some sense, although I have done some things that turn out to be connected later with experimental issues. It's not quite true, the quantum Hall effect, of course, was originally an experiment that people found needed a theoretical explanation. The things I did connected with quantum Hall were certainly, a few years before, motivated by experiment. But that's a sort of weak connection, although the topological ideas I introduced have become very important in both theory but also experimental condensed-matter physics since then. I'm aware very vaguely, but I've never looked seriously at the experiments.

**ZIERLER:** As an introduction to the *PC* *Magazine* work, this notion that you're slowing down, your publication list certainly does not suggest that by the late 1980s.

**SIMON:** If you look, there are fewer papers in '89 and '90 than in the early 80s or late 70s. It looks like I'm not slowing down because it's still more papers than most people write in a year, but it's less than previously.

**ZIERLER:** So slowing down relative to yourself, not relative to your peers.

**SIMON:** Yeah, it's relative to me, but it's not only that there are fewer papers, there are many fewer exciting papers. It's not that they're bad papers, but they're not big deals. I'd have to look at the exact years, but there was a period of a few years that I was conscious that I really needed to find something new.

**ZIERLER:** Was this at all related to when you got your secretary in 1990, that you needed more bandwidth to work on research?

**SIMON:** No, I didn't get the secretary in 1990. I got a new secretary probably around '88. It wasn't connected with that. One of the other things I negotiated when I came to Caltech that was critical–at most places, it's very unusual for a mathematician to have a personal secretary or part of a personal secretary. It's much more usual in other areas of science, probably because they're often paid from grant money, and there's much more grant money in areas of science other than mathematics.

But at Princeton, one of the things I did was, of course, I had a joint appointment. People in physics tended to have half a secretary. They'd share it with usually another faculty member. I didn't say, "Oh, I should get a quarter of a secretary because I'm half in physics." I assumed I'd get half a secretary, which I did and used very heavily. And I knew that I would have trouble working without a secretary. One of the other things I negotiated when I came to Caltech was that I would have a secretary. In fact, I wound up with a full-time secretary. This is the kind of thing you get, but then there are budget problems 20 years later. Caltech honored that commitment to me except, perhaps for the last few years, when my secretary passed away, and I was close to retirement.

It was decided I wouldn't get a new secretary, although I'd never learned TeX, my secretary was so good. I did have someone to help. But I had a secretary from the start when I came to Caltech. The thing that happened in '88 is, I got a new secretary, so I had a secretary for a few years that was not very good, maybe even been fired. Then, I had a secretary in the late 80s, and I'll tell you a story about her and the next secretary. The way I described it is, she was a bright woman, but she checked her brains at the door. She was smart, but she just did the job, didn't really think things through. She actually decided to leave because I think she decided to go off to graduate school, so we did a new search. The person who was the top of my list in that search fortunately said no. She was actually the wife of a graduate student, and she presumably would've left, and she took a different secretarial job at Caltech.

My second choice was someone named Cherie Galvez, who was originally from the Philippines. In fact, her father Aquino's press secretary. Her mother was some kind of professor of English. She had secretarial skills, and she and her husband, who I think was also Filipino, had moved to Singapore. He's an architect. He got some offer from a Los Angeles firm, so they moved to California. She had no professional experience in the academic world. She'd worked in a corporation. She was, in fact, responsible for putting out some Singaporean corporation's annual report and other such things. She didn't really have much experience, so that's why she wasn't top of the list, but I figured I'd take a chance.

This is still one of my favorite stories when I realized what a gem I had. Second week on the job. I had written a paper. The preprint had been written, and in those days, it had to be re-typeset by the typesetters, it went through a refereeing process, and I got the galley proofs to look over. By the time I got to them, it was late in the day, so I went through the paper, but I reached the references, and you know what could be wrong with the references. I wrote a little note, told Cherie, "I'm going to be in late morning tomorrow, but please mail this manuscript back to the journal." I come in, and she's clearly very nervous. She says to me, "I know you told me to mail this in, but I'm not sure there's something right here." One of the references in the thing says, "J. Hannay, CALL JAN SEGERT TO GET THIS REFERENCE."

This is a direction I had given to the previous secretary, which she had just typed instead of calling Jan Segert. It wound up in the preprint. No one commented on it in the preprint. It wound up getting re-typeset. The referee didn't notice it. Some of my friends said, "It would've been really funny if it appeared in print." But one of the things I learned is that nothing would go out of that office that Cherie Galvez hadn't gone through with a fine-toothed comb.

**ZIERLER:** You got an editor and a secretary.

**SIMON:** Oh, boy, I got an editor. I can tell you, galley proofs come back, you look quickly. Cherie would go through the original manuscript and the actual paper line-by-line. One of the thing she had to do when she was doing these annual reports was compare it to the original. She was used to going through line-by-line. A couple years after she got there, I had a book that I worked on for many years. This was, again, before TeX. But the publisher was experimenting, and it was retyped in something called nroff-troff. Just from counting up errors on a couple of pages–it was, like, a 400-page book–I think the version we got had at least 10,000 errors. It was painful. But Cherie went through and pointed out all the differences between the typescript that went in and what came out.

Cherie, by the way, you ask anybody else who's had any interaction with me, any of my post-docs, she's famous. You deal with various levels of the bureaucracy. Any time there was any problem, she was on a friendly basis, she made a point of talking up anybody. If I had any problem, she just dealt with it. She was just amazing. When I was department chair, some people probably knew this, she was essentially my spy in the sense that everyone trusted her. If they had any problem, they'd come and talk to her. And she'd tell me, "Oh, there's this problem here."

**ZIERLER:** Everybody should be so lucky to have a secretary like that.

**SIMON:** Oh, yeah.

**ZIERLER:** Was your Guggenheim Fellowship a sabbatical year in '88, '89? Did you travel for that?

**SIMON:** I certainly did not travel. You have to remember that by then, I had five kids in various levels of school. Taking them out of school was difficult. I'm guessing that I used that–Caltech typically either gives you half a year at full pay or a whole year at half pay. Assuming that wherever you're going will pay the other half. I presumably used the Guggenheim so I could stay in Pasadena. I presumably did some more travel since I wasn't teaching that year. But I traveled every summer. Eventually, it became a bit much for my family, so we cut back. But I do not think I was away on leave until 2005 from when I came to Caltech.

### PC Magazine

**ZIERLER:** How did you get involved with the PC Magazine work? What was the origin to that story?

**SIMON:** It's actually complicated. You can ask first how I got involved in computers. My first contact with computers was very early on, when IBM first introduced the PC. They gave a fair number of PCs to Caltech for faculty, and they also had one person who had worked there for many years. I suspect someone wanted to get rid of him. But he was an expert on APL. He actually had an office in mathematics, and he was supposed to help us learn the computer. But he was only interested in APL. I had no idea what computers could do. Of course, that's how he set it up. Booted into APL. All I used it for was APL.

My secretary at the time was using a computer for some amount of technical typing, and somebody had come in to give her tech support, and I saw what looked like a really strange thing on the machine that I now think was just a directory listing. But I really had no idea how computers worked. I visited Georgia Tech, and there was a guy there named Michael Barnsley who was very interested in iterated function systems, eventually formed a software company. But he was showing me various things. He was using Basic, but I could see he was doing lots of other things. I said, "How do you get to that screen that isn't in Basic?" He said, "Oh, you type SYSTEM." The first thing I did when I got back, I tried to type SYSTEM into APL, it didn't work.

I did a little bit of looking in the manual, and I found out how you could exit APL, and I was off to the races. I learned a lot about how to use computers. One of my colleagues, a famous combinatorialist named Rick Wilson, among his other talents, was one of the world's greatest 8088 assembly language programmers. He could look at an assembly language program and say, "I don't understand why he did it that way. He could've saved three cycles if he did it this other way." He was just fantastic. We talked a lot. He invented a program that would get into the guts of the PC to allow various things, control and alt and a letter key. He learned about the underlying thing to make–I got a little involved in this. I designed a program that he programmed called Stackey (because it stacks keystrokes).

We started a small shareware company. Through CompuServe, I got involved with some of the other people in the shareware world. In fact, at some point, I was the first President of the Association of Shareware Professionals. There was some reason why people were thinking I was washed up. I was spending a fair amount of time on computer work. Anyhow, there was some shareware-related issue, problems with resident programs. I was going to be in New York to visit the Courant Institute. It was decided I should go to PC Magazine and try to get them to support this. I talked to the editor-in-chief, didn't get very far, but it was suggested I come back the next day. After I did that, one of the sub-editors said, "Oh, I hear you know something about mathematics. We got this program called Mathcad. Could you do us a review?"

I said, "Oh, that sounds interesting." I'd actually written a few reviews for a shareware magazine. I became very quickly a reviewer for PC Magazine. I was their standard reviewer of math software. But I did other things. I wrote some of the first articles on their Windows Registry. At that point, by the mid-90s, I was writing some computer books, my agent said she'd been approached, would I be interested in writing a book on the Registry? I said, "There's no book there. No way." Of course, the first book on the Registry sold a million copies. That shows what I knew. Not by me, obviously. But I was doing technical things for PC Magazine. I was doing quite a bit.

For five years, I probably spent a week–I had some postdoc take my classes–in Las Vegas, Nevada. You know why? COMDEX. For COMDEX, I was busy from 6 in the morning until 11 at night because it wasn't just when the show floor was open. As a member of the press–PC Magazine was, of course, the big press vehicle–I had breakfast with press reps from companies, there were parties for us in the evening. It was incredibly busy. The industry was an amazing thing to see in those days until it slowed down. The last COMDEX was probably 2000, 2002. Maybe not the last, but sort of a phase transition where it went from 150,000 attendees to 20,000. There was this big change. It happened in math software, too. The software matured. I made a real contribution when I was writing software reviews. I certainly changed Maple for the better.

**ZIERLER:** Did you see this as serious scholarly work? Was it public outreach?

**SIMON:** It was in no way, shape, or form scholarly in the usual sense. Although, at some point, Rick Wilson and I either decided or were asked–we did write an article for The Notices on math software, and we actually invented a series of benchmarks. This was "scholarly" to the extent that it was with The Notices. But I thought it was a hobby that was just fun, and the world was fascinating. It was clear that computers were changing the world, and I could have a real impact on it. Now, this was something that probably impacted my output a little, but not that much. By the time I was writing the books, I was back in the research saddle.

**ZIERLER:** To flip the question around, was your work on software relevant at all for your research? Was it helpful?

**SIMON:** No. The only serious scientific computing I ever did was this anharmonic oscillator when I was a graduate student. I've never used software in my research, although it's true that when I was writing these analysis books, I had a student that did some of the figures for me in Mathematica, and part of his thesis was doing calculations. I suggested some calculations the student do on locating zeroes of orthogonal polynomials that led to a whole series of papers that were based on mathematical experiments done on the computer that suggested what might be going on, so there was another piece of scientific computing that used mathematical software, but I was not the person using the software.

**ZIERLER:** Did you ever interact with Stephen Wolfram?

**SIMON:** A little. I certainly interacted with him when I was reviewing *Mathematica*. We interacted a little bit when he was at Caltech. Not that much. And then, my main interaction with him was when I was the mathematical reviewer. We had some strong words occasionally because I was not always positive about–one of my big things was that the user interface mattered. The interface that had been traditionally used in the mainframe terminal days by Maxima was eventually replaced by both Mathematica and Maple. Maple, I definitely had an impact on. Mathematica, too, at some point, had a big change. But in the case of Maple, they came out with this first Windows version, and it looked mathematically powerful, but the interface was just impossible. This was in the DOS days. If you had an output that took more than a screen, it just scrolled off the screen.

There was no way of seeing what it was. It was just a terrible interface. I described this to my editor at PC Magazine, and he said, "There's no point in writing a review that reads, 'This program has some nice features, but my recommendation is, don't ever use it,'" which would've been more or less reading between the lines because the review would've said it was such a terrible interface. He said, "We're not going to review it." I called up the people at Maple who sent me this copy and said, "My editor says we can't review it." They yelled and screamed. Two weeks later, I get a totally revamped interface. They paid attention. Since then, they've been very good about interfaces.

**ZIERLER:** Between serving as Vice President of the AMS and being on their editorial boards committee, the late 80s, early 90s, what did the service work do for you in terms of having a bird's eye view of mathematics across the board? What was happening at that point?

**SIMON:** Vice President really doesn't mean much. You're essentially just a council member. You don't have much more. And I'd already been on the council. You get a certain view of really mathematical politics more than real mathematics. But it was very interesting. Not a high point of my service to the community. It's important these things get done, but the council members were more political.

**ZIERLER:** Where was Avron by the 1990s? Was he still at Caltech?

**SIMON:** No. He left Caltech probably in '84, '85 to become an assistant professor at the Technion. He did come back for a year or two in the late 80s on some kind of sabbatical, and then he went back to the Technion. We worked together more when I visited the Technion for several summers. He's been at the Technion ever since. He officially, I think, retired and then was brought out of retirement to become the "czar for quantum." Part of the impact of quantum computing is people now talk about the area of quantum. He oversees all the quantum research, which doesn't include what I do, which is quantum mechanics. Of course, he got very interested in quantum computing himself before he retired, and he's very friendly with the Technion president, so he was appointed to run this. He was President of the Israeli Physical Society. He's had a very distinguished career. Interestingly enough, as he points out, he went in the opposite direction of me. He was born in a religious family. But he calls me his rebbe.

**ZIERLER:** Was he off the *derech* [Hebrew; "the path" of being religiously observant] by the time you got to know him?

**SIMON:** Yes, absolutely.

**ZIERLER:** Did you do *kiruv* [Hebrew; bringing one back to observant Judaism] on him? Did you try to get him back on?

**SIMON:** No.

**ZIERLER:** You cited your work on orthogonal polynomials as the next big project after the Schrödinger operators. But you don't really start publishing on this until the 2000s.

**SIMON:** Yes, and no. One of the things I was sort of aware of is, if you take a one-dimensional Schrödinger operator, and you discretize space to get a lattice, the Schrödinger operator becomes a certain kind of matrix. It's basically a tri-diagonal matrix with the potential along the diagonal and ones off diagonal. If instead of putting ones off the diagonal, you put more general–also, the diagonal has N-dependent thing, which is the potential at the site N, you allow the hopping term to also be N-dependent. You have bs on diagonal, a_n's off diagonal, and you get what's called a Jacobi matrix. Jacobi matrices are in one-to-one correspondence with measures, and the corresponding eigenfunctions are the orthogonal polynomials. The theory of orthogonal polynomials is intimately connected with this generalization of discrete Schrödinger operators.

And I sort of knew this already in the mid-1980s. One of the people I met, who's a big expert on orthogonal polynomials still to this day, Mourad Ismail, who was in Arizona at the time where I visited, told me, "You really should look into this work on orthogonal polynomials." To my chagrin, I never really looked very hard. I knew there was some connection, and I did occasionally look at this more general class of operators. In particular, I learned enough about the subject that I knew it had a different approach to inverse scattering, the inverse problem, and that led to my looking for an analog in the continuum case. I did some interesting work on inverse problems that is connected.

There are two ways of doing it for orthogonal polynomials. The analog of one of them had been found by Gelfand and Levitan, and I decided, "I should really figure out what the other analog is." This is this problem I mentioned in the first talk that I came back to on and off for ten years. There were people I knew who did it, but I didn't really pay attention to the literature. In the mid-90s, I shifted into various things about spectral theory. I was involved in what's called the singular continuous revolution, and that led to some natural questions. I had some very good graduate students. In particular, Killip did look at some of these orthogonal polynomial results. In particular, there was a conjecture of Nevai that seemed to be connected with the spectral theory problems.

It quickly became clear that I should pay more attention to the literature on orthogonal polynomials, which I thought at the time just meant orthogonal polynomials on the real line. This was about 1999 or 2000. It really is something that I'd sort of been on the periphery of for 15 or 20 years but hadn't really thought about it. Then, I had a conjecture in spectral theory of Jacobi matrices or Schrödinger operators that sort of mixed–it doesn't matter what the exact conjecture is. I got a preprint from someone named Denisov, who was finishing up his PhD, I think in Moscow, but he claimed to solve the problem. I couldn't understand it at all, but it clearly had some good ideas. It was clearly connected with work in orthogonal polynomials involving Szego's theorem.

But it was clearly a very impressive piece of work, and Nick Makarov at Caltech was also interested, so we agreed to push for a post-doc for him. He came to Caltech, and his first semester, he gave a course on a continuum analog of not orthogonal polynomials on the real line but orthogonal polynomials of a unit circle, which are called Krein systems. But the first three weeks, he talked as background about orthogonal polynomials on the unit circle, which is an analog of what happens on a real line, but there were many new subtleties. I actually stopped going to his course because I got so involved in trying to understand this work on orthogonal polynomials on the unit circle and what the whole subject is.

I quickly realized that there was a real playground available for me there because many people in the orthogonal polynomial community didn't realize really much of what they were doing was really the spectral theory of the operators that naturally come up in the study of orthogonal polynomials. One of the operators is just the Jacobi matrix, and on the unit circle, it's a different unitary operator that comes up again in a special matrix. I realized that there were all these results that had been proven for the discrete Schrödinger operators that could be carried over to this orthogonal polynomial on the unit circle framework. My initial idea was, rather than write lots of little articles, 50 short articles on 50 types of results, I should aim for a long article, about 150 pages.

But then, it became clear as I was beginning to think about writing this that actually, there really wasn't a decent exposition of the basics, and I found new proofs of various things, so probably, I'd need 250 pages, which eventually turned into two books, where the total, I think, is 1,500 pages. Almost all of it is new. It's really research, it's not a review article. That's too strong, there's exposition of things we already know. It meant that there were natural questions that had been studied by these OPUC people, these orthogonal polynomial people, but using very different methods. Some of their methods were very useful.

They had some potential theoretic ideas that were very useful in the study of Schrödinger operators, so I wrote an interesting article about those sorts of ideas that has become a standard reference. It's not so different from the discrete Schrödinger operator work, and many of the people who do the discrete Schrödinger operators will now also do OPUC. This has become a standard reference on the subject, he said modestly. It is the book for which I was awarded the Bolyai Prize.

**ZIERLER:** Your graduate students, as you get into the 90s at Caltech, are exclusively from math. What's the story there?

**SIMON:** Well, there's one exception that I'll tell you about soon. The story really is who comes to work with me. The other fact that's certainly true is that any student that works on areas I work on is not likely to get a job in a physics department.

**ZIERLER:** Why is that?

**SIMON:** Because what they're doing is regarded by most people as mathematics. First of all, because of my whole style, they're proving things. That already makes them suspect to some physicists. For many of the problems I work on, while they may have a background in physics, you can explain them as purely mathematical problems. You really have to learn a lot of mathematics to do work and research with me. I would tell people, "It's very useful to have had a course on quantum mechanics, but it isn't absolutely essential. It's not the same as having had a real course in, say, complex analysis which are essential."

**ZIERLER:** Would you count Fritz Gesztesy as a significant collaborator in the 90s?

**SIMON:** If you asked Fritz, he would point out that he has more joint papers with me than anybody else. He celebrated the day he passed Elliott, who I think was number one at the time. He certainly was significant. We did a series of papers that are quite nice, and he's always been a good friend. I think from the time I was 50, he started saying, "When's your 60th birthday?" He organized my 60th birthday celebration, which was quite elaborate.

**ZIERLER:** This is Simonfest.

**SIMON:** Simonfest. Correct. Of course, the other organizer was Cherie. She's actually a co-editor of the proceedings. But a lot of that went smoothly partly because of her. But Fritz was great. We did some interesting work in inverse theory that is really quite nice. He, again, is someone I didn't discover. He discovered me. He found his own money and came to visit Caltech. After a while, I realized he was quite good. I can't remember whether he actually ever had a formal post-doc appointment at Caltech or not, but he spent a lot of time here in the 90s, and we still interact quite often.

**ZIERLER:** Last question for today. The honorary degree you got from the Technion in 1999, tell me about that. Did you make a family trip? Did you have the opportunity to visit Israel?

**SIMON:** You have to remember, my wife, first of all, has two sisters that made *aliyah* [Hebrew; resettlement in Israel], one in the mid-70s and one in the early 80s. She's always had lots of cousins who probably went directly from the old country to Palestine. We actually spent every other, on average, summer in Israel from probably about 1990 onwards until we started spending every summer there. And by 2000, my wife's father retired and moved to Southern California, was here for many years, and once his eyesight became that he couldn't drive anymore, he felt he couldn't live in Southern California, and he moved into a home near one of my wife's sisters, so her father was also there. We were certainly there in that summer independently of anything else. My understanding is that there were three faculty members at the Technion who lobbied for this honorary degree. One, of course, was Yossi Avron.

But there's a quantum chemist there who made his reputation on this complex scaling type of stuff, who I had interaction with in the late 70s named Moiseyev, who was, I think, chairman of the Chemistry Department at the time. And there was an electrical engineer who I mainly knew personally. He was a post-doc at Caltech and actually lived in our part of town. My memory is, I had a kid who took piano lessons with his wife. He also supported this. You have people from three different departments, you take it more seriously. They lobbied for it. I only knew about it because the Technion said, "Congratulations, we're giving you this honorary degree." Just like I'm now on the board of governors at the Technion. I know that because I got asked if I'm willing to be, and that's because some provost there decided to look at people with high citation numbers.

**ZIERLER:** Within Israel, is Technion a center of mathematical physics?

**SIMON:** No. Not really. Probably Hebrew University is. Because of the neighborhood where my kids are and everything else, we now spend time in Jerusalem. But as I mentioned, Avron had Last as a student and Last has Breuer as a student, and Last and Breuer are on the faculty of Hebrew University. And Agmon, who you heard me mention, is an essential figure in Schrödinger operators. About to have his 100th birthday. Still cooking. Quite lively to talk to. I would say Jerusalem, probably, but there's always been a little bit there. There was occasionally a little bit at Weizmann, and there's been some at Tel Aviv. Probably, Technion is after Hebrew University. But Israel is pretty good in mathematical physics.

**ZIERLER:** Just as a corollary to that, on a personal level, did you and your wife ever toy with the idea of making *aliyah* [emigrating to Israel]?

**SIMON:** I'm hampered by the fact that my language abilities are not very good. Early on, two years after I was promoted at Princeton, even though I discouraged offers, I actually got an offer from the IHES, which is an institute outside of Paris. That's sort of the French attempt to be like the Institute for Advanced Study. It has lots of post-docs, great place to be. I had an offer from them. I decided my kids were going to grow up speaking French, and I wouldn't be fluent in French. So the language is one issue. But it's clear I would not have the kinds of resources, both in terms of post-docs and salary, in Israel, so no, we never toyed with making aliyah. Although, one of the really maddening things–there are several very good mathematical physicists who, at various times, had an interest in going to Hebrew University before the homegrown ones came along. And their response to them was, "Well, if we could get Barry Simon, we'd do it, but..."

**ZIERLER:** But at least in retirement, you could spend more time there.

**SIMON:** That's right. now, I sort of spend half the year there. But it's still not quite full *aliyah*. My Hebrew's not very good.

**ZIERLER:** And the problem is, Israelis won't let you try your Hebrew. They'll just speak to you in English.

**SIMON:** Well, some of them. That's certainly true in the academic world. Now that I'm there, and I'm a citizen, and I have a driver's license, in to deal with bureaucrats. It works out, usually.

**ZIERLER:** On that note, we'll pick up our next talk in the 2000s. We'll go from there.

[End of Recording]

**ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It's Wednesday, December 15, 2021. Once again, I'm so happy to be back with Professor Barry Simon. Barry, as always, thank you so much for joining me.

**SIMON:** My pleasure.

### The Torah Codes Controversy

**ZIERLER:** Today, we're going to pick up not so much on the chronology, but on a thematic subject, and that is your involvement in the Torah Codes issue. Just to start off, as a way of introduction, what are the Torah Codes?

**SIMON:** If you don't mind, as an introduction, I think there are a lot of interesting personalities involved, so why don't I begin by telling you a little bit about them, and then we can talk about what the Torah Codes are? There are what I sometimes insist in my writing are not the researchers, although that's what they call themselves. They're the searchers. These are the proponents who really were searching for Torah Codes, whatever they are, and I'll explain what they are. While there were lots of people involved, the two most important ones are Eliyahu Rips and Doron Witztum. Rips is actually originally from Russia. He's a professional mathematician, did some very distinguished work. As you will find out, there are lots of Russian mathematicians involved in this story, and it's connected with Rips.

Rips actually was almost a saintly figure. You talk to Russian mathematicians, and they have this sort of aura of him. He, I think it was the Prague spring, actually protested and set fire to himself. Wound up in a Russian prison, went on a hunger strike. While he was in a Russian prison, he actually proved a very important result in group theory. Eventually, he got out after a lot of pressure from the West and came to Israel. I don't know whether it was when he was still in Russia or just after he came to Israel, became very religious. Precisely because of his connection, he ran across the Torah Codes. And they so convinced him that he essentially became religious.

**ZIERLER:** Do you know what his point of contact with Torah was, if he had a secular upbringing, especially in the Soviet Union?

**SIMON:** As far as I know, he had a totally secular upbringing, but he may have been searching a little. I don't know how he was introduced to the Torah Codes, but he told me once he saw codes for the Gaon and Vilna crossing each other, and he suddenly decided that this could only be there because there was a God in heaven.

**ZIERLER:** We should explain that this is a reference to the Vilna Gaon, who's one of the great heroes in Litvishe Judaism.

**SIMON:** Doron Witztum, I think, is a *sabra* [Israeli-born] but I'm not positive, was a physics graduate student in theoretical physics, and actually dropped out and somehow got involved in Torah Codes. He and Rips did lots of "experiments" together. That'll come up later in the story. A third of these searchers that I should mention is someone named Harold Gans, who is an American who worked as a codebreaker for the National Security Agency. As far as I know, he didn't have a huge amount of mathematical training. He had a master's degree. Never did any formal research in mathematics, but he studied codes. And as I'll explain, in my opinion, the codes he was looking for as a codebreaker had nothing to do with Torah Codes. It's totally different technology, as I'll explain when we get there.

But the people who were pushing codes made a great deal of the fact that he was a codebreaker, and what he claims is, he actually was very skeptical and came to debunk them, and he heard people talking, and he was absolutely convinced. And he's retired from the NSA and is basically a lecturer for one of the religious organizations pushing codes. The last one I should mention is Michael Drosnin, who all the other people I mentioned think is a fake, but he was very important because he actually wrote a book. He learned about the Torah Codes and claimed to find in the Torah a code that predicted the assassination of Yitzhak Rabin.

Now, as I like to say, it wasn't a prediction, it was a post-diction because of course, he found it long after Rabin was killed, but he actually turned this into a book that was a bestseller. It made a huge splash, got lots of media, and my indication of how much it was in people's minds is, there's a New Yorker cartoon where someone is sitting at the table and says to his wife, "What's for dinner tomorrow?" and she says, "Oh, we'll have to look there," and points to a book that has Drosnin's name on it. So it made the New Yorker. That's the sign of big time. Then, there are the skeptics, who are mostly mathematicians. Besides me, there's my rebbe, Rabbi Yitzchok Adlerstein. When we get into the story, you'll hear he didn't start out as a skeptic. There's Brendan McKay, a distinguished combinatorialist, who I actually ran into later.

Some of the work he did is very relevant to random matrices and things I wound up working on. He's Australian and is based in Australia. As a hobby, he's always liked to debunk fantastic claims, particularly religious claims. He's a rather virulent atheist, and he likes to say that he was particularly struck by the Torah Codes because usually, it took him about five minutes to figure out what was going on, and this really was very hard for him to figure out. He's a very good computer programmer, that's going to be relevant to this, and a very interesting character, the most important of the skeptics. He did some work with an Israeli mathematician named Dror Bar-Natan, who actually left Israel and has been at the University of Toronto.

He was at Hebrew University. He's a topologist of some sort is my memory. And I think he had some contact with an outreach organization in his youth that was rather negative, so he also did not come from a positive viewpoint towards what the Torah Codes people were selling. The last person I should mention is a fellow named Alec Gindis. Gindis, again, as a Russian, came to the US, got with some kind of software expert, made a huge amount of money, and actually provided funds at various points to these skeptics. In fact, there was a famous time we all got together in Jerusalem. I was there anyways, and of course, Bar-Natan was, but I think the other people all had their expenses paid by Gindis. A very colorful and interesting figure.

There are other involved mathematicians. Four actually signed a preface to a book that I'll discuss later on. They are among the most distinguished mathematicians. It's David Kazhdan, Ilya Piatetski-Shapiro, Joseph Bernstein, and Hillel Furstenberg. Three of the four are Russian. Furstenberg is not. He was born in Germany, but in his youth, came to the United States and was an undergrad at Yeshiva University. Three of the four are religious, so they're among the frum mathematicians. Piatetski-Shapiro is not. At one point, Kazhdan and Bernstein were two of the three religious mathematicians on the Harvard faculty. Kazhdan, during the high point of this, was the chair of the Harvard Math Department. Kazhdan, for example, is now at Hebrew University, is a Shaw Prize winner.

Incredibly, Gelfand regarded him as his best student. Bernstein was also a Gelfand student, was at Harvard for a while, is now at Tel Aviv University. Furstenberg got the Abel Prize two years ago. These are really the top of the crop. And Piatetski-Shapiro was, again, a very well-known group representation person. He's actually passed away. Most of the people I mentioned are my age, but Piatetski-Shapiro is probably 15 years older. Two other mathematicians I should mention, Shlomo Sternberg, who I mentioned before, who was one of my teachers at Harvard, is the third of the frum mathematicians at Harvard, and Yisrael Aumann. Yisrael Aumann is a game theorist, but his work was important enough that he got a Nobel Prize in economics, and he is actually the patron saint of much of the economics group at Caltech, so there is a Caltech connection.

They're mathematical economists, and you hear them talk about Aumann, and he's clearly their patron saint. The Torah Codes were used as a fairly effective tool in outreach. As you know, during the past 40 years, there's been a huge outreach program in the orthodox Jewish community who attempt to take nonreligious Jews and get them involved in religion. There are other outreach rabbis and speakers in outreach whose names will appear who I should mention briefly. One is Rabbi Noach Weinberg. He's the founder of Aish HaTorah.

**ZIERLER:** Rav Noach with the *tallit katan* [prayer shawls] over, and over, and over on his body, the famous pictures.

**SIMON:** Yes. His nephew is married to one of my wife's cousins. Rav Noach's older brother, Joseph, will also play a role. He was the rosh yeshiva at Ner Israel in Baltimore and was the official Rabbinic advisor to Aish, believe it or not. Two other people who will be mentioned, Rov Dovid Gottlieb is actually a lecturer for Ohr Somayach. He started out actually as a professional philosopher, was on the philosophy faculty at Johns Hopkins, and at some point came, I think, under the influence of the Bostonner Rebbe and became religious, and eventually became a lecturer in outreach, gave up his academic career. And there's someone who was born in Los Angeles, is very friendly with Rabbi Adlerstein, is now the head of what's called either Darche Noam or Shapell's, which is a big outreach yeshiva in Jerusalem, that's Rabbi Shaya Karlinsky.

Two other people will get mentioned. One is a fellow named Gerald Schroeder, who wrote a book called *Genesis and the Big Bang*. I will say something about that before I get into the Codes. He actually has a PhD from MIT in planetary science or something like that. He did his thesis on the study of radon concentration in basements. There was a joint program between physics and geology. He wound up as a post-doc at MIT for about four years and was always described by Aish and other people as a professor of physics at MIT. When it was Simon versus Schroeder, it was the Caltech versus the MIT professor. I actually contacted some of my buddies who were really professors of physics at MIT, and they looked into it, and he was only a post-doc there.

He left to a staff position at the Atomic Energy Commission before he went and wrote this book and stopped doing anything connected with physics. But he was described as a professor at MIT and a member of the Atomic Energy Commission. I gave up on Schroeder, but someone who likes to continue to argue with Schroeder is a physicist at Bar Ilan who's actually quite distinguished named Nathan Aviezer, whose name may briefly appear. Those are the dramatis personae. If I had the predilection, I could've written a book called *The Codes Caper* and made a lot of money.

**ZIERLER:** Between the outreach, the kiruv, and the Russian connection, is Chabad-Lubavitch involved in this at all?

**SIMON:** Not involved at all in the Codes. Although, for example, Kazhdan became religious because of Chabad in Russia. Many of the Russians who are religious got involved because of Chabad. I mentioned that I brought tefillin when I visited Russia. Since I knew I couldn't buy my own tefillin, I needed to get tefillin that had Chabad approval. I originally contacted Kazhdan because I knew he was connected with Chabad. But Chabad is not related. As far as I know, they've not done anything with the Codes.

**ZIERLER:** You've laid out the cast of characters. Now, when we get into the definitions, the meanings of Torah Codes, just orient me chronologically. When does this story get started?

**SIMON:** Before I do that, let me do one other introductory thing I want to mention because it's my other thing with outreach. Many people tried to get me involved in outreach, and I just don't have the time. I think it's a wonderful thing. We had students at Caltech occasionally, I've done other things, but I've not been seriously involved. On the other hand, Rabbi Adlerstein has always spent a lot of time connected with outreach. On the other hand, I was, therefore, asked my opinion of various things, and in particular, I was asked to take a look at *Genesis and the Big Bang*, which was Schroeder's first famous book, particularly in the context of someone who'd written a book review for Jewish Action.

To say I was aghast when I read his book would be an understatement. His basic point was, if you blindly took some formula for–gravity is associated with a time dilation in very strong gravitational fields. You put in the formula for what the gravitational field is for a large mass and a certain distance. He plugged in, at that time, the total expected mass of the universe, took the radius of the universe as it was listed, and put it into Newton's law to compute a gravitational field. You used that field to compute a time dilation. Because the mass of the universe is so large, this is an enormous number.

Of course, the mass isn't in one place, it's spread out. But you could still do it. And you get this huge number, so you get a gravitational dilation, and you plug seven days and multiply it by this, and you get the age of the universe. And he thought this proved that all of Genesis must be correct because that's where the seven days came from. First of all, it shows he doesn't understand general relativity, doesn't understand the formula, doesn't understand anything. I wrote a rather strong letter to Jewish Action, which was about half a page. He wrote a rebuttal, which was three pages. That was that. But it comes up every once in a while. If you do a Google search on Simon, *Genesis and the Big Bang*, you find all sorts of things where this is mentioned.

But this was a run-in I had, and it became a punchline almost because I think some of what Aish does is very good, although they tend to misuse science, which doesn't endear them to me, and I'm not endeared to them. But at some point, when they began to decide maybe they shouldn't use the Codes so much, they instead shifted to using Schroeder and *Genesis and the Big Bang* more, to which I would comment to people, "Of course, Schroeder makes the Codes look good."

**ZIERLER:** Maybe we should contextualize how you understand the Torah Codes within the long tradition of gematria [the numerical value of letters in the Torah] and darshening [working through the] meaning.

**SIMON:** We should first, then, talk about what the Codes are, and I should talk about your timing. The run-in with Schroeder was about '92. Codes, as I'll describe it to you, were actually first seriously done by someone named Rabbi Michael Dov Weissmandl who was a Czech rabbi in Czechoslovakia. Started actually doing this all by hand, which is sort of amazing because you really need a computer to do much. But he got into it in the late 30s, wrote about it, then his family was wiped out in the Holocaust. He wound up in New Jersey, did some writing, and that was the beginnings of the Codes. But it became serious when, I think, Witztum and Rips began these experiments, and that was probably mid-90s. My involvement was probably from '98 to 2003. I regard myself as sort of retired, although every once in a while, someone asks me about them, or I go someplace, and I'm dragooned into talking about them more seriously.

There is, of course, a huge tradition of gematria and other numerological things that are connected with hidden things in the Torah. There's a huge tradition about there being hidden things in the Torah. Indeed, one of the people who writes about these hidden things in I think the 16th century referred to something called *dilugim*, which is usually translated as skips. He explicitly says, "Well, it isn't really known what these things are." As you'll see, the Torah Codes involve what are called ELS, equidistant letter sequences, and since they involve skips–they were also called *dilugim*. There was a claim that this really was rediscovery of this traditional method that people didn't know about, but there's no indication that's really correct.

With an ELS, you take the Torah text, written without vowels, as of course is true in the Torah, you drop all the spaces between words, so you get this long sequence, and you skip equal spacings. You start out at one letter, you go forward 305 letters, then another 305 letters, and in that way, you might get a word.

**ZIERLER:** We should clarify you're talking about the written Torah, the Chumash.

**SIMON:** Well, I'm talking about the Torah, which means the Chumash, the five books of what's sometimes called the Pentateuch, so Genesis, Exodus, Leviticus, Numbers, and Deuteronomy. In fact, it's particularly popular to use Genesis to find these ELSs, but it's all over in that original text. That has a special significance because it's by tradition, given directly by God to Moshe in the desert, and the other books are, in fact, supposed to be written by individuals, who were *nevi'im*, prophets, and were inspired by God. But the Torah has no intermediary. It's believed to have been written and given by God to the Jewish people.

**ZIERLER:** The art of skipping spaces, that works both in a Sefer Torah, a Torah scroll, and a Chumash, a printed book?

**SIMON:** Well, it's the same text. Of course, you're not supposed to count vowels. You take the printed book, it's the same text. It doesn't matter what you do with it. But you don't keep spaces. You might look at every 305th letter for some number, and you get a word. This way, you find hidden words in the Torah.

**ZIERLER:** Is there a rabbinic basis for this before the modern era?

**SIMON:** No. It's claimed there were one or two places–the rabbis have played around with the Torah in lots of ways, and there are one or two places where someone might have done this a little bit, but without a computer to do searches, the number of possibilities–individual words are almost meaningless. You look at the text of the full Torah, and you take, I think, any six-letter word, and it will occur hundreds of thousands of times. Essentially, you expect to find any word up to eight letters, and you probably won't find–pick a typical ten-letter word, and it probably isn't there. With some spacing. Of course, you can have arbitrary spacing. Single words are not so interesting. What becomes interesting is, if you have related words, which are "near" each other. What does near each other mean? Well, that's a complicated issue. Because of course, these spaces can be very big.

If you have a five-letter word near a four-letter word–and I remind you, most Hebrew words are not so long–one has a spacing of 300, the other has a spacing of 600, it's certainly not going to be true–there will just be a few letters that could be near each other. But there's a way they can be made visually to look near each other. Suppose you have one of these ELSs that has a skip length of 310, and you take the text, and you start writing it down on lines that are 308 letters long.

Then, this word that looks of letters that are pretty far apart actually will occur on lines that are essentially a diagonal. Since the lines are 308 letters long, and the skip length was 310, they'll be almost a diagonal with a spacing two. It looks like it's very close to each other. And the other one might go and cross some other way, but they look like they're actually crossing. If you write the text this way, it's visually quite striking that they actually appear near each other.

**ZIERLER:** Can we understand this process at all in the tradition of gematria? Or this is a total innovation? And we should explain, perhaps, what gematria is.

**SIMON:** Gematria has to do with numerical values of letters, so in that sense, it's got nothing to do with gematria. There's a method that is well-understood called *roshei* *teivos*. I'm not sure I can, off the top of my head, remember exactly what it is, but I believe it's forming words out of taking the first letters of a phrase in the Torah, so there are other things that have play with the letters, but not in this particular way. Again, there's so much writing on the Torah that there are people who've done things close to this, but my memory is, there are only two or three people who have done something like this in history. But certainly, in order to actually find these things and do the experiments I'll mention in a second, you need a computer, so there's not going to be a tradition of this.

**ZIERLER:** Before we get to the merits of the Torah Codes, perhaps we should further contextualize if there is a rabbinic basis for supporting this kind of innovation. In other words, we say that it's a living Torah, that we have a relationship with the Torah. We should always strive to have a deeper relationship with it. Therefore, we can figure out new ways of experiencing it.

**SIMON:** Yes, and no. It's a living Torah. There will be some people who say if you don't have an actual tradition, you don't have a *mesorah* for something, it's very dangerous to start using it. We'll talk about that a little later. But you can wind up getting very striking pictures. If you pick the lengths carefully, you will find these amazing collections. There's a famous one they like to show of a number of Chanukah-related words, candle, Maccabee, that appear near each other. Again, they're not really near each other, but if you write the text with exactly the right length, they actually look to be near each other.

You see this, and it really is quite striking. These are totally uncontrolled because who says what words to look for? My derogatory name for this is latke codes. Not that they had latkes, but I said you could search for anything. You could search for latke. Sometimes, some of the proponents, in fact originally, would like to quote absolutely huge probabilities that they claim how unlikely these combinations are.

The problem is the following. To get a huge number is easy. You take, say, two words, menorah and Maccabee, that happen to be "near" each other. Maccabee happens to occur with a spacing of 300, the other with a spacing of 250, and you compute the probability of finding menorah with 300 and Maccabee with a spacing of 250, and you get an incredibly low probability. The problem is that this is what's known in the statistics literature as an a posteriori probability. You compute a probability after you find it without a well-defined a priori thing of the universe of objects you're looking for.

Suppose it wasn't a spacing of 300, it was a spacing of 302. Would you count it? Now, who's to say the magic words are Maccabee and menorah? I would like to say they would be maccabee and latke. That's why I call these latke codes. The problem is, you can get these amazing pictures, but the probabilities that people quote are totally meaningless.

**ZIERLER:** What was the rabbinic reaction when Torah Codes came out? What did Rov Noach say about this?

**SIMON:** They're experiments, so there's something that is at least more serious science. There's actually an article that appeared in a scientific journal. But when it was originally just shown, it really is an incredible–you take someone who comes into a lecture, they have some small interest in Judaism, they see these pictures, and they get blown away. They hear this quotation of probabilities. I believe some of the outreach rabbis, including Rov Noach, this was incredibly effective, and they thought since it was effective, it was wonderful.

**ZIERLER:** It was effective because unaffiliated Jews could wrap their heads around the idea that the Torah could not have been created by people.

**SIMON:** Correct. On the other hand, I will tell you the story now of Rabbi Karlinsky. The skeptics are sort of anti-Codes. You say the word Codes to Rabbi Karlinsky, and he almost foams at the mouth. He tells the following story. He runs an outreach yeshiva. Someone gets someone interested in Judaism, and they decide they really want to spend some time studying it, learn a little Talmud. They go to an organization like his. Both Ohr Somayach and Shapell's, and Aish also has such an outreach, but the former two are more serious level, used when people are really getting seriously into it and learning about it.

Many times, he will get students who come in who have gotten turned on by the Codes, and even people who were frum from birth would learn about the Codes. In the late 90s, within a certain community, it was just this amazing, wonderful thing. He tells the story that he was always somewhat skeptical, and one Purim, he and some of the students may have drunk a little bit, he was a little light-headed, and he decided to tease one of the students. He said, "I understand. Suppose you found a code that said you should keep Shabbos on Sunday."

**ZIERLER:** That's a provocation.

**SIMON:** The student said, "Oh, you wouldn't find it." "Yeah, yeah, but suppose you found it." "Oh. Then, I'd have to think we might have to keep Shabbos on Sunday." At this point, Rabbi Karlinsky realized how terrible this was because we have no real tradition, but it could be terribly misused.

**ZIERLER:** Would we put this in the same category as the Karaites, who rejected Torah *She-be'al-Peh* [the oral Torah; that which was communicated to Moshe and handed down the generations through the oral tradition] and who ate in darkness on Shabbos?

**SIMON:** Some people could say that. It's just very dangerous to use something which you don't have a tradition for and which you can essentially find anything and start throwing numbers around. Rabbi Gottlieb has a similar situation. There are many rabbaim who are very anti-Codes because they think it's dangerous, and by the way, there are also Christian Codes. There are ELSs. There's a wonderful ELS. I can't remember exactly what it is, but I think it has Jesus and messiah crossing each other somewhere in Isaiah.

**ZIERLER:** This should be the exit ramp for frum Jews when they think about the Torah Codes right there.

**SIMON:** The people from Aish who continue to push Codes would say, "Those don't have a scientific basis," and they don't really have a good reason for why those codes are worse than some of the latke codes they use. Of course, there are these other things, which are rather different. But I gave a lecture one time at Yeshiva University of Los Angeles on the Bible Codes, and afterwards, someone came dragging a friend. He said, "You really have to speak to my friend because he heard about the Torah Codes, he decided, 'Gee, this stuff really must be real,' and decided he should become a serious, Shabbos-observing Jew. Two weeks ago, he was introduced to these Christian Codes, and he wants to convert. What can you tell him?" I said, "It's all nonsense." But the point is, it's very dangerous. And this exactly shows why it's so dangerous.

**ZIERLER:** Let's engage on a technical level. I wonder if you can explain why you need computers and what the supposed math is that legitimizes Torah Codes.

**SIMON:** You, first of all, need a computer because remember, some word occurs hundreds of thousands of times. One of the things that became popular at some point is, there are so many ELSs, you look for what are called minimal ELSs, one with the smallest space. Of course, in order to find one with the smallest spacing, you need to do this search of this huge text for all possible times the word, say, Chanukah, occurs to find the one with the smallest spacing. You need a computer for that. Indeed, in the famous Chanukah code that people like to show, where they made the big deal about minimal ELSs, Chanukah isn't used, it's Hachanukah, even though we rarely use Hachanukah.

Why? Because in this particular picture, the Chanukah is not minimal. There are other places. But if you add the Ha- in front, it becomes minimal. This sort of illustrates my big push against the latke codes, the issue of what I call wiggle room. The fact that you can manipulate them means that these things are essentially not significant. You really can't compute probabilities. Now, we can talk about mathematics. Witztum, who was a graduate student in physics, had a serious academic background, began to ask himself, "How might we prove that these things really weren't some artifact of just luck?" He had the idea that, "Well, what we need to do is look for some systematic way of combinations of words that are close to one another and some way of figuring out how unlikely that is.

They invented some absolutely cockamamie method of measuring how close two ELSs were to each other. Wasn't based on visual but some mathematical formula, which at least made things well-defined. One of the mathematicians I forgot to mention is Persi Diaconis. Diaconis is a statistician, has a joint appointment in mathematics at Stanford. Has a very strange history, got into mathematics late. Is actually a professionally ranked magician. One of the sweetest, most interesting guys, and really clever. While he's officially a statistician and a combinatorialist, he really is noteworthy for applying these things to other parts of mathematics. He has some amazing papers on understanding random sequences of matrices.

Anyhow, he's a really impressive, fantastic guy. He got involved. I suspect I know why. I'll come to that in a moment. But he was consulted, and being a very clever guy, he came up with a way of deciding how likely or unlikely some combination is. In the actual experiment, we had a list of names and dates, which were correlated to each other. We had, say, 100 names and 100 dates, the correct names and correct dates. And we used our method of finding minimal ELSs or some other way that these pairs occur in the Torah and how close the names are to the correct dates. He said, "If you want to see how unlikely this is, why don't you just do a different permutation?" In fact, I believe it was 30 names and 30 dates.

You have a huge number, 30 factorial, of ways of permuting so that the wrong dates or only some of the right dates are next to the names. You have the list of names that you fix, you have the dates, which have a correct listing, but there are lots of ways of permuting the dates so that most of them are associated with the wrong–and you do the experiment again to see, in this particular different pairing, how close the names are to the corresponding dates. And you don't do all of them because it's too much. You use some random way of picking 1,000 randomized pairings, and you see what rank you have among these 1,000 possibilities you did.

And if it's a low rank, that says, "Gee, the fact that it occurs that way in the actual text with the correct pairing is some indication of real significance." The famous paper that Witztum and Rips wrote–there's a third author, but the third author, I was told, was just to do the computer programming for them, so he's typically forgotten. They took a list of medium-famous rabbis and medium-famous dates. They wanted to show that they were not choosing it. It was an a priori list. They took some encyclopedia, took all rabbis whose articles were between one and a half and three pages long in this encyclopedia, which means someone like the Rambam didn't appear. But they got 30 rabbis, and they took the dates of their births, and they did this mix that we talked about.

They found out of a thousand permutations, I don't know the exact numbers, it occurred, I don't know, eighth in this list of 1,000, which is fantastic. One of the things, by the way, that happened before the actual paper appeared, Witztum wrote a book with some preliminary versions of this. As you may know, there's a tradition of getting approbations, approvals from big rabbis, you write a Sefer, a book about your interpretations of some volume of Talmud or something else, and you get some big rabbi to write a letter that says, "I think this guy is wonderful." The standard is, "My father knew his father."

These are letters that people write as favors. They give it some luster, but the writers don't take it that seriously. Witztum decided to do the same thing with some mathematicians for his book. There was a preface I believe was probably written by Kazhdan, who was struck by this. A number of religious mathematicians thought it was interesting, an intriguing thing that was being done. And he got four famous mathematicians to sign this letter that didn't say, "We approve this," it just said, "We think this is interesting research, and it's probably worth following up." He got Kazhdan and Furstenberg, who later, by the way, said he regrets having signed it. Bernstein and Piatetski-Shapiro also signed this, although when I consulted them, essentially, both said, "Don't ask me. I signed it because Kazhdan told me to sign it. It was for Rips, and everybody knows what a sainted person Rips was. How could I not sign it?"

Rabbi Adlerstein also was struck with this. He was originally a proponent. He and I knew each other. He was not quite my rebbe when I was originally exposed, but he suggested to one of the local Aish rabbis that there was this well-known mathematician in Los Angeles. They should perhaps get me involved. I might become a wonderful lecturer on the subject.

I was invited to attend one of these presentations that they were giving on the Codes. It was given by someone I actually knew. He actually had a prepared script. He didn't really understand much of the mathematics involved. I sat there, and it was not quite as bad as my reaction to Schroeder, but I was pretty much aghast. Because it was clear to me that much of the beginning, before they got to the actual experiment, which I didn't understand, but the original latke codes were clearly misusing a priori probabilities. It was clearly just *narishkeit*. The other one, I needed to study.

I was told that it had appeared in a journal, and of course, if it appears in a journal, it must be correct, what we were told. Of course, I know enough about journals–as I said in one of my articles, I'd been an editor of a journal for many years at that point. 15 years then, 35 before I'd stepped down. It has incredibly high standards, and I wouldn't eat in a restaurant whose kashrut only had a standard as high as the journal. Scientific journals, the referees are busy. They do the best they can. But I know referees whose attitudes are–and it's almost my attitude–it's not your job to decide whether it's correct. You assume the author knows what they're doing. It's to figure out if it's plausible, there isn't anything obviously wrong.

And it's important enough to appear in this great journal. But it was presented in the lecture, "It appears in a scientific journal. That's proof it must be correct." And then, there are these famous mathematicians whose names I knew–at the time, I don't think I knew any of them. I'd probably met Kazhdan but not the others. I was just totally aghast.

**ZIERLER:** Before you approached the Torah Codes from a technical level, as a frum Jew, on an emotional level, did you want it to be legitimate? Were you disappointed when it turned out to be nonsense?

**SIMON:** On a personal level, I don't like black magic. There are good reasons to have faith. And I understand there are some that are divine, but gematrias are a nice seasoning in your cholent. But it's not what you eat. But again, from the very beginning, since they started out by presenting these latke codes as being somehow amazing, and I knew that they weren't amazing, I was never at a point where I could be disappointed or not disappointed. It was obvious nonsense from the start for me. In fact, if they'd started with the more scientific things, I might've taken it more seriously.

At my wife's cousin's house, there was an Aish rabbi. I was introduced to him, and he essentially looked at me, "You don't have horns?" was what he said to me. Because at this point, Aish and I were–but we had a very interesting discussion. He said "We talk about the high-impact, low-science codes, which I call latke codes, and low-impact high-science codes. This experiment, which puts people to sleep, they don't say much about it. It's interesting to someone like you, but it's supposed to be real science because it appeared in this journal, after all."

**ZIERLER:** I wonder if there's a duality to your reaction as well. Obviously, as a mathematical physicist, you're offended when you see research that's nonsense, but as a frum Jew, are you also concerned that this is a bad image problem for *frumkeit*?

**SIMON:** I remember in the middle of this, Rabbi Adlerstein went to his rebbe. My rebbe has his own rebbe. This is the rosh yeshiva of the Chafetz Chaim yeshiva, which is where he went, who's now passed away.

**ZIERLER:** This is in Queens.

**SIMON:** In Queens. He was, at the time, probably in his late 70s. In fact, I have a son who was a student there, also. It's named because he was a student of the Chafetz Chaim. He was a remarkable guy in many ways.

**ZIERLER:** By the way, I know that you became frum later, after you had the chance to be a yeshiva *bocher* [boy], but just in terms of your own rabbi, do you consider yourself a Chafetz Chaim guy?

**SIMON:** No.

**ZIERLER:** You don't have a yeshiva affiliation personally?

**SIMON:** Not at all. My other two sons both went to Toras Moshe, which is in Jerusalem. The rabbi there, in fact, has a PhD in mathematics.

**ZIERLER:** Going back to your rebbe goes to his rebbe.

**SIMON:** He asked the question, "Can you lie to someone to get them to keep Shabbos?"

**ZIERLER:** Classic rabbinic question.

**SIMON:** He told me he was expecting to get an answer that, "The Seal of HaKadosh Baruch Hu [Hebrew; literally, the name of the Holy One, blessed is He] is *emes*, is truth." The best way of describing it is, you've got to bring people in. Someone said to me, "You shouldn't care about this. You bring them in, and so you lie to them a little to bring them in." You can't do that, that's not right to me. But you bring them in. And the Torah Codes were incredibly effective at taking someone with a little interest and piquing–if they have no scientific background. It's very bad for people who have a scientific background because they see through it. But people who are sort of wowed by these…

**ZIERLER:** To go back to, I think, our very first conversation, where you emphasized that you really separate your Torah worlds from your science and math worlds because they don't speak to each other, does the Torah Codes, which so obviously wants to connect both worlds, only emphasize the point that you made, that there isn't any need to connect them? One does not need the other to be self-sustainingly legitimate?

**SIMON:** It's not only that. It's that an attempt to make them connected is likely to have some faulty basis. It's not that it has to. Aviezer has a book, it's not my kind of book, but it's actually pretty good. You can do some writing that attempts to link some aspects of science and Torah. But I once said, "Books on Torah and science that I've seen–and there may be a few exceptions, but probably not–are either bad Torah or bad science, and usually they're both." I think that's certainly true of *Genesis and the Big Bang*, for example. And I think it's true of Codes.

**ZIERLER:** To just be as simple as possible, in your relationship to God, you need faith, and that simply does not work in science. It's not relevant in science. You have evidence in science, observation.

**SIMON:** Yes, and no. There's a famous midrash that I love to quote. In fact, it's sort of sad because there's a rabbi high up in the OU who was in charge of their kashrus, who became friendly with Bill Clinton. He had people write weekly *derashas* [thoughts on the Torah] for Clinton. Clinton claimed he liked to read it. I actually wrote a *derasha*, which essentially repeated this famous *medrash* [Rabbinic story] about Avraham. When he was young, he went out and saw how magnificent the moon was. He decided he should worship the moon. The moon set, and the sun came out. But eventually, he decided there had to be something that had caused the sun and the moon, and that's what he should worship. You look at nature, and as the theoretical physicist said to me in the lecture I told you about, it's hard to imagine that all occurring at random. There is something about science and nature that really does mean they're not quite totally separate. But explanations are going to be different. By the way, I submitted this *derasha* to go to Clinton, and the Monica Lewinsky scandal broke the day before, so I never got anything back.

**ZIERLER:** He was a little distracted. [Laugh]

**SIMON:** Correct.

**ZIERLER:** When did the Torah Codes controversy kind of simmer down?

**SIMON:** Rabbi Adlerstein and I actually made a pilgrimage to the yeshiva in Baltimore that J. B. Weinberg was the rabbi of. One of the things that Rabbi Adlerstein convinced me was that these things were so dangerous and so bad, we had to get some big rabbi to take a position. The obvious choice was, in fact–and we went to see him. I remember at that time, I did allow my airfare to be paid by Gindis. On the way there, Rabbi Adlerstein said to me, "Rabbi Weinberg I regard as one of my rebbes. If he says I have to stop, I'll have to stop. But you don't have to stop. I don't want you to stop." It was amazing. Rabbi J. B. Weinberg clearly had thought about this, and he had various reasons he was sure they were wrong.

There was this amazing thing, there was one point when he was so negative about it that Rabbi Adlerstein had to play devil's advocate. He said, "You can say in my name you can't use this, and I'm going to discuss it with my brother." Then, at some point, he got pushback from his brother, and he was convinced that the only proper thing was that myself, Harold Gans, and someone else were going to meet with him, and he should hear the other side before he took a definite position. Shortly after this happened, he was diagnosed with cancer, and we never met. He was dead six months later. Before this, we met with Rav Shmuel Kamenetsky.

**ZIERLER:** We should say that Rav Kamenetsky is considered perhaps the *gadol* *hador* in the United States.

**SIMON:** At the current time. And his father before him was one of the *gadol* *hadors*. *Gadol hador* means greatest rabbi. He was just aghast. But he said, "Look, this is terrible, but it's Rabbi J. B. Weinberg. You have to convince him." By the way, Rabbi Karlinsky was definitely a Talmud and, in some sense, Rabbi Kamenetsky was the rabbinic advisor to Rabbi Karlinsky. Rabbi Karlinsky had been after him, but his position was he didn't want to get involved. We also met with Rov Shternbuch, who's a big rav in Jerusalem, known as an intellectual. Before we could say anything, he said, "Torah Codes are obviously *narishkeit* [Yiddish; foolishness] to anyone of the slightest mental acuity.

But if they're effective to convince those who are of less than the greatest mental acuity, then who am I to say we shouldn't use it?" You have to decide what battles you want to fight. Essentially, the rabbis we went to see decided it wasn't a battle they wanted to fight. I can understand why you wouldn't want to use your intellectual–for a period of a few years, I gave probably a dozen anti-Codes talks in various places, in semi-religious settings. To show you how charming Rips can be–Rips actually came to one of the ones I gave in Jerusalem. Afterwards, he came up to me with this very charming smile. He said, "That's the best talk I've ever heard. [dramatic pause] Except for the content."

**ZIERLER:** That's great. [Laugh]

**SIMON:** Because I really did put on a good show. Drosnin, in an interview, had said, "When my critics find predictions of the assassination of a prime minister in Moby Dick, I'll eat my words." I had this amazing picture with Princess Diana and other related words in *Moby Dick*. You see some of these things McKay produces, and you understand why the latke codes are totally *narishkeit*.

**ZIERLER:** To put a bow on this particular aspect of our conversation, if not the Torah Codes itself, if we could zoom out again on what the Torah Codes was trying to do in demonstrating that Torah clearly could not have been generated by humans because of this amazing capacity, are there other aspects of the Torah that do have that characterization? Do you see the Big Bang in *Bereishis* [The Book of Genesis]?

**SIMON:** You do see them, but there are two problems that you have to bear in mind with an example like the Big Bang in *Bereishis*. One is the so-called problem of the God of the gaps. Part of the issue is, if you claim that something like this can't be explained any other way, and then science comes along and finds some other way of explaining something, where do you stand? That's one of the problems. I'm not sure I quite subscribe to this, but the other problem is, I certainly remember in discussing Codes, there are some people who feel you can't have anything that proves the Torah is without a doubt divine because that would take away people's free will. It's an argument I've heard. It's not one that appeals to me.

But I understand the need to bring people in the door because we have a lot to offer. As someone said to me, "We just have to get them in the door. Then, they see singing *zmiros* on Shabbos, and you've got them in." And I understand that. One of the Aish rabbis was going around after my article in Jewish Action appeared saying, "Because of Barry Simon, the intermarriage rate is going to go up." I understand why he thought that.

**ZIERLER:** It sounds like for you, in terms of kiruv, bringing in unaffiliated Jews, Jews who do not have a background in Torah, the way to do that is through conveying values, not through trying to show evidence.

**SIMON:** That's correct. What we have to offer is a combination of values and a system that fits together.

**ZIERLER:** The *emes* [truth] there is that we're here, and we still have these values from thousands of years ago.

**SIMON:** The *emes* is also, if you try living it for a while, you see what its value is.

**ZIERLER:** We talked about the Torah Code wars, now let's go onto a different set of wars, the math wars. But as prelude to that, first, we need to talk about the Stevenson Committee at Caltech from '94 to '96. First of all, which Stevenson? There are a few Stevensons at Caltech.

**SIMON:** Dave Stevenson in geology.

**ZIERLER:** What is the Stevenson Committee?

**SIMON:** Caltech still has but has long had a "core curriculum". Caltech has relatively few graduation requirements. The idea is, although it depends on the department, and mathematics was the most extreme, Caltech has all these wonderful courses. You want students to learn some basic material that makes them professional, but you want to also give them lots of opportunity. There are relatively few requirements. But one set of requirements is Institute wide. They are core courses that all students must take. Many schools have this. Until 1995, from I think the 30s or 40s, all Caltech students had to take two years of mathematics–that's six quarters because Caltech is on quarters–two years of physics, and essentially four years of humanities and social sciences. The math and physics were specific courses.

The humanities and social sciences were from a menu. And I can't recall what else there was. I think you had to take at least one course in either biology or geology and earth sciences. But there began to be a lot of pressure about this and discussion about whether this core needed to be updated. One of the reasons was that we became aware of the fact that many of our graduates don't know how to write coherently, don't learn how to speak. As I'm fond of saying, it's not so much that physics is the science of the 20th century and biology the science of the 21st century, it's that physics is the science of the century that ended in 1960, and biology is the science of the century that began in 1960. In 1998, we expected our students to take two years of physics and no biology.

Of course, until David Baltimore, the Caltech president was always a physicist and was run by the physicists. Of course, students still have to learn physics, but perhaps they should have to learn a little biology. There was a committee that set up how to redesign things to add some biology, some communication classes. But the other part of the picture was that we didn't want to just add on courses. We didn't want the number of courses in the core curriculum to get larger. If we were going to add something, we had to subtract something. Stevenson was made the chair of a committee that had, I believe, at least one representative from each division, but clearly we needed both someone from physics and someone from mathematics. I forget who the physics representative was, but I was the representative from mathematics.

We would systematically look at it. There was a preliminary report. I remember there were too many things the faculty board wasn't happy about, so we actually wound up taking two years before we came up with the final proposal. One of the things we decided we'd do was poll each of the divisions about what they thought should be in these required math and physics classes. One of my favorite Caltech stories is that of all the divisions, only one came back and told us they thought we should include calculus on Banach spaces in our required math class, and that was the division of humanities and social sciences. Because of course, half of the division are economists. They'd been influenced by Aumann, as I mentioned.

I still remember going to meetings of some committee that happened to meet over there, and I walked into the room, and written on the board is, "Let X be a Polish space." That's a mathematical notion. They're very mathematical, the economists. We, of course, decided not to do calculus on Banach spaces, although I should tell you, at Harvard, there is a calculus sequence, the one that I took, for example, that does calculus on Banach spaces. There really should be such an honors class at Caltech. The problem is, it wouldn't be big enough. And it's not clear how you figure out who goes in it because all our students think they know everything. A number of times, we discussed whether that might be possible, and we never really did that. We sort of did that a little bit in passing, maybe in a more advanced class.

But the Stevenson Committee, it was decided what we needed to do was go from six quarters to five quarters in math and physics, add a quarter in biology and a quarter in science communications. Then, we had to figure out how we went from six to five. In physics, they just lopped off one course. In math, we actually had a different way of thinking about things. One of the changes was, it used to be that all our students come in having taken advanced placement calculus, but we know when we test them that they don't understand calculus at the level we really want them to.

There used to be essentially two quarters of basic calculus, but the students complained, "Most of us know this." The solution was, "We'll take the students at their word," so we would cut down these two quarters into one quarter, and there was a further push. One of the things that the mathematicians are pressured about, the physicists would like us to do multivariable calculus on day one, certainly by the time we get to the second semester, because they need that for electricity and magnetism. But there's no way we can possibly do that because they first of all have to newly understand one-variable calculus, and you need to do linear algebra before you can do multivariable calculus.

We told the physicists a long time ago there was no way we could do that. But the biologists say, since the new scheme, one of the things was that people would be pushed to take this required term of biology in the first year, they wanted to be sure that sometime in the first two quarters, they learned some basic probability. We came up with a really terrible recommendation. We split probability and statistics. The first quarter of the math sequence that the Stevenson Committee recommended was one quarter, which did some of the basic calculus, leaving the rest of the basic calculus, the series and other things, to the second quarter. Five weeks of that and then five weeks of probability because it used to be five weeks of probability and five of statistics.

We also split linear algebra so that some of it was in the second quarter and some of it was combined with statistics in the fourth quarter. I taught the first quarter for five years, as I'll tell you in a second, but the students eventually rebelled. It may have been in the last of those five quarters I taught it for, we'd already changed. I don't remember now. It may have been just afterwards. But it turned out the biologists really didn't use much probability, so probability and statistics are now back in the second year and in the same semester.

It's a much more sensible curriculum. In the original thing, I decided I was pushed. "Why don't you teach this?" I've always taught just advanced classes, but I was convinced to teach the first term of required math, the first experiment of these five weeks. And I didn't like the book that was being used, which was Apostol's calculus. I didn't like much. I wrote my own notes for that. We used a probability book that wasn't too bad, so I taught five weeks of–you should realize that at Princeton, I typically taught classes with 25 or 30 students. At Caltech, the basic advanced classes I teach will have between 10 and 20, the topics classes will have five. Math 1A is the largest or second-largest class at Caltech.

The first term of the applied math class, which is not required, but almost every student and many graduate students take, may be slightly larger. That's taught in the Applied Math Department, not Mathematics. But this is a class that has roughly 200 students. Much larger. It was very interesting. We had these large lectures, and then there were sections, so I had to manage ten TAs. It was a very different experience. It was interesting. I was doing this different curriculum. The real point was to teach them what a proof was. You may have seen this famous picture of me in the epsilon and delta gloves. I don't know if I told you where that came from. One year, I had a particularly lively class. It was really quite remarkable. One of the standard lines that I gave every year was, "Epsilon and delta are a calculus student's finest weapons."

Probably my third year teaching the course, I walk into my last lecture, and the epsilon and delta gloves are sitting there on the desk in the front, a gift from my students. And I get back to my office, and they'd stolen a Pasadena traffic sign and posted it on my door. It said, "No passing zone." It was a particularly lively class. I would also tell students, "If you don't understand an epsilon-delta proof, you don't understand calculus." I remember after one of those lectures, walking back, and I happened to be behind two students who didn't know I was there, and one was saying to the other, "I took calculus for three years in high school. How can he say I don't understand calculus?" They don't.

**ZIERLER:** Some questions about broader trends at Caltech that might give some context to both the Stevenson Committee and the redesign of the core curriculum, and how that affected the kinds of courses you taught afterwards. A few things are going on in the mid-1990s. One is that the shift in undergraduate interest from physics to computer science is underway, and another is that as we get closer and closer to the present, fewer and fewer Caltech undergraduates go onto graduate school and instead want to pursue careers in industry. I wonder how either or both of those trends might've been a factor in the Stevenson Committee and core curriculum redesign.

**SIMON:** They were not in that committee. The trends you're talking about are a little later. There was a later core curriculum redesign in about 2010 or '12 that, in fact, cut down the required courses to only three quarters math and physics. There was a lot of discussion. I can't remember what the resolution was about what was to replace it. But I think there are fewer courses, but there also was a lot of discussion about something that–for example, there may now be a formal computing course that students have to take. I was getting close to retirement, and I knew I was not going to teach undergraduates again, so I didn't pay that much attention. The trends you're talking about I think came up in the second level of redesign, which was, in many ways, much more radical, but less controversial. It was amazing. Every little change we wanted to make–I don't know what the fraction is, but probably 20 to 30% of the Caltech faculty were Caltech undergraduates, and any little change we wanted to make in the original core–"You can't do that. It was one of the most important courses I took when I was here."

**ZIERLER:** The newly designed Math 1A in the late 1990s, how do we get from there to your involvement in the so-called math wars?

**SIMON:** I didn't pay much attention to high school mathematics, but now I had to care what my students came in knowing. I was supposed to be teaching them proofs. When I was a high school student, I had a year of "Euclidian geometry," which did these terrible two-column proofs that are the worst possible way of learning about proofs, except for every other to paraphrase "Winston Churchill"–they're not a good way to understand proofs, but you actually spent a year thinking about what a proof is. Part of the reform of the math high school curriculum, starting in about 1985 to 1990, which some schools absorbed and some didn't, was to introduce all sorts of things. One of the things I did was a survey of my students to find out how much proof they had in their high school geometry class.

It was roughly equal thirds. One-third had had the traditional class I had had that probably high school students had had for 100 years. One-third had a month of proof. One-third had no proof at all. I was and remain aghast by this. After mulling this over for a while, one day, I started probably the evening before, but I'm a pretty good writer, so I wrote this–and I had some idea of how long editorials were supposed to be–editorial, which you can find on my webpage, called *A Plea in Defense of Euclidian Geometry*. Just for the heck of it, I sent it off to the LA Times. By then, I was the chair of the Math Department at Caltech. I was actually not the chair because we have no math chairs. I was EO.

But I mis-described myself as the chair of the Math Department. And literally, 30 minutes later, I got back an email accepting my editorial for the LA Times with the standard contract, which I signed, which I didn't read or understand. Without my realizing it, I gave them syndication rights, so this editorial, for the next three years, every once in a while, I'd get a flurry of letters people wrote me because a reprinting of this in another newspaper had suddenly occurred. Of course, the LA Times got paid for this every time they reused my editorial. I didn't get paid for the original one, let alone for its reprinting. I'm sure they made a lot of money off me, but that's life. I also got several emails from people who were in what I would call the math wars. One, I like to tease, was a letter that said, "Oh, I'm so glad to read your editorial. You can be cannon fodder."

Basically, what happened was, I was not the only person who was concerned about the change in the curriculum, which didn't only involve Euclidian geometry. It's a whole trend, that has continued and reoccurred, of claiming that tracking is immoral. Whether tracking is good or bad is complicated. One of the arguments against tracking–tracking, of course, means putting the better students in a different class–is that the better students can help the weaker students. Of course, they can also discourage the weaker students. I believe that tracking isn't a terrible thing if you have great high school teachers. Unfortunately, in part because we don't pay teachers very well, don't give them very good working conditions, on the whole, we are lucky, we do sometimes have good high school teachers.

But a lot of them aren't so good. I think not tracking is much worse. In addition, there was a huge tendency to what I'd call dumb down–that there's a significant fraction of students who have trouble understanding even the watered-down curriculum, but the curriculum I went to, there were some students who had a lot of problems. Dealing with that is a hard issue, and I'm not quite sure how to do that.

But if some of the students don't understand some of the material, we just won't try to teach that material. The caricature of the new curriculum that was put into place is, "We don't want to challenge anyone because then some of the students won't be able to do it, and they'll feel bad, and we don't want that. So we won't ask anything of them."

**ZIERLER:** Because Caltech undergraduates are really the *créme de la créme*, what aspects of the K-12 math teaching are relevant for Caltech education, and what are just your overall concerns about math education in the country?

**SIMON:** I was more concerned about my students in the sense that they should be able–I'm concerned about training not just Caltech students, but students who are going into STEM. There are students who aren't going into STEM, and they're a problem. But we are competing with China. My biggest concern is for students who wind up going into STEM. The editorial was more a cry from the heart than, "This is something I care about so much I'm going to spend lots of time on it." But having stuck my head up, I wound up getting sucked in because there was a very active group of people who were fighting back what people were calling the math wars.

There were certain people, most of them associated with education schools, who were claiming studies show blah, blah, blah. I'm not sure there were very good studies. But essentially, tracking was bad, you're trying to teach too much. And then, there was the reaction that said, "No, you want to try to help all students, but your solution for helping all students can't be to hold back the good students. You have to try to deal with everyone. The traditional way is not so bad. We may need to rephrase things to be clearer." And there were some professional mathematicians, three in particular, a topologist at Stanford named Jim Milgram, differential geometer at Berkeley named H. H. Wu, and an analyst at Wisconsin named Dick Askey, who later, I had much to do with because he's a big guru in the theory of orthogonal polynomials.

The so-called algebraic side, not the side I worked on. But we had a lot to do with each other, and he remained very active in his science. Wu essentially was full-time in math education. Milgram was close to full-time. I knew Milgram somewhat, and he sucked me in. I'd met some of these people, I've encouraged them. I was not planning to do much myself because I had too many other things on my plate. I was a department chair, I was doing my research, I had graduate students. I get a call from Milgram one day that there is a new framework for teaching mathematics. One of the other things, by the way, that the bad guys in the math war were also pushing that made me aghast but has definitely become fashionable, that the traditional curriculum is Eurocentric.

**ZIERLER:** Like, white male Eurocentric.

**SIMON:** It's now become white male. In those days, the phrase white male was not so whatever. More recently, it's evolved from Eurocentric to white male mathematics. But it's the same thing, and it's recurred. This time, it looks like the bad guys are really going to win. There's a new framework, the draft framework, that's got all the bad stuff. It's total victory for the time being because these can be looked at again. There's a new framework every ten years. But there was a new framework around 2000 that had been proposed with various changes that were looking good, and the LAUSD, the Los Angeles Unified School District, which is the second-largest in the country–even in those days had a budget of $7 billion, big operation–had a textbook commission to try to recommend textbooks to meet the new framework.

One of the appointees on this committee was the representative–it turns out, Los Angeles County has a superintendent of education, even though it runs no schools. The superintendent, who was supposedly on the side of the good guys in the math wars, from my point of view, had a representative, and his choice had been too nasty. I know the guy, though I didn't know him at the time, and he can be rather acerbic. He was essentially kicked off this committee, and they wanted me to replace him, and it wouldn't be very time-consuming, and would I please agree to do it? And like a jerk, I said yes. I wound up, for six months, being on–it wasn't that bad in the sense that it probably only took a day a week out of my career. It was very educational for me. I learned an enormous amount.

It was so unlike any Caltech committee I'd ever been on. Basically, we often had meetings that ran from 9 in the morning with a lunch break until 5 at night and got nothing done. In part, because at Caltech, it's well-understood, all the work is really done by the chair of the committee. Other people get input, but the chair is there to be policeman. The chair on the LAUSD committee was totally different. He was a political beast, some bureaucrat. The other problem was that I had a very forceful personality, and for the first two months, it looked like I was leading people in the right direction. There was, again, a member of the state board of education who kept calling me up. "We're winning." Eventually, the final recommendation was a "compromise," that was totally watered down to nothing.

There was an incredible amount of politics involved. One of the opponents to my side was a Latino activist who threatened to go on a hunger strike–and I still remember, that the superintendent of the LAUSD was also Hispanic, as I was told by the LA Times reporter who was covering this, who I developed a good relationship with. The superintendent was Latino, so he could say, "Let him starve." I could never use that line, but it really amused me. It was politics. Again, from those days, it was nasty. Given the way politics is now, I wouldn't have been shocked, and it's mild comparatively. But I got involved in this nasty politics, and it was not a pleasant experience, but I learned a lot. My side thought I put up the good fight. I felt we hadn't gotten much done. I decided this was not a way I wanted to spend my time, so I never worked on it again.

**ZIERLER:** At the same time this is happening, one backdrop, at least chronologically, is the widespread adoption of personal computers, that computers were in the homes, in the classroom, and were increasingly becoming an educational tool in math. Were you following these developments?

**SIMON:** Yes, and no. Remember, this was at the time when I was the *PC Magazine* columnist for computer math. I knew about the more sophisticated tools. I didn't know much about the tools that were available to high schools. This was 2000. We didn't really discuss it in the committee. There may have been some computer workbook, but it was not like it was ten years later.

**ZIERLER:** The math you were thinking about was not the math of computers, it was pen and pad.

**SIMON:** It was definitely pen and pad. The material, in principle, was the same material that was done in the traditional curriculum, or at least a subset of what was done in the traditional curriculum. It was our argument that certain topics shouldn't have been there. One of the things that's always been a huge flashpoint in the math wars is the importance of the formula that solves quadratic equations. And tracking came up peripherally. It was very interesting. H.H. Wu, who I mentioned from Berkeley, was also on this committee. Except when he attended, which was not that often, he attended by Squawk Box. He phoned in on a telephone.

I didn't, of course, know that tracking was, by this point, considered a sin. Even though I met some high school teachers who were quite sensible, although tended to lean in the other direction, but sort of admitted on the side tracking was really necessary, it made no sense not to track. If they had a really good student, since they couldn't track them, they skipped them. But the first meeting, I started saying something about tracking, and said some things that in the context, were just terrible. Before I finished, the voice comes out of the Squawk Box, "What Professor Simon means to say is," and he cleaned up my language perfectly. But as I said, it was an interesting experience.

I understand why educational bureaucracies get nothing done. It's incredible. And it got nasty at some point. By the time it was done, I had input, but I was not officially allowed to vote on the final committee report because one of the opponents had discovered that one of the computer books I'd written was published by McGraw-Hill, and McGraw-Hill, of course, has textbooks. It was claimed I had this terrible conflict of interest. It was really quite an experience.

**ZIERLER:** Did the articles you wrote for *PC Magazine* demonstrate for you that you needed a longer format to have your ideas? Is that where the idea of having computer books, monographs, essentially, came from?

**SIMON:** Totally different. No. No. The *PC Magazine* articles were on specific things, and they were certainly long enough. I'd learned they were supposed to be so long, and I became an expert in writing up a software review in 500 words. That was not the issue. Through some CompuServe forum, I'd hooked up with a guy named Woody Leonard, who already was writing computer books. The first version of Windows that used more than the original 640 kilobytes–in those days it was not gigabytes or megabytes, but kilobytes.

It was using more than one megabyte of memory. There were technical issues involved with the structure of the processes were used. There was also this discussion about shifting over to OS 2. There was this incredible mix, but it was clear the first version of Windows that used more than a megabyte, Windows 95, was coming out. Woody suggested we write a book about Windows 95, a user's manual, as it were, but for sophisticated people.

**ZIERLER:** What was your insight that would not have been possible from a regular computer programmer?

**SIMON:** I just felt we could do a good job of writing it. Our schtick that made it different–we had two schticks, actually. The first was, we decided we'd write with a certain amount of humor. I don't know whether it was good or bad humor. But I think I mentioned last time, the book was called *The Mother of All Windows Books*. Saddam Hussein had talked about the mother of all battles, so we called it that. We had these icons that had discussions with each other in the margins about what was going on. They were essentially alter-egos for the two authors. One of mine was CTO Mao, and the other was Erwin, who was Schrödinger's cockroach.

Woody had heard a story that somebody at IBM had written some kind of technical manual for IBM, which had mentioned the Schrödinger's cat paradox, and some PR person at IBM was aghast that IBM would put something out involving a dead cat. They insisted the cat had to be changed to a cockroach. IBM had a book that discussed Schrödinger's cockroach. We felt this was so fine, we invented a character called Schrödinger's cockroach. The book had some amount of humor, and it sold actually rather well. I still met people who really felt it was the best Windows book they saw.

The books that sold best in that era were things like *Windows for Dummies*. There were imitators. We wrote a book that was intended to be Windows for not-dummies. It was a very interesting time. By 2005, the PC revolution was done, but the time of the revolution was remarkable, the developments and excitement. It really was an exciting time. It was an interesting hobby to be involved with, even though it probably meant I wrote fewer papers.

**ZIERLER:** It had wide appeal? All kinds of people bought the book?

**SIMON:** It probably sold 60,000 copies. A math book sells 2,000 copies, and it–now, of course, you can learn some of the ins and outs of things it isn't easy to learn about. Windows 11 came out, so I did a Google search and found some videos that told me about hidden aspects of Windows 11. Actually, when I learned about it, they said, "This is in Windows 10," which I didn't know. There are lots of things that get hidden in the operating system. In those days, you couldn't use Google. Google didn't exist. You'd get a book like ours that would give you lots of tips. How did we learn? We experimented a lot and talked to some people at Microsoft.

**ZIERLER:** How much of being EO was a drain on the rest of your responsibilities?

**SIMON:** It was not really so bad. There were two or three reasons. One is, EOs have less responsibility than being a department chair at many places because the division chair does some of those things. Another is that Cherie really was fantastic in terms of taking the load off of me. She never did inappropriate things, but there was a lot of nonsense that I could ask her to do, which I normally might have had to spend time on, myself. The only negative thing was, many times, something came up, and you were the person who had to handle it. Unlike if there's a paper that has a deadline, you're a week late, it's no big deal. But something comes up, not only are you responsible, but you have to solve it today because if you don't, it's too late. And that came up every once in a while. Wasn't that often. It was probably fair that I only had to teach two quarters instead of three quarters. In terms of time, it took about as much time spread out over the year as a course, maybe a little more than that.

**ZIERLER:** Situated between a regular faculty member and division chair, what power or role can the EO play in things like hiring or tenure decisions?

**SIMON:** That has actually nothing to do with being EO. There's a hiring committee. In math, particularly, it's different from physics because the division chair–it's very strange. Math hiring at Caltech is different from almost any other kind of science hiring because if a biologist is coming up for a promotion or being hired, the chairman of biology can explain what the person's done to the other members of the Council of Barons, the other division chairs. You can describe it to them. Mathematics is such an esoteric subject that it's really true that it would be hard for a mathematician to explain why exactly the other mathematicians are so excited about someone. The technical background is not something that many of the other people on the Council of Barons have seen. It gets much worse because this has to be explained by the division chair in PMA, who's not been a mathematician ever.

For that reason, the hiring committee actually meets with the division chair. The EO has no special significance, at least in my era, except the EO was always one of the people on the hiring committee. And for my entire time on the faculty, probably until the last two or three years, I was on the hiring committee, and I would often meet with the division chair the day before he had to present a math appointment to try to prep him on the appointment he was talking about. I had a lot to do with appointments in math during my time here. In fact, the year I arrived, it was almost unheard of until then to not promote someone from assistant professor. There was someone who I felt was OK but not really the caliber we should've been looking for.

I convinced Robbie Vogt, and we figured out a way of essentially–since the division chair has to put an appointment through, the division chair, if everybody is unanimous, can go to the IAC and say, "I need you guys to help me kill this appointment." He didn't have to do that, but I've had something to do with hiring. The fact that I was EO was irrelevant. I was a key person in mathematics hiring my entire time at Caltech.

**ZIERLER:** Let's end on a technical discussion. We talked last time about your pivot into orthogonal polynomials. We really didn't talk about some of the individuals who were relevant in this transition for you.

**SIMON:** You have to go back a little further. The key transition, in many ways, which wasn't so much a transition but was a pivot, was what I referred to last time as the singular continuous revolution. Singular continuous spectrum is a mathematical possibility that–one of the things I joked about was, the first part of my career, I spent most of my time trying to prove that singular continuous spectrum never occurred, and the last half of my career, I tried to prove it always occurred. My first contact with it was in understanding the issue in few-body quantum mechanics, either two-body or N-body quantum mechanics. At the time, my advisor, Arthur Wightman, referred to this singular continuous spectrum as goo because it had nothing to do with either scattering or bound states, which were the only things that seemed to make sense for these few-body systems.

Its absence was the no-goo hypothesis. There were lots of results from the mid-70s until '85 that essentially verified this, and I was involved, although not so centrally, in some of these things. In the late 70s, a very inventive British mathematician named David Pearson found a rather surprising but simple example, where you, in fact, got this singular continuous spectrum. And then, Avron and I found–I'll come back to what was key to this–that in one of these almost periodic, but it was still regarded as sort of a curiosity. In the almost periodic end, one of the things that came to the fore was the general analysis of what are called rank one perturbations, what happens to spectrum when you perturb one dimension in the space. It was a general formalism.

Singular spectrum was clearly associated with some particular function that entered, and it probably was '92 or '93 at a point when I really was spending time on computers. I was still doing some interesting things, but we had a visitor, so I often benefitted by people who, because of who I was, invited themselves to come to Caltech. There's a German mathematician who I'd had interaction with from the 70s named Weidmann. He became a big fan of some things I've done. Many of the people who'd invited themselves were, in fact, his students. Later on, a key person, who was for many years the chair at Rice, was my post-doc for a number of years, David Damanik–there's Rafael del Rio, who's one of the key people in the transition an undergraduate in Mexico, then was a graduate student in Frankfurt, where Weidmann was, and then returned to Mexico City, and he invited himself to come.

"Sure, why not?" He came for a month, and he gave a seminar that involved this funny function, and he proved a rather strange result, although his proof was very complicated, and it was clear something better should be true. He gave a talk on it, and within two or three days, I realized that first of all, there was a much stronger result than what he'd proven that was true that involved what we call Baire generic sets. Essentially, the exact result he had, I found a very easy proof. But it was clear there was a somewhat more subtle result that would be much more interesting. He and I started working on this, and as had happened earlier, it must've been that Tom Wolff wasn't in town because I came across a problem in harmonic analysis.

At an earlier time when I had a problem in harmonic analysis, I brought in Tom Wolff, and we wrote a paper I may have mentioned. This time, he wasn't around, so we involved Nick Makarov. And we had these discussions. At one point, Cherie said, "del Rio came to me and said, 'I come into this office, they talk, and I can't understand a word either is saying.'" But we had these back-and-forths, and we eventually found a rather nice solution to this problem. There was clearly this large explosion of results that really proved, in some ways, this singular continuous spectrum–you needed things not too close to the usual, but once you were out of the usual, it was actually quite a common phenomenon.

I should also mention with this result that del Rio, Makarov, and I proved, it turned out that someone else had proven the same result. There's a guy named Sasha Gordon, Alexander Gordon, who was originally a Russian mathematician, student of Molchanov, who I first met in Moscow in 1981. When I gave these lectures then on the work that Avron and I had been doing on almost periodic Schrödinger operators, Molchanov realized that Gordon had a result we should bear in mind. I was introduced to him, and he gave me this proof. The most spectacular result that Avron and I have in our papers was, again, a result on singular continuous spectrum in that context that was a combination of things we'd done earlier and this work of Gordon, so I was very aware of Gordon.

At the time, I really felt he had not gotten the credit he deserved, even though we were careful to give him credit. One of the problems is, even if I'm writing about something someone else has done, in this case I had contributed quite a bit, but even if I haven't, I often get a lot more credit than they get because I can write in a way that people can understand it. And I always felt bad about that. Again, Gordon had proven the same thing we'd proven with slightly different methods, and he never really got the credit he deserved. He wound up leaving the Soviet Union after its fall.

For a while, he finally did get a position at one of the colleges in North Carolina, where Molchanov was working then. But I always felt a little guilty that he's not gotten the credit he deserved. For example, he died recently, and his partner contacted me. I told her I thought I might've been responsible, and she said, "No, he always felt you were nice." It's a funny thing about science, people often don't get credit they deserve, and someone else gets some of the credit they should've gotten. I did what I could.

**ZIERLER:** What would this look like in an ideal situation for him to have gotten the credit he deserved?

**SIMON:** If he'd gotten the credit he deserved, when he came to the United States, he wouldn't have had trouble getting a position. He had a nonacademic position for a few years, and his advisor, Molchanov, had to work really hard to get him a position. He shouldn't have had trouble getting a position. He was much better than that. He was rarely invited to conferences he should've been. A few years later, actually as part of this series I wrote, there's a paper that he was coauthor of, and he got credit for that. That's a highly quoted paper, and he got some credit for that, so I'm happy about that. But credit is a funny thing in this business.

**ZIERLER:** For our next talk, that's going to be one of the themes because the number of awards and honors that you received after the year 2000, it's remarkable just in terms of the number, but also the chronological cluster.

**SIMON:** We'll leave with the wisdom of the division chair before the current one. He once said to me, "One of the things I've observed about awards is, they don't obey Fermi statistics, they obey Bose statistics."

**ZIERLER:** Would you please translate that? [Laugh]

**SIMON:** As you know, fermions repel one another. They don't want to be in the same state. And bosons condensate. He was observing that the clustering you observed from me was not an unusual phenomenon.

**ZIERLER:** There you go. [Laugh] Last time I said we'd pick up in the new century, after 2000. We had so much to revisit. Next time, for real, we'll pick up in the 2000s.

**SIMON:** Well, I would point out that at least the Codes and the math wars extended beyond 2000. Of course, the math wars have just reignited. There's currently a petition against the new framework that has a lot of Caltech signatures. Not mathematics because mathematicians are oblivious, but Preskill signed, I signed. It's the exact same fights, but in this new context because you can somehow bring in white privilege.

**ZIERLER:** We'll come to that, too.

[End of Recording]

**ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It is Thursday, December 23, 2021. Once again, it is my great pleasure to be back with Professor Barry Simon. Barry, once again, thank you for joining me. It's great to be with you.

**SIMON:** Great to be with you.

### Spectral Theory

**ZIERLER:** Today, we're going to focus, finally, on some post-2000 work. I'd like to start with a technical discussion. We've already talked about your transition or pivot to orthogonal polynomials. Tell me about your work specifically in spectral theory of orthogonal polynomials. And maybe we could just start with some definitions. What is spectral theory?

**SIMON:** It's actually a hard thing to define. In some sense, it goes back to the discovery of the spectral theorem by Hilbert at the start of the 20th century, and its extension to the unbounded case by von Neumann about 1927, which was, in fact, critical to quantum mechanics. The spectral theorem says, if you're given what's called a self-adjoint operator, which is any observable in quantum mechanics. It has, associated with it, a set of certain so-called spectral measures, and it's the study of those measures and what they tell you. If the observable happens to be the Hamiltonian, what they tell you about the dynamics.

The relation between dynamics as defined by an operator and these spectral measures is what's called spectral theory. But even if it's not dynamics, it's a way of relating these spectral measures to various properties of the operators. If you're given the operator, you can construct the corresponding spectral measures, and in some cases, there's a distinguished vector, so there's a single measure. At least in some cases, you sort of are given how to go from the operator to the spectral measure. And there's an inverse problem, namely, if you're given the measure, can you go back to the operator? In the context of one-dimensional quantum mechanics, this was actually studied by Gelfand and Levitan, in a famous paper, about 1950, that physicists and mathematicians often use because sometimes the spectral measure is completely described by giving scattering data and information on bound states.

The original Gelfand-Levitan is, "How do I go from scattering data plus bound state information to the potential?" It's an absolutely beautiful piece of work. They actually knew this was sort of a continuous analog. If you made space discrete, the corresponding differential operator became a difference operator, and difference operators corresponding spectral measures associated with orthogonal polynomials. The issue of how you go from a spectral measure back to the underlying difference operator is solved by the theory of orthogonal polynomials. And Gelfand and Levitan said, "Oh, this is a continuous analog," and they were actually motivated by the theory of orthogonal polynomials.

I can't resist, even though it will sound like I'm making fun of Mark Kac, but he's a great mathematician. But somehow, he didn't know the history, and about 20 years later, he went around claiming he'd discovered that the discrete analog of Gelfand and Levitan was the theory of orthogonal polynomials, somehow not realizing they'd been motivated by that. He had this great line, "Be wise, discretize." I remember hearing this a couple of times, and one time, Peter Lax was in the audience, and I was next to him. I said, "Peter, I really don't understand this. This is what Gelfand and Levitan did." Peter looked at me and said, "I know, but he's having so much fun."

There's this connection I actually knew long before I started doing "spectral theory", and in fact, my work I may have referred to a couple of sessions ago on my own approach to inverse scattering was motivated by the fact that in the theory of orthogonal polynomials, I knew there was a different way, a continued fraction way, of solving this inverse problem. That suggested to me there was another approach besides Gelfand-Levitan to doing the inverse problem. I'd always known there was this connection, but in fact, there are natural questions about asymptotics of orthogonal polynomials, classification of orthogonal polynomials. There was a huge community working in this area, and I was only vaguely aware it existed.

About 1985, I visited the Arizona State University in Phoenix, and there was a fellow there, a mathematician originally from the Egypt but who'd been in the US for many, many years, named Mourad Ismail, who said, "You really should look at orthogonal polynomials, as it's close to what you did." And to my non-benefit, I didn't take him up on it then. Because of this sequence that I first got into the exotic spectral theory, the work I'd mentioned last time, I think, with del Rio–the theory of orthogonal polynomial sort of has two different sides, that I've named algebraic and analytic.

Algebraic means, really, the study of special families. There are all sorts of interesting algebraic relations between them. This is sort of much of the classical subject. The analytic is more trying to understand relations between the corresponding measures, which they didn't quite understand were spectral measures, and the properties of the orthogonal polynomials. There, the big gun was a very interesting fellow named Paul Nevai, who was Hungarian originally, I think he got his PhD in Moscow, but has spent most of his career at Ohio State. I was sort of aware of them, but not very closely. But Killip had discovered a conjecture of Nevai. It became clear when Killip and I were doing our work that this was intimately connected with exactly the set of problems that this orthogonal polynomial community had been working on.

In particular, as part of our work, we proved the conjecture of Nevai. Actually, we proved it up to a remaining fact. I had a post-doc named Dirk Hundertmark. It was clear, this basic fact was probably something he and I could work on. And we did this extra fact and proved Nevai's conjecture, so I got in contact with Nevai. And I still wasn't quite drawn into the subject as much. I also mentioned that Sergei Denisov had come as a post-doc, and he started lecturing on the theory of orthogonal polynomials on the unit circle. I had realized there was a connection between Schrödinger operators and orthogonal polynomials on the real line.

I'd never heard or understood this theory of orthogonal polynomials on the unit circle. It clearly was very similar. There were similarities, but also interesting differences. It became clear to me that there was this whole community working on orthogonal polynomials, and the basic questions they were asking could be translated into questions in the spectral theory of the discrete analog of the Schrödinger equation. This opened up the possibility that, "Well, maybe ideas that had been developed on the Schrödinger operator, the spectral theory side, if you will, could provide input into what the orthogonal polynomial people were interested in. But conversely, some of the ideas they developed might give new insights to the spectral theory side."

That's really what I focused on from about 2000–not that I didn't, every once in a while, go back and write some paper that was related to the earlier areas, but I really focused on this interrelation, and it meant that I was dealing with a very different community of people. It's true that as the years develop, you interact with different people. But there was sort of a continuous, smooth evolution. Particularly, the mathematical physicists working on non-relativistic quantum mechanics, quantum field theory, and statistical mechanics was one big community, and the orthogonal polynomial community was a very different community. There was essentially, until I got involved, really no one working in both areas.

And it's a very different community. It's a much friendlier mathematical physics community. I know one guy who worked in mathematical physics who got interested in probability who said to me, "It's amazing, probabilists all support each other, and the mathematical physicists all have a tendency to undercut each other or each other's students." And there's some truth to that. It has to do probably with personalities. But in orthogonal polynomials, everyone gets on. It's a very much more friendly community than the mathematical physics community was, at least in my time.

**ZIERLER:** Would you offer some conjecture as to maybe why that is?

**SIMON:** I think more than anything else, it has to do with certain personalities. If the community's a little bit of a backwater, people tend to support each other. There isn't so much of this aggressive dog-fights-dog. If you look at theoretical physics, my impression is, traditionally, the high-energy community is not particularly friendly to each other, whereas I think the condensed-matter physicists tend to be much more supportive of each other. I think this is, again, connected with the fact that when you're at the "cutting edge", it draws aggressive people. I really think, more than anything else, it has to do with the personalities. Not me, of course. I'm always sweetness and light. But some of the other leaders.

**ZIERLER:** [Laugh] Just to clarify, spectral theory of orthogonal polynomials, is that the theory of OP, or are there other competing theories?

**SIMON:** It's not competing theories. It's really a set of tools to understand the issues that people in orthogonal polynomials are interested in. It may be a misnomer to say the spectral theory of orthogonal polynomials. It's really spectral theory ideas applied to orthogonal polynomials. It certainly is true that I was able to provide insight into a number of things. I still remember one issue that it just occurred to me, if you took the result that Avron and I had proven about boundary condition independence of the density of states in these almost periodic Schrödinger operators, and you translated that into this orthogonal polynomial language, you got an equality of two things that didn't look equal.

I remember, as an aside, at some conference, people seemed to think it was an incredibly deep, difficult thing, and to me, the proof was trivial because you just carried it over. But I was looking at it from a very different point of view than they were that let me do all sorts of things that they hadn't been able to do. On the other hand, I also discovered they had some very interesting points involving potential theory ideas that turn out to be very useful. There are people doing Schrödinger operators who, because of my writing on the subject, have gotten very interested in using these potential theory questions. It's been a very fruitful clash of cultures. The Romans and the Britons come across each other. It really is a clash of civilizations in some sense, and it can sometimes enrich both civilizations.

**ZIERLER:** Reflecting on the differences between these two communities, the mathematical physics community, where you're always straddling math and physics, as the name would suggest, in orthogonal polynomials, would that put you further into the math or physics camp?

**SIMON:** Well, that's an interesting question. Certainly, in orthogonal polynomials, they don't think of themselves as having much to do with physics. Although, traditionally, many of the families of orthogonal polynomials that have been studied came out of physics. You look at the names associated, there are several classes of famous classical orthogonal polynomials. Jacobi polynomials, Hermite polynomials, Laguerre polynomials. They're all mathematicians, but they all also did important things in physics. Orthogonal polynomials often have a role in physics, and it's certainly true that there are questions in orthogonal polynomials that people doing quantum computing need to know about because these orthogonal polynomials come up.

But certainly, the people who do orthogonal polynomials are either members of the AMS or SIAM. There are, of course, lots of applications in other kinds of mathematics, and there are some people who would say some of the theory of orthogonal polynomials should be regarded as applied mathematics, so the Society of Industry and Applied Mathematics, SIAM, actually has a section that essentially studies orthogonal polynomials and related ideas, whereas, for example, the APS doesn't even have a section in mathematical physics. Indeed, I now am a member of SIAM as well as the AMS and the APS.

**ZIERLER:** By way of introduction of your interest in promoting his work, I wonder if you can talk a little bit about Samuel Verblunsky and his legacy.

**SIMON:** That wasn't really promoting. Killip and I had this lovely result about orthogonal polynomials on the real line, and we realized it was really an analog of a result that Szegő had proven when he was 19 years old. In fact, the paper was published when he was a lieutenant serving in the trenches of the first World War. A result on, essentially, orthogonal polynomials on the unit circle. Although, originally, it didn't appear that way. It appeared in a totally different context. But Szegő, a few years later, realized it really was a statement about orthogonal polynomials. Szegő's original idea, he only did it for measures that are called absolutely continuous.

For the spectral theory ideas I was interested in, this question I raised about mixed spectrum that we answered and, in fact, are answered by the best version of Szegő's theorem, involve extending it to allow so-called singular continuous pieces. And in much of the orthogonal polynomial community, if you ask people who first proved this, one of the answers would be Kolmogorov in the 40s. In fact, Kolmogorov only proved a special case. Some people would say, "It appeared in a book Szegő wrote in the 1950s." But that didn't seem right to me, so I sent a message to Nevai asking if he had any idea who first had proven Szegő's theorem, essentially in the most clear analog of what Killip and I had.

Nevai didn't just write back to me, he wrote back to me CC-ing 20 people, who I didn't realize at the time–this was my first exposure to these names–were all the leaders in the theory of orthogonal polynomials. Many of them are now buddies of mine. He said, "It's an interesting question you raise. I have no idea. Maybe somebody else that I've copied on this knows." I got back a reply from a fellow named Leonid Golinskii, who's a very sweet guy. It turns out, not only is he doing orthogonal polynomials, but his father before him also did orthogonal polynomials in this great Russian tradition. I say Russian, although they're based in the Ukraine, so they would probably be insulted by me calling them Russians.

And they're, in fact, Ukrainian Jews, to boot. Golinsky wrote back and said, "I can't get ahold of the paper because it appears in a journal that isn't available to me, but I'd heard it might've appeared in"–and he gave me a reference to a paper I'd never heard of that was in one of the London Math Society journals, I can't quite remember whether it's Proceedings of the London Math Society, but one of the LMS journals, by someone named Samuel Verblunsky. The reference he gave, I think, was one of two papers that appeared in 1933. As I read these papers, my mouth fell open because not only had Verblunsky been the first to write it down in this form, but the paper had all sorts of ideas–this was at the time I was beginning to write my book on orthogonal polynomials on the unit circle–that had been rediscovered.

Somehow, he'd never gotten credit for these papers. It's a little bit strange. I think, to some extent, the Russians may have consciously suppressed his work. There was clearly, on some other work Verblunsky had done, some bad feeling with Krein and Kolmogorov. You could see there were a couple of Russian papers that mentioned him, then they started only referring to the standard Russian expert who had written papers. It was a very strange phenomenon. They didn't give him credit. I discovered in this book of Szegő, where people had been saying this result first appeared, a reference to Verblunsky's paper, so I asked my secretary, Cherie, to see if she could figure out if this paper was ever referred to in the book.

Now, these days, that would be very easy because a book like this is digitized, it has a reference number, and you just search on the reference number. But the book wasn't digitized in 2000. Cherie, being Cherie, went through page by page, came back, and said, "No, it's not referred to." It became clear that one of the things I should be doing when writing this paper was to give Verblunsky some credit for what he'd done. And there were several very good opportunities for this because the most basic coefficients that entered in the theory of orthogonal polynomials, a sort of analog of what are called the Jacobi parameters for the real line case, didn't have a single name. They had, like, ten different names.

The most common name was reflection coefficients because of some crazy application of orthogonal polynomials to geophysical problems. It was a terrible name, so I gave the name Verblunsky coefficients to these parameters, which I'd say now has stuck. There are various results that have been attributed to other people that I decided I could just rename after Verblunsky. And since my book has become the standard reference–and I felt very good about doing this. He actually lived quite a long time. He passed away about 1996 or '97, so before I got in the field, but not so long before. It's been interesting to take someone from the ashes of history and reintroduce them into the subject.

**ZIERLER:** An overall question on your decision to transition or focus on orthogonal polynomials. Was this part of a larger trend in mathematical physics among people in the field you would consider peers? Or was this something where you were out on your own, essentially?

**SIMON:** Well, depends on which part of the field you talk about. There's no question that on the side that looks at almost periodic Schrödinger operators, non-relativistic quantum mechanics, I dragged that part of the field into the subject. Now, almost everyone, not quite everyone, who writes about that will immediately try to address the question, "Oh, I can do this for Schrödinger operators. What about orthogonal polynomials on the unit circle?" I really did drag that whole part of the field.

On the other hand, the people who tended to focus on more traditional parts of non-relativistic quantum mechanics in three dimensions or multi-particle quantum mechanics and statistical mechanics were not happy I had moved into mainly doing one-dimensional stuff. You have to remember that by 1990, for a variety of reasons, I was mainly doing things in one-dimensional theory. It wasn't so much that I made a conscious decision as my research led me in this path. But it's quite clear that many of those people regard me as a traitor for leaving the field. And it's still true.

My last NSF grant got turned down because for whatever reason, even though I was careful in the grant to say, "This is not a proposal in mathematical physics, it's a proposal in the theory of orthogonal polynomials," which there really is a whole group of people supported by the NSF in, somebody then said, "Oh, Barry Simon?" threw it in mathematical physics. One of the reviews gave me a fair, which is middle-ranking–it's very hard to get a grant with a fair ranking–saying, "This is an interesting grant, but it has nothing to do with mathematical physics." I said it has nothing to do with mathematical physics. I'm sure this is someone who felt it was terrible of me to leave the interesting parts of mathematics and start doing this crazy orthogonal polynomial stuff.

**ZIERLER:** Perhaps the word traitor is extreme, but is the notion that you left the field a fair assessment of what you actually did?

**SIMON:** I pay attention to it, and I still write an occasional paper. I certainly wrote a number of papers on the subject. The current main project I'm working on is a book on statistical mechanics of lattice gases. That's going back to things I did 40 years ago. On the other hand, it is certainly true that I focused primarily on subsets of what I did in the 70s. That's partly because as we discussed, when I went to Caltech, I realized, because of the array of colleagues I had, I would probably be narrowing my interests. It's not so much that I "left the field", but my interests did narrow.

**ZIERLER:** Did this change the kinds of graduate students that you attracted?

**SIMON:** Probably to some extent. In the 80s, I had a few graduate students who really were not very mathematical, but who wound up with jobs in physics departments. It's very hard for me to imagine a grad student I had after 2005 who would wind up in a physics department. Even one guy who had started out as a graduate student in physics is now in a math department at Rice. So in some sense, it affected it a little bit.

**ZIERLER:** A general question as it relates to all the work you've done on editorial boards of various journals. Aside from the desire, obviously, to perform a service to the community, when is this work an asset to your own research insofar as it simply forces you to stay on top of the literature more than you might otherwise?

**SIMON:** First of all, if you look at all the editorial boards I'm on, it's a phony. The one editorial board I was on for 35 years was Communications in Mathematical Physics. I was a real editor. I handled 50 papers a year, did a lot of work sharing in some of the bookkeeping, but it was a lot of worthwhile effort. All the other editorial boards, I only agreed to be on them if it's understood that they're using my name, and I don't have to do any work for it. Often, I get approached, "We're not going to ask you to do anything, but we'd like to put your name on the masthead." The Journal of Spectral Theory, when it was being founded, I was consulted, and I'm still sort of one of the key advisors, people the editor-in-chief–there's sort of a group of the editor-in-chief, the managing editor, and I that deals with many of the policy issues of the first level. The founder of the Journal said, "We really want to have you and Elliott Lieb on the editorial board, but we won't ask you to do anything."

**ZIERLER:** What, then, is the political value of those affiliations, in terms of setting the trend for where the field is going or even hiring decisions for faculty members?

**SIMON:** I don't know. People are on editorial boards because they're doing a service to the community. It is totally ignored in hiring decisions, in chairmen deciding whether someone deserves a raise. It's just something one does because you're doing a service to the community. Like refereeing. Sometimes, you referee something, you may learn and understand something you wouldn't have otherwise, and it can help your research. But it's mainly putting back in time, and it's the right thing to do because after all, somebody else is refereeing your papers.

**ZIERLER:** In a similar vein, the three honorary degrees you've been awarded, in 1999, the Technion, University of Wales in 2006, and in Munich, the Ludwig Maximilian University in 2014…

**SIMON:** Let me just correct you. The people in Swansea would not be very happy to just be called the University in Wales.

**ZIERLER:** Let the record stand, we're talking about the University of Wales, Swansea. Why these three institutions, and why at that time? Can you make these three seemingly random awards make sense?

**SIMON:** How are honorary degree recipients picked? There's some committee either somebody's on, or other faculty are asked for recommendations, and there's a decision that there's someone there pushing, usually on the faculty at that institution. The first was the Technion. It's no coincidence, Yossi Avron, who calls me his rebbe, was on the faculty. Not only was I his mentor, but one of his students and one of his grand-students, I was the mentor. Yossi had the idea that he really wanted to push this. That might not have been enough. The Technion is a big bureaucracy. But it happened there was a quantum chemist, who had done complex scaling, which we discussed earlier, who knew of my work. And Yossi knew this, so he also came on board. And there was someone in electrical engineering who knew me.

There were people in three departments lobbying the committee that decided who got an honorary degree, and I got the honorary degree. In Wales, it's a much smaller university. There's a fellow named Aubrey Truman, who originally came to Princeton in the late 70s because Arthur Wightman was there, but he learned a lot from me. He decided he wanted to have the International Congress of Mathematical Physics in Swansea and twisted my arm so I was chair of the scientific committee, and he was the local organizing committee. We worked together, and we actually spent some time there. He decided to lobby for this. It's not actually an honorary degree, it's called an honorary fellowship. They have strange names for everything.

My favorite story is that while I was there getting this honorary degree, he said, "Oh, I have to introduce you to the vice chancellor. He's the head of the university." I said, "I don't understand. If the head of the university's the vice chancellor, who's the chancellor?" "Oh, that's Prince Charles, of course." Munich is a big center of mathematical physics, has been for a long time. I think the guy pushing hardest there was a fellow named Heinz Siedentop who'd spent several years as a post-doc at Caltech in the work that'd gotten him the most attention. And there were other people on the faculty there who'd helped push it.

I'm a member of the Austrian Academy of Sciences because Walter Thirring, who was a big power there, decided to push for it. These are always decisions made by local people, and you need someone who's decided that they want to spend a fair amount of effort trying to get someone or other an honorary degree.

**ZIERLER:** Do you have any insight as to why Caltech does not confer honorary degrees?

**SIMON:** I know Dick Feynman was terribly opposed, but I'm sure he was not involved enough. But if anyone had ever asked him, "Should we do it?" he'd say no. He turned down honorary degrees, two of the famous stories. In fact, one of the things I feel he was very rude about is that he really should've accepted Princeton's honorary degree because he owed it to Princeton. There's a famous quote you can look up on the web about Dick Feynman and honorary degrees. The first honorary degree he was offered was from Chicago, and there was a letter written where he turned it down that you can find. I don't think that's the factor, I just think somehow Caltech never did it. You have to decide, "If I haven't done it in the past, why should I do it in the future?"

**ZIERLER:** It's unfortunate for people like you who have received this, you really can't reciprocate on an institutional basis.

**SIMON:** Again, I shouldn't insult the people who pushed my degrees, but there's a pecking order in science. Usually, what happens is, it's people who are at good institutions but who owe something to someone higher up the pecking order. They're not doing this because they expect something in return, they're doing it because they feel they're paying you back. I'm sure all the people who worked to get me honorary degrees did it because they felt they owed me a debt of gratitude for what they got from me when I was their teacher, in some sense. For example, if there were honorary degrees, I might've pushed to get my advisor, Arthur Wightman, an honorary degree. That's the analog.

**ZIERLER:** I asked you about different kinds of graduate students in your latest transition. What about your collaborators, all that you've written in the past 20 years? Have you had different kinds of collaborators or people you've kept working with over and over again?

**SIMON:** There are certainly people I've worked with over and over again. As you may know if you look at the web, I think I have, at this point, 115 coauthors. Of that 115, most are fewer than three or four papers. But I certainly have people I've collaborated with many, many times. My most frequent collaborator is Fritz Gesztesy. My second and third are Elliott Lieb and Yossi Avron. I still remember the day that we submitted the paper that put Fritz ahead of Elliott, he walked into my office all excited that he'd finally done it. Elliott and I wrote a lot of papers when we were both at Princeton. Actually, we've done very little since I left Princeton. Fritz got more responsibility, so he couldn't visit Caltech as often. He didn't quite shift as thoroughly into orthogonal polynomials as I did.

We sort of stopped doing things together. I'd collaborate with many of my collaborators because they'd come visit me for a month or two. But that's harder to do as you get more responsibilities. For the last 15 years, I've had a series of over ten collaborations, I'd have to count up how many with two people who were post-docs together around 2002 or '03, and we have a paper we just submitted last week. Pre-COVID, they would come to Caltech for two weeks, and we'd work hard together. Zoom actually is not bad for working, so we've continued to do some stuff.

**ZIERLER:** In 2009, were you more happy or more grudging to become executive officer again?

**SIMON:** In many ways, some fraction of issues with the department, I was being asked to do because the division chair didn't trust or like the executive officer. There wasn't another obvious candidate. Actually, there was an obvious candidate, Ramakrishnan, but he didn't want it, and I said, "Fine, I'll do it," and he followed me. It was grudging.

**ZIERLER:** Second time around, did you have an easier time of it?

**SIMON:** I probably did, but I think that's because there were harder issues the first time around. The first time around was harder, not because I didn't have the experience, but because of the issues. Tom Wolff was, I think, 48 when he was killed in an automobile accident. It was really very traumatic. It was a very tough time. Didn't have to do with whether I did or didn't have experience. We happened to have a lot of retirements. There were a number of factors. That was also the period when the new curriculum came in, which increased the load of the EO for various reasons. It was easier the second time around, but it was not because I knew the ropes. The issues just weren't as bad.

**ZIERLER:** What was the impact on math in the new curriculum regime?

**SIMON:** We had to figure out how to handle the new advanced placement exams. Dealing with advanced placement, we found a very good solution in the end, but we found a very good person to do it. There was beginning to be a big push to accept students who had somewhat weaker backgrounds because they came from weaker schools. They were usually very smart but weren't up to the same speed. We essentially had a math camp, as it were, the summer before, figuring out who was going to do that. We actually found someone very good who, even though he left Caltech, would come back for summer. There were things like that, which just took time to set up and arrange that were, in my mind, at least, connected with the changes to the curriculum. It is also true that there were some things that were easier because I knew the ropes. I knew beginning of every year, I had to meet with the post-docs and explain to them the rules of the road, as it were. It is true that I did benefit to some extent from knowing the ropes.

**ZIERLER:** Now that I'm alerted to the distinction in your CV between real work versus honorary work with the editorial boards, your work for the IAMP on the executive committee and then as vice president, was that real work and a real commitment on your part?

**SIMON:** Yes, and no. First of all, it's not like, say, the AMS. Being the president of the AMS is a big deal. Even being the president of IAMP–the IAMP, every three years, has an international congress, and basically, you're organizing that conference and worrying about a few prize committees. It's not a terribly onerous job. It's also true that I had my arm twisted to be president in the early 80s, and I was just trying to set things up at Caltech, and I said, "No, I just don't have the time." I convinced someone else to take the job. It seemed like a little more work. Being on the executive committee, you get input, but it's basically just a few email exchanges. It's not like being the editor of CMP. Every week, you're worrying about something. These other things, every once in a while, something comes up.

### Late Career Recognition

**ZIERLER:** We've reached a point in the narrative where you have a number of prizes that are clustered together, and you gave a cute scientific concept behind that. In 2012, it's the Henri Poincaré Prize, in 2015, the Bolyai Prize, 2016, the Steele Prize, 2018, the Dannie Heineman Prize. Just to orient people who might not be familiar with these communities, is there one that's far and away more prestigious than the others?

**SIMON:** Maybe the Steele Prize. The Heineman and Poincaré are prizes in mathematical physics. It's a relatively limited community of people. I think people assumed that when it was my turn, as it were–the Poincaré Prize was only started just before 2000 is my memory, so there's this huge backlog of more senior people than me, like Arthur Wightman. It was clear my generation would come up around when I got the Poincaré Prize. Actually, Jürg Fröhlich, who's also my generation, got the Poincaré Prize the time before. But I think people would've been surprised if I hadn't gotten that. The Heineman Prize is a little bit broader. The Poincaré Prize really has been given to someone in the kind of mathematical physics I do. The mathematical physics that is the Heineman Prize has sort of varied.

About half have been to theorem-provers, but about half have been people like Murray Gell-Mann and Murph Goldberger, who are theoretical physicists that are somewhat mathematical, but wouldn't call themselves mathematical physicists, and we wouldn't call them mathematical physicists. But again, I don't think anyone was surprised that I got it. In fact, one previous winner wrote to me and said, "I'm really pleased to see you got it, but I can't believe you didn't get it years ago." But the Steele Prize for lifetime achievement, essentially, can be given to any American mathematician, so it's a bigger deal in some sense.

**ZIERLER:** As a matter of intellectual genealogy, Poincaré, Bolyai, Steele, Heineman, do you see yourself as part of any particular tradition for any of the awards?

**SIMON:** Steele and Heineman are people who gave money to set up the prize. They don't have a tradition. Bolyai, of course, that's a very different tradition. Bolyai was a Hungarian mathematician. It has a very interesting history. It was named after this relatively obscure Hungarian mathematician, one of the inventors of non-Euclidian geometry, about the 1820s. The Hungarian mathematical community, around 1900, decided they wanted to set a prize up that was supposed to be the analog of the Nobel Prize for mathematics. Of course, they didn't have the same amount of money as Mr. Nobel, so it didn't have prestige for that reason. But the first two went, in fact, to Poincaré and Hilbert. And then, the first World War came because they only give them every five years, and they stopped giving it.

It totally died away, then was reinvented after Hungary broke off from the Soviet Union about 2000. It was decided they were not going to be a Nobel Prize, they were going to give it for a book that had real impact on research. But the book had to be written in the past ten to eight years. Again, there was a Hungarian orthogonal polynomial person who thought my books on orthogonal polynomials on the unit circle were exactly the kind of thing they should be honoring. But he was chair of the committee, and he felt he couldn't properly push. Five years before I got it, he decided he couldn't really push effectively.

I was nominated, but he then made a point of not being the chair, but being on the committee the next time because he felt he could more effectively push for it, and it's clearly his doing entirely that I have that prize. Again, it's a nice honor. The Hungarians were very nice. But it's a relatively lower prestige prize than some of the others.

**ZIERLER:** When you were a Simons Foundation fellow in 2013, what did that allow you to do? And I'm curious if you had any interaction with Jim Simons as a result.

**SIMON:** Zero. This is the foundation. It has nothing to do with Jim Simons. I think I may have mentioned that I'd arranged that I was going to have a full year's leave the last year I expected to teach. Caltech has this arrangement where, by agreeing to retire, you get two years' pay without having to do anything, and I thought I was going to arrange three years because as part of taking the second term as EO, I got a promise of a full year's sabbatical. I was expecting in 2013-14 that I was going to have a full year's paid leave from Caltech. When the division chair and I were working on it, the provost–I can't imagine any other institution in the world where the provost gets involved with this minutiae with an individual–said, "If you go on sabbatical, you have to come back to Caltech," because they don't want you to go on sabbatical, get stolen, and you've tried out some other institution on Caltech's dime.

Many institutions have that. I remember when we stole someone from Berkeley, we had to pay Berkeley for his time. That's the purpose of the rule, and Caltech has that in place. But the provost decided the rule was, if I was going on scholarly leave, that wasn't really coming back to Caltech, so I could not have a sabbatical without essentially coming back and teaching for as long as the sabbatical. Well, Caltech has three quarters. I wanted three quarters' leave. He wouldn't give me two quarters, he'd give me one quarter, but I'd have to come back and teach at least one quarter. Then, I had the idea, since there was Simons money, "Suppose Simons would pay my salary for one of the quarters. Could I get two quarters off and then come back and do that?"

I had to negotiate with the Simons Foundation because officially, they're half support for half the year, where the institution pays for half the year, but this was two-thirds of a year. Anyhow, they agreed to that. But the only people I dealt with were the people who ran the foundation. I certainly had no interaction with Jim. I don't think I've had any interaction with Jim since the party I mentioned earlier.

**ZIERLER:** One of the more fun-sounding awards, Jew in the City Orthodox All Stars. First, what is that organization, Jew in the City?

**SIMON:** I'd never heard of it until I got this award. It's essentially a small organization run by a woman named Allison Josephs, who's a *baalas teshuva* [Hebrew; Jewish woman who became religiously observant]. She grew up in a conservative household but became really religious. She became convinced that there really was a need for an organization because of various people she'd talked to, particularly potentially people who became *baalei teshuva* [Hebrew; plural of *ba'al teshuva*] who realized that there wasn't a conflict between the secular world and being religious, that you could do it in both at the same time. She's since branched out, and it's actually a pretty big operation at this point.

They particularly focus on people who, for one reason or another, have gone off the derech, as they say, who had been religious but because of some bad experience, sexual abuse by teachers, all sorts of factors, but who are thinking maybe they want to come back. It's a very interesting, and I think worthwhile, organization she runs. It came about at the time that Sex in the City was the big show, so she called it Jew in the City. She decided to have these Jewish Orthodox All Stars, people who had somehow made it in the secular world. Joe Lieberman was an early Orthodox Jewish All Star. I think I was the second or third class. I'm not sure where she got my name, it just came out of the blue. But when I got the offer, I asked Rabbi Adlerstein if he'd ever heard of them, and he looked into them and said, "You should accept it."

It was a very interesting group, a mixed bag. I was one of seven all stars. There may have been one other academic who couldn't come for various reasons. I think it was an Israeli. One of the things she did, they have a very slick operation, there were three of us from the LA area, so she came out and did a video interviewing us. If you look at the videos online, they're kind of fun. One was a guy who, in fact, is in the Disney operation as a cartoonist, and one is the daughter of a big-shot in the fashion world, who actually lives about a block from me. She's Jewish-Iranian, I think, originally. She was not particularly observant, but she became observant, and she was given her own fashion line. She was a big-shot in the fashion world, and she was also a Jewish All Star. There was a reception that was actually at her father's house in Beverly Hills, the fanciest house I've ever been in.

**ZIERLER:** This is a reception you could eat at. [Laugh]

**SIMON:** Correct. And of course, there was a thing in New York. For them, it's a big fundraiser. It's a fine organization. In fact, they just put out a video. I tend to put up a shabbat shalom greeting video for my Facebook friends, and tomorrow, I'm going to put up a Jew in the City video. It's an interesting organization.

**ZIERLER:** More broadly, I know you don't have time to do kiruv on your own, but are you happy to play along when various Jewish organizations or even individuals want to interact with you or promote you as the famous yarmulke-wearing math and physics professor in the sense that that's good PR for *frumkeit* [Yiddish; the Jewish religious world]?

**SIMON:** There are two different things. One, I rarely get that kind of request. If I get that kind of request, and I don't think they're going to abuse it in some way, I'm delighted. But more often, I get a message like, "I had this crackpot idea about why the Torah explains string theory. What do you think about it?" I rarely totally ignore emails I get. There are obviously phishing emails. But I get a lot more of those than I get of, "Here's this guy who wears a yarmulke who shows you can exist in both worlds."

**ZIERLER:** How did the 2015 textbook for the American Mathematical Society come about? This is *A Comprehensive Course in Analysis*.

**SIMON:** One of the things Caltech has always had since I've been here is a graduate course in analysis. I taught it fairly often. Most of my teaching has either been topics courses that are very specialized in my research or, in fact, that course. Not that I haven't done other things. When I wrote the book on group representations, I taught a course on it. But that was much of the teaching I did, so I had a lot of experience with the textbooks, and I wasn't thrilled with them. I decided I'd write my own. The first term does real analysis, second term does complex analysis, which actually turned into two volumes, and the third has five weeks of harmonic analysis and five weeks of operator theory. That naturally led to what was originally supposed to be four volumes, but one was so big that Sergei Gelfand, the publisher of the AMS–the son of the most famous Gelfand–insisted that it be broken in two, which is why it's four parts but five volumes. As I was writing it, I realized it would be very natural to put in other things. I actually used it as a way of learning certain things.

I'd never really understood much about wavelets. That's a chapter that wound up in it. I did bonus stuff, and I polished it. I actually approached three publishers. One of them was Springer, which at that point, and it's still true, a lot of their book sales are not sales, they make a deal with universities. Caltech gets it because of some California consortium, but we have access to all advanced Springer math textbooks, therefore, we don't get individual royalties. I raised this issue with them, and their response was, "Your book really isn't for the academic world, it's for the business world, isn't it?"

I realized this guy didn't know what he was talking about. But then, I got moved very hard by Cambridge, which I'd been on the board of and know the editor very well, and Gelfand with the AMS, and eventually, I signed with the AMS. I knew it wasn't going to sell that well because, of course, book piracy is such an issue these days. There's a picture I can send you of the two editors I dealt with, and I've published a number of my books between them, at my 70th birthday conference. There was a small exposition area, and they were exhibiting their books. At that time, I was talking to Gelfand, and my book had been out for six months.

I said, "I'm sure they're already on the pirate sites," and he said, "No, no, no, they can't be. It'll be another year and a half." Well, one of my former graduate students was standing by, and he shows me on his iPad that the books are already on the pirate sites. It isn't that they've done terribly badly, but I would've expected them to do really well, and they haven't sold that much. I would've expected them eventually to sell as much as Reed-Simon. It's going to be a small fraction. I still regard them as my magnum opus. I really worked hard on them.

**ZIERLER:** Another fun award, maybe one that's particularly meaningful to you, the James Madison High School Wall of Distinction in 2016. How far back does the Wall of Distinction go? Did it exist when you were there?

**SIMON:** I don't think it existed when I was there. I don't have any idea how aware current students are, although the principal was at the awards ceremony. It's mainly the alumni association, which I don't think existed very much, but there are a couple of really big boosters. My brother has been somewhat active. I only learned about it because he learned about it, and he started pushing them. Very interesting. My year had a different Disney guy, the one who had invented the Shrek character. There were, again, six or seven people. In some ways, it was a more interesting group than–and it's because my high school has really impressive alumni.

**ZIERLER:** It's an amazing who's-who of alumni on that Wall of Distinction.

**SIMON:** I was aware of the fact before this that there was a period in time when there were three Madison alumni at the same time in the US Senate, from three different parties.

**ZIERLER:** Chuck Schumer.

**SIMON:** Democrat. Norm Coleman, who was a Republican from Minnesota, and Bernie Sanders, who's an independent.

**ZIERLER:** That's amazing.

**SIMON:** And Ruth Bader Ginsburg is an alumnus. Five Nobel laureates from Madison. There must've been some amazing teacher in the late 30s because all our Nobel laureates, while their Nobel Prizes were spread from 1950 to 2010 or so, all the students graduated between 1938 and 1945 or something. The oldest Nobel Prize winner in physics is a Madison alumnus.

**ZIERLER:** Your 75th birthday celebration, was that during the pandemic? Did that take place over Zoom?

**SIMON:** Yes, it was just over Zoom, and it was a three-hour Zoom celebration.

**ZIERLER:** Why the decision to focus on Daniel Wells?

**SIMON:** I didn't focus on it. Normally, I do not speak at my own birthday conference, but I got my arm twisted to speak. I wanted to speak about something other people hadn't heard about, and I'd been working on this statistical mechanics book, and there was this rather remarkable piece of work, a PhD thesis that never appeared in print because presumably, the guy gave up. I'd love to make contact with him. He's still alive. He has a book on Amazon, in fact. Not a math book. It's self-published. It's a lovely piece of work that somehow got lost. I have to write something for a book of articles in honor of Elliott Lieb's 90th birthday, and I decided I'm going to write about it for that book. The only disappointment I have is, there are two extensions, one of which I was able to work out, which was mentioned in the talk, and the other is a conjecture that I am 100% sure is true. It's one of these things I can check for reasonable values in *Mathematica*, so I know it's true. I've done some work and not succeeded. I've tried to get my buddies to work on it, too, and no one's succeeded in solving it, so I'll put it as an open problem.

**ZIERLER:** There's a reference in the slides, a book in process for Cambridge Press, *Phase Transitions in the Theory of Lattice Gases*.

**SIMON:** Yes, that's the book I'm talking about.

**ZIERLER:** How far along is that?

**SIMON:** It's hard to tell. I told them originally about 350 pages. I now suspect it'll be more like 600. It's maybe at about 250 pages now, but to be honest with you, I put it aside for a while because there were some issues I couldn't quite figure out. When you write a book where you're trying to explain things to others, you realize somebody has not done a very good job of explaining what they've done. So I put it aside. I actually just went back to it yesterday. I'm feeling a head of steam. It's probably about halfway done is my guess. I would've said two years. It's probably going to be more like three and a half.

**ZIERLER:** The year before, when you were inducted into the National Academy of Sciences, at this late stage, given how you've been recognized elsewhere, I wonder if one of your reactions was, "What took you so long?"

**SIMON:** Well, it wasn't just my reaction because for years, I was aware, and I actually was aware–I understand a lot more about the process, having now been in the Academy. The election process is rather chaotic. I heard a story that there was a group of people who were trying to push it. It's a very funny process. 50 years ago, there used to be five, six, or seven mathematicians elected each year. For whatever reason, until relatively recently, it went down to more like three. My impression was, nobody really understood why it hadn't happened. I know one guy was pushing hard. Who knows? It's a funny process. But yeah, I'm not the only one who wondered why.

**ZIERLER:** Must've felt good, though, when it finally happened.

**SIMON:** Absolutely. I was very aware of when they were going to be announced. "Oh, didn't happen this year again." And then, one year, I got the phone call.

**ZIERLER:** Is your sense the recognition is weighted at all in terms of, for somebody like you, the mathematical and physics contributions?

**SIMON:** No. If anything, my impression is that while you could have a joint appointment or election, it's not very usual. For example, there was a candidate I nominated who's currently in the system who I think will get elected this year. There's an applied math section, and the applied math section is not really applied mathematics. For example, it's got a lot of probabilists in it, who I would regard as pure mathematicians. I was told that this candidate was being considered jointly, and the most recent thing I was told by the head of the math section is that he had talked to the head of the applied math section, who'd said, "This candidate is sure to get elected this year in our section," and the head of the math section said, "Well, it's going to be borderline."

They made a decision that this candidate is not even being considered in the math section this year, and I think this candidate will get elected in the applied math section. It's a crazy system, but being in mathematical physics, my impression is, there are some pure mathematicians who–the problem is, all the people in the math section are asked to vote on all mathematics candidates. And you haven't heard of most. There are some number of figure who just assume, "Well, it's not real mathematics," which I'm sure hurt me. It's a funny process. I used to think that there must've been some enemy thwarting me, but it's just a strange, chaotic process.

**ZIERLER:** One award that remains out there, perhaps to be had, perhaps not, is the Fields Medal. I wonder if you could talk about the significance of the Fields Medal and what the track record of mathematical physicists have been in getting the Fields Medal.

**SIMON:** There's the Fields Medal, but it's not something I'm going to get because even though it's not an official limit, it has an age limit of 40. The first time within recent memory–I don't know what happened 50 years ago–when it became clear that this thing might not be such a clever limitation was when Wiles proved the Fermat theorem, and he was 43. People asked my opinion, and my opinion was, "It's not an absolute requirement. It's silly. They should give Wiles the Fields Medal." They didn't. They gave him a special prize. And frankly, if I were Wiles, I would've said, "Go away."

But he was a gentleman, and he took it. It was even worse with Oded Schramm. There was now this firm tradition, "We couldn't do it for Fermat's last theorem. We clearly can't make an exception." The question is, what does age 40 mean? Somebody made the absolutely ridiculous decision that you have to be 40 before January 1 of the year in which the Fields Medals are given. Oded Schramm was 40 in January of that year. He certainly should have gotten it, and they should've said, "Yeah, he's 40," but they didn't. In the end, because the work he'd done was so important–and I'm not trying to belittle his collaborator, but he was the innovator, and on some of the later work, he did a piece of work with two collaborators.

One of the collaborators was under 40 at the next congress, and he got a prize. The Fields Medal's a little weird because of that. The big prize is the Abel Prize. In fact, there's been one Abel Prize to a mathematical physicist, Yasha Sinai, who's also a probabilist. Fields Medal, it's a question of what you mean by mathematical physics. There have been people who work in parts of analysis that have an overlap with mathematical physics. For example, there's a flashy French mathematician who went into politics who really did wonderful work that has some overlap with physics. He's not what you'd call a mathematical physicist. On the other hand, he was actually the chair of the Poincaré Prize committee the year I got the Poincaré Prize. He has some overlap with mathematics.

There are probably two Fields Medalists who have overlap. But members of the club, as it were, the only "mathematical physicist" who got a–although, there is a Heineman Prize winner who got the Fields Medal, Ed Witten, and I still remember one topologist I knew was scandalized when Witten got the Fields Medal. Then, Seiberg-Witten, 4 years later, came out and was incredibly important work in mathematics. The topologist said to me, "See? He finally warranted getting the Fields Medal."

**ZIERLER:** This rule that the Fields Medal needs to be given to somebody under 40, I can't help but note, there's the rabbinic stipulation or decree that one should not study Kabbalah until after age 40.

**SIMON:** By the way, if you look at the Abel Prize, every winner, with one exception, has been over 70. I think the median age is 78 or something. The one exception, by the way, was 65, which was Andrew Wiles for Fermat's last theorem.

**ZIERLER:** You're uniquely positioned to comment on this, the notion of doing one's best work as a young person in math and doing one person's best Torah-learning later in life.

### The Power of Youthfulness in Math

**SIMON:** I can certainly say that it is an empirical fact. It's not so easy to explain that almost all mathematicians do their best work under age 40. There are a handful of exceptions.

**ZIERLER:** What do you think that's about? The plasticity of the mind? Energy? Daring? For example, in Torah-learning, there's a building of knowledge that you can add to.

**SIMON:** I would think that what happens in mathematics is that building is not as important as a freshness of viewpoint. Huge breakthroughs are most often done by people who are new and have some fresh insight. But it is still a surprising fact to me. And there are exceptions. I can even think of someone who's almost 50 who did their best work.

**ZIERLER:** In looking over your career, do you think this applies to you as well?

**SIMON:** Absolutely. Absolutely. Not even close. I was 40 in 1986. If you talk about my ten most important things, probably eight of them were before then. Top five, four or all five were before then. It's certainly true for me.

**ZIERLER:** As you look at other mathematicians, does anybody buck that trend?

**SIMON:** Well, as I said, I have a student, Percy Deift, certainly did his most important work when he was, I think, 48.

**ZIERLER:** That's still pretty close to 40, though.

**SIMON:** No, it isn't. If you think about the fact that most people don't start doing things until they're 22–it's 18 years from when you're 22 to 40. 48's another eight years. That's not so close to 40. One of the things that's rather amusing, for this statistical mechanics book I'm writing, each chapter starts with a quote from a paper that's the central paper, in some sense, related to that chapter. There's a chapter on the Lee-Yang theorem, and this is the famous paper of Lee-Yang. I happened to note the ages of the authors of the papers I'm quoting. Every single paper, with one exception, the authors were either 29 or 30 when they wrote the paper. The one exception was David Thouless, where he was 40, for which he got the Nobel Prize. But Lee and Yang did this particular piece of work when they were 30. The stuff that got the Nobel Prize, they were 34. One of the papers is a paper I wrote with Fröhlich and Spencer. It's clearly one of my most important, if not the most important, pieces of work, and I was 30 when that paper was published.

**ZIERLER:** Moving closer to the present, I know you certainly didn't write this title, this is what editors do to get people to read the articles. The interview you gave in Nature, *The Mathematician who Helped to Reshape Physics*. Fair title?

**SIMON:** I would say mathematical physicist, not mathematician. I object a little bit to being called a mathematician. I helped, and it did reshape physics. It's not a terrible title. That was all the idea of the author, by the way. Not just the title, the idea of doing the article. It certainly wasn't my suggestion. When Thouless got the Nobel Prize, he contacted me and asked some questions. Interesting guy.

**ZIERLER:** Is that how you see the trajectory of your career, more as reshaping physics as opposed to reshaping math?

**SIMON:** No. This is discussing one particular piece of work. The Berry's phase and my work related to Thouless. That work has had a real impact on physics. It's a strange phenomenon because Berry's phase is a cute piece of work, but by itself, is not so earth-shattering. But it somehow pointed out that there was this topological structure in non-relativistic quantum mechanics, which has had an enormous impact. If I felt he was summarizing my career, I'd say it's a lousy summary. But he's not, he's talking about one particular piece of work. And that piece of work is an amusing piece of work in general, but its import is not as mathematics. Among other things, mathematicians, if they know what I did, will say, "That's mathematically trivial. Of course, it's true." It's once you realize that of course, it's true, you realize it's one of these discoveries that it was somewhat surprising and made people realize that there's some structure there that now has an incredibly important role in condensed-matter physics. Both Berry and I have been very fortunate. He probably more fortunate than me.

**ZIERLER:** The research belongs earlier in the narrative, but because of his 100th birthday coming up, I wonder if you might share some thoughts about the legacy of Shmuel Agmon.

**SIMON:** Agmon had a very interesting development on his own. I was recently looking at a video, there was a celebration of the stepping down of an editor of Journal d'Analyse, an Israeli math journal with a French name based in Israel. Shmuel was there. It's the last time I saw him. This was six months ago. He was already close to 100. He said various things. He was actually in fine fettle. Originally, Israel was a desert in mathematics. He did get an education at Hebrew University, but he actually got his PhD in France in complex analysis. He fairly quickly became a big expert in partial differential equations. About 1970, when he was close to 50, he became interested in things connected with Schrödinger operators. And he made a number of absolutely spectacular discoveries, three in particular, in non-relativistic quantum mechanics. He revolutionized a piece of one-body quantum scattering, totally fresh ideas.

A small but interesting subject that I'd worked on exponential decay, he totally revolutionized, and he was 60. In fact, he's a counterexample to this over 40, if you just look at Schrödinger operators. Still probably true that he also has important work in elliptic partial differential equations. But it may be true because I actually think his work on Schrödinger operators may be his most important work, and he was over 40 when that was done. I didn't quite realize how old he must've been when he did what I call the Agmon metric, which is what everyone calls it now. That must've been the late 1970s, and if he was born in 1922, he was certainly mid-50s. And a very interesting character. Very charming. Somewhat acerbic every once in a while. But generally, really sweet guy, interesting sense of humor. I really like Shmuel.

**ZIERLER:** We've worked literally right up to the present day. For the last part of our talk, I want to ask some broadly retrospective questions, and then we'll end looking to the future. Simple question right off the bat. In your career in mathematical physics, what stands out in your memory as simply having the most fun?

**SIMON:** If I were asked to pick my three or four biggest discoveries, it's the moment when I realized I could prove the continuous symmetry breaking in the classical Heisenberg model. That was just a great feeling. I don't know if fun is the right word, but it's the closest I can come to it.

**ZIERLER:** Satisfaction.

**SIMON:** It's certainly the most satisfying. And the ones, of course, where I'm doing it with someone, it's particularly fun when you bounce ideas around with some partners. The work Elliott and I did on Thomas-Fermi, lots of fun. It was frustrating at the time because we ran into problems, but we eventually solved them.

**ZIERLER:** To flip that around, what have been the most frustrating moments, when that satisfaction eluded you no matter what you did?

**SIMON:** I tended not to return to things, I'd give up, but only after I tried and couldn't get something to work. If I look at N-body quantum scattering, asymptotic completeness, I knew it was a very hard problem. Didn't spend a lot of time on it, but it wasn't as if I never thought about it at all, and it was frustrating not to do that. The other frustrating thing is sometimes dealing with students that you really think you knew better than they what they should do and they weren't.

**ZIERLER:** A counterfactual question that's impossible to answer, but I'll ask anyway. You alluded to it earlier. Had you stayed at Princeton, would your career have been more or less the same or different than what it became when you came to Caltech?

**SIMON:** My guess is my research has been narrower than it would've been if I'd stayed at Princeton.

**ZIERLER:** Simply because the community is narrower.

**SIMON:** Well, not narrower. If you look at what I'm doing–I didn't have lots of people to talk with. It was a much smaller group of people, so I focused on a much more limited set of things. By the way, if I'd stayed at Princeton, I'm willing to make you a wager I would've been elected to the National Academy 20 years earlier.

**ZIERLER:** That's a statement of Princeton's pull in math, particularly?

**SIMON:** Yes, and if I'd moved to Courant, I would've been in 30 years earlier. I don't know why, but Courant always manages to get its people early into the Academy.

**ZIERLER:** Is mathematical physics as a scholarly community stronger, weaker, or about the same going back to the Arthur Wightman days?

**SIMON:** Depending on how you define mathematical physics, we have some good young people, but not as many as there were 50 years ago. There was this golden era that I've alluded to at Princeton in the 70s. One of the reasons it's golden was, there was this really very impressive group of young people. My impression is they're not so much going into mathematical physics anymore. There are a few. There are some very impressive young people, no question about it. But not as many.

**ZIERLER:** I'll narrow the question to Caltech. I know not mathematical physics, but just math in general, is math stronger than it was when you joined? Have you been a positive influence in strengthening math at Caltech?

**SIMON:** Oh, there's no question Caltech is much stronger. Caltech, before I came–it's orders of magnitude better now. If you ask if it's better than it was in 2000, that's a hard question. We had this amazing influx in 2000 of young people who were really good, and then we lost them all. We have some very good young people now. It's harder to tell. But ask me in ten years.

**ZIERLER:** In ten years, do you think we'll see a mathematician as division chair of PMA?

**SIMON:** No.

**ZIERLER:** What does that tell us?

**SIMON:** That we'll continue to be second-class citizens. I hoped to improve mathematics in position by separating it off, but I've failed to do that. We'll continue to be second-class citizens.

**ZIERLER:** Obviously, it's an imperfect comparison because we have the divisions and not the departments here, but the notion of second-class citizenship, does that translate to Caltech's peer institutes? Would you see that at Harvard, Stanford, MIT, Princeton, Chicago?

**SIMON:** Depends on the institution. No question, if you look at Princeton, math has always, in some sense–not that physics isn't well-thought-of, but math has always had a special place at Princeton. Chicago, that's also true. If you look at what I think of as the big six institutions–they've always been the top six during my professional career. Harvard, Princeton, Berkeley, Chicago, Stanford, MIT, they all have math departments that are not second-class citizens in any way, shape, or form.

**ZIERLER:** This is a legacy of Millikan's that might never go away.

**SIMON:** It's both a legacy of Millikan and a legacy of history. Math had more faculty slots at Princeton than physics, and that's always been true. At Caltech Physics was three times as big as mathematics. It's hard to change that dramatically. Given Caltech's attitude that, if it grows, it grows in areas that bring in lots of money, and that mathematics, by its nature, is not going to be a big moneymaker, bringing lots of money, it's not going to change.

**ZIERLER:** Your work strictly outside the research, the specialty realm, in computers, in education, where have you derived the most satisfaction in working toward the greater societal good?

**SIMON:** I don't know. The computer stuff has been entirely a question of fun. I don't think I can claim I made huge contributions to society, although it is true I improved math software by being an intelligent critic. But I've never been someone who worries about societal good. Science has contributed incredible amounts to society, but it's always by people focusing on doing science, not focusing specifically on helping society. Not always, but certainly on the more theoretical side. In mathematics, it's always just doing the good mathematics, where it's beautiful, and you get satisfaction. By golly, it turns out to have an enormous impact on the world.

**ZIERLER:** But in ways that you can't foresee, and they're not motivated by.

**SIMON:** And that you not only can't foresee or are motivated by, but if you tried to do it that way, you wouldn't do as well in mathematics.

**ZIERLER:** Looking to the future, a few questions. Quantum computation. Do you have a good idea, or at least can you let your imagination run wild, on how that might change mathematical physics in a way that classical computing cannot?

**SIMON:** Well, I, of course, have friends who believe quantum computing is nonsense. I have a coauthor who's one of the most famous critics of quantum computing. But there are those who believe that quantum computers will be able to do something like model an atom, in which case it could be an amazing experimental tool in suggesting what theorems might be true. I could imagine it having an impact. Not very likely, but possible.

**ZIERLER:** What are some of the big mysteries, puzzles, whatever you want to call them, both in mathematics and physics, for which the sensibilities, background, and training in mathematical physics might be the most fertile area, where the person might be coming from to contribute to these breakthroughs?

**SIMON:** I'm going to pass on that question. I just don't think about that kind of thing.

**ZIERLER:** If there's a breakthrough in quantum gravity or a 400-year-old theorem, something like that, does a mathematical physicist have a special toolbox that might not be available to someone more narrowly defined in their research?

**SIMON:** No. Generally, my impression is that people who make the most progress are ones who somehow have a broad background, a broad knowledge base on which to call to pick out the right tools.

**ZIERLER:** Sounds like having the dual research expertise is theoretically of value.

**SIMON:** Oh, certainly. You want to have expertise. But is it mathematical physics? A blend of probability, combinatorics, and a bit of topology on the side? I don't know.

**ZIERLER:** Finally, for you, I know you have 300 or 400 pages left in the book. Beyond that, what else do you want to accomplish?

**SIMON:** I don't know, have some great grandchildren to bounce on my knees.... I actually have a plan after this book to do the second edition. I'd sort of expected it would be ten years. It's been 15 years since I wrote the OPUC. It's stimulated an enormous amount of work, and I actually have a contract with AMS to do a second edition. It's on the list. I'm an old guy. I'm allowed to rest on my laurels, to some extent.

**ZIERLER:** Barry, I want to thank you for spending all this time with me. These sessions have been an incredible amount of fun, a great treasure for the historical record. I'm so glad we were able to do this, so thank you so much.

**SIMON:** You're welcome.

[End of Recording]

[*Ed. Simon and Zierler engaged in an addendum session to discuss additional items at Simon's request*]

**DAVID ZIERLER:** This is David Zierler, Director of the Caltech Heritage Project. It is Monday, March 7, 2022. Once again, I am delighted to be back with Professor Barry Simon. Barry, it's good to be with you again.

**BARRY SIMON:** Likewise. Been a while!

**ZIERLER:** I want to say, for the record, we are re-meeting today because of the depth and the breadth of our conversations, there were just a few loose threads that we've come together to put together, so we can make everything one cohesive, wonderful transcript.

**SIMON:** Plus, one item that we discussed very briefly, and there were developments after the final transcript that just make a great story.

**ZIERLER:** That's right. Hot off the press.

**SIMON:** It's the thing I'm going to use for my standard talk probably for the next year.

**ZIERLER:** The first item is, going back to your Princeton days, we talked about the graduate student and the bomb threat. We did not talk about the one who claimed to have taken out a contract on your life. I've got to hear this story. What was that all about?

**SIMON:** As I mentioned at the time, when we discussed the bomb threat guy, there were a number of students–what was interesting is that almost all the serious issues happened the first year I was Director of Graduate Studies. The bomb threat guy, that's when the Witten story took place, and the story I'm about to tell you began then. There were two people, one in math, one in physics, who had reputations of being talent scouts, particularly good at identifying people who otherwise fell through the cracks. That was Johnny Wheeler in physics and Ralph Fox in math. And they were really very good, no question about it. Johnny had an Italian post-doc who liked to pretend he was the next Johnny Wheeler, not that anyone could be the next Johnny Wheeler. He decided to find his own talent. He was visiting Trieste and heard about some young guy who was still actually in college in Yugoslavia but who visited briefly and impressed this post-doc. He managed to convince Johnny that this was a great talent.

There's no doubt that this post-doc on his own couldn't have gotten by the rules without making an exception to the standard application procedure. But he convinced Johnny, and of course, Johnny walked on water, as far as everyone was concerned. This admission took place the year I was on leave, but he started the first year I was director of graduate studies, and I didn't pay much attention to him initially. But a couple of weeks into the term, one of our experimental particle physicists, who was quite excitable, came to see me all upset and concerned. Virtually all the first-year students who didn't have NSF fellowship funding worked as research assistants in experimental projects because that was where there was more grant money available, and the prevailing thought was that even if you were a theorist, you should see some experiment. This young guy decided, "I'm a great theorist. I'm too good to waste my time with experiment," and refused to do anything. My guess is, some of my other colleagues would've shrugged and complained a little, but the excitable particle physicists said I can't pay him, so I had this real problem.

I essentially wanted to lay down the law, but this was a complicated enough case that I went to see Murph, who was the department chair – Murph Goldberger – and we discussed what to do. Murph, on these kinds of questions, had more wisdom and sensitivity than I did. I was a young guy then. I like to think in my older age, I've grown a little more sensitive. He said, "This is a young guy away from home. Let's give him a little slack. I'll find some money to pay for him for this quarter." As background, I should tell you, the problem was that this guy did not have a very good background, although we didn't realize that. He actually talked a good game but really didn't play a good game. We didn't know any of that. Murph arranged that the second quarter, he actually was a research assistant for Johnny Wheeler. In fact, it may have actually been that Murph didn't find his own money, Murph said, "Johnny got us into this, we'll let him pay for it." I think that's actually what happened. At the end of the year, this student said, "I'm too good. I shouldn't have to take any of your exams," and he refused to take our qualifying exam that people have to take at the end of the first year.

Again, I wanted to throw the book at him, but Murph said, "Well, we should give him a little slack." Murph kept wanting to give him slack. The second year, there was a final place, and I went to see Murph, who said, "This should probably be the last one." I said, "Yeah, Murph. This is the last exception." I sent the student a strongly worded message that this was the last exception we were making, and he'd better be prepared to take the general exam at the end of the year." If he didn't want to, he should just go back to Montenegro. I probably should've written a more temperate message, but he was terribly insulted and was fairly unstable, as you'll hear as the story develops. I didn't think I appreciated all this. He was clearly an excitable guy. He had been encouraged at some point to see a psychiatrist on Princeton Health Services, and he'd been seeing him. At one point, he began to make threats to the psychiatrist of suicide. I think both the psychiatrist and the dean the psychiatrist reported to were not very professional, and word came back that not only did he threaten to commit suicide, but he said the only reason he wanted to commit suicide is that if he killed himself, because I had impinged his honor, he had all these relatives back in Montenegro whose duty it would then be to come and kill me to make up for the fact that he'd committed suicide because I besmirched his honor.

This is something that sometimes happens in academia, which you don't realize when you get involved in it. I can't remember exactly when in the process, but I think it was not more than about a month later, I get a call from this assistant graduate dean who had been dealing with him who was very upset and concerned that the student had been in his office and had told the dean that he was so upset with me that he had gone to Trenton and paid $5,000 to have a contract taken out on my life. Now, he also expressed a great deal of animosity towards Johnny, who he felt had also insulted him. At some point, one of the psychiatrists involved had said, "The real problem is that he hates his father." Because the two people on the Princeton faculty he admires the most are you and Johnny Wheeler, you're sort of substitute father figures. Since he hates his father, he wants to–this was not something one ignored, exactly. I, of course, went to see Murph. There were lots of developments, some of which, in retrospect, are a little bit amusing, although given the final stages of this story, are not so amusing.

**ZIERLER:** Did you detect an anti-Semitic angle at all here?

**SIMON:** Not at all. In fact, he may have been Jewish. I don't remember for sure. But not even a slight element of it. There was Keystone Cops incident. I don't know how much you know about Princeton, but traditionally, there was the Borough of Princeton, which is Nassau Street and the area around it, then the surrounding area of Princeton Township. At some point, Murph decided he should contact the Princeton police because making a threat like this against the faculty was really serious. Since Jadwin Hall, which is where the physics department was at the time and still is, was in Princeton Township, we contacted the Princeton Township police, and we talked for quite a while. Then, at some point, the Princeton cop says, "Oh, my goodness, this threat took place in Nassau Hall. That's in the Borough. We can't get involved."

**ZIERLER:** Then, who could?

**SIMON:** Well, we did get the Borough involved, but it was just a threat, until something really happened–we also contacted Princeton Security, and the head of Princeton Security said, "I don't think this threat is serious, and I'll tell you why. $5,000 is the wrong amount. If he went down and just found someone who agreed to do a contract, whether he'd do it or not, it wouldn't cost more than $500. There's no way it would cost $5,000. If he wanted to get something that would really get done, it would be $50,000. $5,000 is just not the right amount. I think he made it all up." It sort of died down, but he refused to take his general exam and was essentially terminated, stopped being a student. But he hung around Princeton. He no longer had a student visa, and Murph consulted someone in Princeton who dealt with immigration. The word came back from someone in immigration, "Well, we can pick him up and bring him to Newark, but before the paperwork was dry, he'd be out, and there's nothing we can do. The current policies are such that we don't really follow up on cases like this."

That's the way things were about immigration in 1974 or so. For a while, I think he was sleeping on the floor in John Milner's apartment. He started hanging around the Institute, and Milner was a sweet guy. At some point, due to some pressure from someone at the Institute–I only heard about this indirectly–he was allowed to take some kind of oral exam, which I had nothing to do with, and he didn't know anything. It sort of died away until after I was at Caltech. The original thing was '73, '74. In 1983, I came back to Princeton because my advisor, Arthur Wightman, had a 60th birthday conference. He was, again, showing up on campus, making threats against me because he knew I was coming back. I know Murph got so concerned at Caltech, he actually consulted the FBI, who didn't do anything. I remember I essentially had a Princeton security bodyguard with me the entire time I was at the event, then I went back to Caltech. About a year later, we heard that he had walked into some police office in either Trenton or Princeton and claimed to have put cyanide-laced tea bags on a shelf in a supermarket in Trenton, and indeed, he'd done that. He wound up in prison, and when he was released, by then, it was such that he was deported. It ended rather sadly. There are cases, of course, where the violence happens, celebrated cases. It's a sad side of academia, and as we said, the fact that you often have students who are unstable.

**ZIERLER:** Were you ever legitimately concerned for your safety?

**SIMON:** For the first week probably, after I'd heard about the threat, you bet. I lived in Edison because of the Jewish community, not in Princeton. I consulted a cop there. There was a very different reaction from Princeton because he had apparently spent a year on the Washington police force, where he'd been in the area that contained the Yugoslavian embassy, and he did not have a very positive view of Yugoslavians. He was, therefore, very concerned. But yeah, I was a little concerned. I was not unconcerned when I went back for Arthur Wightman. He actually showed up at some public lecture during the conference. He walked in, and I remember feeling threatened.

**ZIERLER:** Did you tell your wife about this, and did she let you go into work?

**SIMON:** Certainly, I told my wife. There's no way I wouldn't tell my wife. The problem was that probably, Princeton campus was safer than my house in Edison. Why should she not let me go into work?

**ZIERLER:** You mentioned Murph. What about up the chain at Princeton? Did you get support from administration?

**SIMON:** Of course, security got involved. No other administrators were really involved. I remember one case where I didn't get support. Every once in a while, there would be a flare-up, and he'd make more threats. I don't remember all the details, but I remember being very disappointed in my colleagues. There was some point where there was a sequence of threats, and I actually wanted him to be made persona non grata on campus, he wouldn't be allowed on campus. And I don't know why this came to a physics department meeting, but it did. My idiot colleagues decided, "Well, since he just threatened and hasn't done anything, how can we not let him on campus?" The vote was close, but it was not passed, and I felt not supported by my colleagues.

**ZIERLER:** While we're on the topic of Murph, we talked a little bit about the draft for Vietnam and didn't return to it. Tell me about Murph and the draft board. What was the story there?

**SIMON:** As background, I should mention that I was very much against the Vietnam War, like almost all of my contemporaries, starting as a graduate student through essentially the ceasefire. Draft was an issue, both as a graduate student and as a faculty member. There was some tightening of graduate student deferments, but I think because I had an NSF Fellowship, I had no problem getting a deferment, a 2S, as a graduate student. The first year that I was an instructor at Princeton, we applied for a 2A, which is the occupational deferment, and this was a point when they eliminated student deferments, to my memory. Whoever wrote the letter for young faculty at Princeton, it was not a very good letter. When I looked at it, I said it sounded as if they were actually trying to take graduate teaching assistants and turn them into employees. It was not a very good letter. In fact, I got classified 1A. I think that was probably just before the lottery, so independent of birthday, I would've been eligible to be drafted.

But there was an appeal period, and I went to see Murph. Murph, you should know, was even more strongly against the War than most people I know. My first really vivid memory of Murph is of taking a course with him as a graduate student, and he had post-docs take almost all his lectures. He would come back and give a lecture occasionally, and he would apologize for missing class, but essentially, he said, "I have contacts in Washington, so I'm spending all my time there, trying to get us out of this stupid war." Murph, under Johnson, maybe under Kennedy, was on PSAC, the President's Science Advisory Committee. In later years, he was quite active with the Defense Department. He ran a summer thing doing DOD research. He had lots of contacts. I told Murph I'd been classified 1A and that I was appealing. He said, "Don't worry. I'll write them a letter. I know how to write a letter." Literally one week later–we were told normally the appeals process is negative and takes about three months–I get reclassified 2A with a note on the classification letter saying, "Please be sure to have your employer write us again next year so we can continue your deferment." Murph obviously wrote a letter that explained how vital my research was for national defense. And there's a second part of the story that I don't remember quite all the details to. The original thing happened when I was an instructor, so probably before I was married.

The second thing happened when I was an assistant professor, so it was probably after I was married. I did get reclassified, but I began to feel very guilty because many of my contemporaries were in this terrible draft system, forced to go fight in a war that they didn't believe in. I actually contemplated going to Canada. I don't remember whether it was that I was going to not request a deferment, and if I got hit by the lottery, I'd go to Canada, or if I was just going to go to Canada directly. I actually consulted the dean of faculty at Princeton. It must've been my first year as an assistant professor because after that, the dean of the faculty was a physicist, who I knew well, and this was not who I'd been consulting. Essentially, I wanted to know what would happen if I requested a leave of absence to go to some Canadian university because of the Vietnam War situation. I assume, particularly if I didn't get drafted, that I'd be able to come back when it all was over, and I wanted my position to be held in abeyance, that I could come return to it. He split the baby in half and said, "We'd certainly be willing to give you a leave of absence without pay, but your appointment clock would still run. You have a three-year appointment. If it ended, we'd owe you nothing." I thought about it some more and decided that while this would be an elegant gesture, the people I was feeling guilty about wouldn't be helped by it, so in the end, I didn't do anything except continue being vocal about the War.

**ZIERLER:** In retrospect, how risky was that?

**SIMON:** To ask?

**ZIERLER:** To not go.

**SIMON:** Not at all because I had this deferment. It would've obviously been somewhat risky if I had turned down the deferment, but it depended on the lottery. One did pay attention to whether one's birthday came up, even if one was deferred, and I don't think my birthday was ever very high. But that would've been the only risk.

**ZIERLER:** Was this a point at which you were already asking *shailas* about what you might do in this situation?

**SIMON:** No, no. The stuff I was asking *shailas* in those days was, "When do I keep Shabbos when I'm in Japan?"

**ZIERLER:** Were you aware more generally on what rabbinic guidance might've been in a situation like this?

**SIMON:** No, and I don't think the Halakha's going to be clear on this. I think it would depend on which rabbi you were asking. But my guess is, my final decision that I was not helping anyone by going to Canada, so I shouldn't do it would've been what most rabbis would've said.

**ZIERLER:** Well, it worked out.

**SIMON:** It did. I took part in several marches on Washington. Civil Rights and Vietnam was quite a time. I think it was a healthier political split than we have in the country now because you were at least fighting about real issues. Now, somehow, it seems as if we're fighting about *narishkeit* [Yiddish; foolishness].

**ZIERLER:** Maybe Ukraine will change that a little bit.

**SIMON:** Yeah, we'll see what happens. It's crazy.

**ZIERLER:** Let's end on a happy note. The other story to pick up, of course, is the Daniel Wells story. We didn't finish how your paper went from a single author to three. What happened there?

**SIMON:** We couldn't have finished it because our last interview was in the middle of December, and the dramatic developments I'm going to talk about were at the end of January. Let me remind you of some of the background. When I started writing this book on statistical mechanics of lattice gases, phase transitions, I came to this natural question I discovered, because of some references, an unpublished thesis of someone named Daniel Wells who had really good ideas that didn't seem to be in the literature. I put a version of it in my book. It was a natural question that his whole framework raised, which he clearly had answered one special case of. Not that the thesis answered it, but we had a reference to a preprint. Of the two cases, one involved higher-dimensional spins on spheres, where he had done two-component spins, and it was natural to worry about D-component, and the other was a comparison to higher scalar spins, but instead of having spin-half, it was just the usual model, spin-one, spin-three-halves, etc. I discovered a cute argument about doing the multicomponent spins, and by using his ideas, I reduced the other question to an algebraic result. For each spin, there was a sequence of inequalities you needed. For spin-one, it was actually false. That was easy to see.

But I could do it by hand for spin-three-halves, and eventually, I did it by hand for spin-two, but that took a while. But I was able, in Mathematica, to compute it. For each spin, you had an infinite number of inequalities, but you compute the first few in *Mathematica*, or as many as you wanted, and *Mathematica* seemed to suggest these inequalities were true. It was a nice little fact about finite sums that was easy to state. Clearly seemed to be true, but I couldn't prove it. I actually worked on it with a couple of my coauthors. We made no progress. I consulted another faculty member at Caltech.

(ADDED NEW PARA) And in the meantime, I also learned a little more about Daniel Wells. I gave a talk on this stuff, including the conjecture, at my 75th birthday conference, and one of the people in the audience was a computer science professor at Caltech named Leonard Schulman. About two or three days after my talk, he sent me an email saying, "I went to your talk, it was really very interesting, and I was struck. I did a little research, and here's an Amazon link. It appears Daniel Wells has written a chapter from a novel, which he's selling on Amazon, and it's the same Daniel Wells because he posted a little biographical sketch, and it says he got a PhD. Maybe you can locate him." I couldn't figure out from what was posted on Amazon how to locate him, although in retrospect, he did say he'd gotten a second PhD in computer science from the University of Illinois at Urbana, and he'd been a post-doc at Texas A&M.

I had friends in math at Texas A&M, so I consulted them to see if any of them could locate any information on him, and none of them could, nor could the people at the University of Indiana, where he got his math PhD. But I should've probably consulted the computer scientists at the University of Illinois, who, it turns out, do know him. But I didn't. There were a couple things, this and something else, which are really new and interesting in the book. When you're writing a book, and you make an interesting discovery that's not in the literature, do you publish a paper on it or not? It's going to get published eventually, but it's going to take some time and may get buried in the book. Generally, I don't need to pad my bibliography, so I don't usually publish such things. But I think in the last three years, I've probably had half a dozen papers I've written, and only one of them has been in a regular, ordinary journal. All the others have been either in a journal issue dedicated to or an article in a collection of articles published in a book, either in honor of somebody's birthday or in memory of somebody's death. One of the things I found that was ideal to fit into, the *Journal of Mathematical Physics* had an issue in memory of Freeman Dyson, so I published an article there. Elliott Lieb is about to have a 90th birthday, I think in July of this current year, and there's a book coming out in honor of his birthday. I was invited to submit an article for this book.

Of course, the chances of not getting accepted are essentially zero, but it does go through a refereeing process. The Wells stuff seemed to be an ideal submission. I decided this fit in very nicely because Elliott has a paper that's not totally disconnected from the kinds of questions I deal with here. I wrote this article with a deadline of January 31, and it was January 14, to my memory. Took about a week and a half to do the write-up because I could cut and paste from the slides of my talk, so it was relatively easier to write up than often. I finished the first draft on a Friday. The article includes a discussion of the conjecture about this general spin, but the conjectured statement about finite sums. Desperate situations require desperate remedies, and I did what, in these days, is the most natural thing. I wrote an email to Terry Tao entitled, "A challenge." I told him it was connected with the Ising model, but, "Here's this statement about finite sums." Terry is, in my opinion, the world's greatest living mathematician. There are many times in my life I wouldn't have given anyone that name, but Terry really is phenomenal. Among other things, he's not only incredibly smart but also very broad, he's basically an analyst but has done things in logic and number theory.

But he also is noted as a problem solver. There's a problem in applying Fourier analysis to data that Emmanuel Candes, who, at the time, was at Caltech and is now at Stanford, did his work with Terry, and got a big prize. But basically, they met each other in line picking up their kids after daycare. Terry's at UCLA, but his wife works at JPL, so they both have kids in the same daycare that's not too far from Caltech. Candes had asked Terry about this problem he'd been working on for a year, and two hours later, Terry called him with a first draft of this solution that became this incredibly famous, important piece of work. And there are other stories like that. Terry's an incredible problem solver and really fast. I sent this email at, like, 10 am on a Friday. After Shabbos, when I logged in, I had an email that was a preliminary solution to the problem, proof of the conjecture. I said it in a way that's dramatic. In fact, it wasn't from Terry. An hour after I wrote to Terry, Terry wrote back and said, "That's a sort of interesting problem. I have a post-doc who's been working on inequalities that aren't so different. Why don't I give it to him?" In fact, the post-doc had this solution.

It was very computational, three or four pages of complicated calculations, which I didn't like. I didn't want to have to go through them all. We eventually talked. He's a very interesting guy, actually originally from Honduras, grew up in poverty, and because of the math olympiad, got interested in serious math. There's no place to do it in Honduras, so he wound up being a graduate student in Rio, did some interesting work that caught Terry's attention, so he's now Terry's post-doc. His post-doc's ending this year, and I just heard from him last week that he's probably going to Virginia Tech, where he has an offer. Very interesting guy, very sweet and very smart. He and I together found a relatively simpler way of–he had one very good idea to implement these complicated calculations. We found a way of, I thought, always avoiding the calculations, then it turned out to only work in half the cases, so I went back to him and said, "I can't get it," and he very quickly found a way around it. He's really very sharp. It was obvious he should be coauthor, so I picked up a coauthor, which had this proof of this conjecture as part of the paper. I still haven't met him, but we've talked several times on Zoom.

The first time we talked, I gave him some background, sent him the paper. In fact, I sent Terry the paper, originally. We agreed that I should probably work a little bit harder to see if I couldn't locate Daniel Wells. I spend more time than I probably should on Facebook. I have this whole group of friends on Facebook who are mainly mathematicians and theoretical physicists. A really interesting group. All of us spend too much time chatting on there. I told them the story about Terry, and of course, the typical response was, when I said I had a reply from Terry within 24 hours, that that was slow for him. I said I was trying to reach Wells, I put the link up from Amazon, and I asked if anyone had any idea how I might reach him. There's a graduate student at the University of Pennsylvania in mathematics who is part of this group, and he said, "I actually like to think that I'm a good internet sleuth. Here's what I think his address is, and here are some email addresses for what I think is your Daniel Wells." I sent an email and said, "If you're not the right Daniel Wells, please ignore this, but I'm trying to reach this Daniel Wells," and it turned out to be the right one. It was a sad story, he wrote up his thesis and submitted the preprint that I had quoted, and it got rejected.

That's the point where an advisor would say, "Sure, journals often reject papers. Just send it to another journal." But unfortunately, before he even took his final exam, his advisor passed away, so he didn't really have a close advisor, so he just gave up and decided to leave mathematics. He never followed up with the paper. But in the end, he agreed to be a coauthor. In a period of five days, I went from a single-author paper to three authors. Part of my paper was describing Wells's thesis, so he finally got his thesis published. It's a nice paper, and it's a great story. The point is, one can describe the proof, at least in half the cases where you don't need this calculation, in a talk, so it's going to make an ideal, fun talk because it's a nice piece of mathematics with an application to physics and a nice backstory.

**ZIERLER:** We already talked about your plans for the future. Given these developments, does that change anything for you?

**SIMON:** No. I'm still working on the book.

**ZIERLER:** It's a nice story about colleagues and the good work that they can do.

**SIMON:** Correct. Joint papers are rarely like this. But Wells did his work in 1978, I think, and really didn't contribute anything after that. I had this intense period about a year ago. Then, José Madrid, who's the third author, did this work. Madrid and I did simplify it, so we did work jointly, but it's three people putting in together. It's a nice story about how academia can work sometimes.

**ZIERLER:** Well, Barry, on that note, I'm so glad we reconnected to tie up these loose threads. Happy Purim, and have a wonderful time in Israel.

**SIMON:** Yes, I plan to.

[END]

#### Interview highlights:

- The Meaning of Mathematical Physics
- Eureka Moments and Proofs
- Caltech Undergraduates are Very Special
- Science and Torah
- Brooklyn Roots
- From Math Competitions to Harvard
- Arthur Wightman
- From Grad Student to Princeton Professor
- Becoming Religious
- Phase Transitions and Symmetry Breaking
- Ed Witten Enters the Scene
- The Switch to Caltech
- The Import of Schrodinger Operators
- PC Magazine
- The Torah Codes Controversy
- Spectral Theory
- Late Career Recognition
- The Power of Youthfulness in Math