In his career, Edray Goins has pushed the boundaries of pure mathematics, and he has worked tirelessly to expand and amplify under-represented voices in mathematics. Goins does not see each endeavor in separate terms. Rather, his dual interests inform a unified research agenda that recognizes the historic barriers of access that minorities can experience, identifies ways to break through those barriers, and demonstrates the incredible potential and benefit to the field in its entirety when a diverse group of individuals set their minds to solving some of the most intractable problems in math. Goins's own life and experiences are testament to this fact.
Growing up in South Los Angeles, it was obvious that Goins had special abilities in mathematics and science, but his path to Caltech for his undergraduate education was hardly pre-ordained. Despite being on the other side of LA, Pasadena felt like another world to Goins, and the distinctions were made even stronger during his time as an undergraduate and the racial unrest that the city experienced. In the discussions below, Goins describes his Caltech education in ways that are both instructive and powerful: in some regards, he received excellent support and encouragement from professors and friends who saw immediately his powerful academic talents; in other regards, he felt alienation or micro-aggressions as an African American student.
Taking the best of Caltech's education served Goins well in his next steps. At Stanford, he completed his thesis on Artin's conjecture of icosahedral Galois representations, and in the process, he solved a mathematical problem that had eluded the field. In his career, Goins has made pioneering contributions in the areas of algebraic geometry, Galois representations, and representation theory, among others, and as his explanations attest below, he has a special talent for conveying abstract mathematical concepts to non-experts.
Goins's appointments and affiliations run the gamut of the world's elite mathematical institutions, including the National Security Agency, Harvard University, The Institute for Advanced Study, and the Max Planck Institute. He also returned to Caltech as a postdoctoral scholar, which provided a different view of the Institute at a different point in Goins's life. Prior to joining the faculty at Pomona, Goins was professor of mathematics at Purdue University. During his summers, Goins is an energetic promoter of math education to under-represented students, and he derives great pride in helping them solve complex problems and navigate their next educational opportunities.
In partnership with the National Science Foundation, Goins is working to expand access to mathematics with each passing year, and he conveys optimism that the dividends will only continue to grow. His honors include being named one of the Emerging Scholars of the Year in 2004 by Black Issues in Higher Education, and he currently serves as President of the National Association of Mathematics, Inc.
DAVID ZIERLER: This is David Zierler, Director of the Caltech Heritage Project. It is Tuesday, November 2, 2021. It's my great pleasure to be here Professor Edray H. Goins. Edray, it's wonderful to be with you. Thank you so much for joining me.
EDRAY GOINS: Yes, thanks for having me.
ZIERLER: To start, would you please tell me your title and institutional affiliation?
GOINS: I am Professor of Mathematics at Pomona College in the Department of Mathematics and Statistics.
ZIERLER: And how long have you been at Pomona?
GOINS: I officially started, I believe, June 1, 2018. I'm now starting my fourth year.
ZIERLER: One of the many big questions, of course, after so much time spent at big research universities, why was it important for you to come to teach at a smaller liberal arts college?
GOINS: It was really a sequence of reasons. One, for a very shallow reason, I grew up in Los Angeles. I wanted to move back to California, and the opportunity came up, so I decided to go for it. Some more substantive reasons were, I really felt that I could make more of a difference in the field of mathematics by going to a place where I could train more students to eventually go into my field. Being at Purdue, where I was for 14 years, I didn't really have the opportunity to work with a lot of minoritized groups. We didn't really have a lot of underrepresented minorities as grad students. At Purdue, most of the minority undergraduates would go into engineering, they wouldn't go into mathematics. I really felt that if I were going to do something to maybe try to increase the number of minorities going into math for grad school, I had to work with minority students as undergraduates.
Pomona has quite a number of math majors, and quite a number of those are minorities. The math major's actually the most popular major at Pomona, which really surprised me. There actually are more math majors–when I say math, I mean more generally mathematical sciences, so math, statistics, what have you–at Pomona than there were at Purdue, which was insane to me because there's something like 2,000 undergraduates at Pomona versus 40,000 students at Purdue. But still, there were many more math undergraduates, math students of color, at Pomona than there were at Purdue.
ZIERLER: You mean absolute numbers, you don't mean percentage of overall class?
GOINS: No, I mean absolute numbers. It was shocking.
ZIERLER: What explains that?
GOINS: Well, that's why I wanted to come here. That's exactly why I wanted to be on the faculty. I think it's a series of reasons. One, I know that the faculty here are very concerned with having a very supportive department, trying to have a lot of encouragement of the math majors. There really is a strong sense of community amongst the students here. There are lots of things like that that I think really cause students to feel that they just like being in the math building. That was not the case when I was at Purdue. The math building was the place that you had to go maybe if you had some questions on an assignment. But a lot of students just did not want to go to office hours.
At one point, I had a class at Purdue that had over 100 students. No one came to office hours. But still, it was 100 students that I had just in that one class alone. Here, I have maybe two classes a semester. Each class might have between 10 and 20 students. I'll easily get five to ten students coming into office hours every single week. There's just this sense that the faculty are really easy to talk to, people want to come to office hours, they really want to spend time in the building. So, I think because of that, the math department in general, and the math major in particular, has a really strong reputation of just being a friendly thing to do. I wanted to be a part of that, just to see what it was that they were doing right.
The Meaning of Minoritized
ZIERLER: There are so many questions about terms that I'd like to ask you. Most of them are going to be in the world of mathematics. But the first, as it relates to diversity issues, the unique term, as you used it, minoritized students as opposed to minority. Can you explain your use of the term minoritized? What does that mean to you, and where do you see it in historical context?
GOINS: I realized that there are terms that have different meanings that have changed over the years. Underrepresented minorities, student of color, person of color. Nowadays, there seem to be popularity for using BIPOC. Black, Indigenous, Person of Color. In general, with a lot of those terms, the idea is that there is a small group that maybe has had historical injustices imposed upon them. I think there is a growing trend to kind of go away from using terms like underrepresented minorities, more because it has the stigma of, "These are students that maybe can't cope with the situation that they're in. They're suffering things like impostor syndrome. That you have to help because they may not survive otherwise." All of this really falls into the guise of a deficit mindset. That these are students who can't make it, so you have to kind of baby them, hold their hands to make sure they'll be OK.
Minoritized groups implies this idea that maybe they are smaller in number based on the situation that they're in. I believe nowadays, you have something like maybe 60% of the college students nationwide are women, but typically, in mathematics, you might have maybe 10 to 30% of the students in a math class. So it's not really fair to say that women are a minority in college, but you can say that perhaps they are a minoritized group when it comes to a mathematics course. I don't even want to use the term, say, historically underrepresented, because it's not really clear what that means and what the stigmas are there. When I do use minoritized groups, I am thinking of more of an active way of thinking of why the students may not be in my classes.
For example, I might say that Black students might be a minoritized group because perhaps I'm not doing something right to make them feel comfortable in my classes or in a math building. Definitely, when I use minoritized group, I am thinking the historical terms of underrepresented minorities, also women, but these would just be groups more generally that may not feel comfortable doing math. I am actively trying to ask the question, "Why don't they feel comfortable doing it?" so that I can hopefully change things.
ZIERLER: Would the term minoritized connote, or should it or should it not connote, that minoritized is something that is externally being put upon these groups?
GOINS: I think that's a fair way to say it. Yeah, I think that is definitely a good way of thinking of it. Certainly, there are some groups that, for historical reasons, may not be in STEM more generally. There can be lots of reasons. For example, women may not feel comfortable majoring in mathematics, being in engineering, or what have you. But of course, there's this growing trend of looking at women when computers first came out, this idea of women as human computers. My understanding is that back in maybe the 20s and 30s, back when computers were really starting to come out, not digital computers, but really having the need of having a core set of people who were willing to do computations, it was primarily women who were doing the work.
Something happened over the years that this idea of computers eventually translated into something that only men do. There, if I want to say historically underrepresented, I don't know if it's fair for me to say that women were historically under-represented in computer science. Something happened that they became a minoritized group. I do think of it as an imposition on that group in some way.
ZIERLER: We'll talk much more about this, but as a bridge to your career in mathematics, at a very basic level, to understand your motivations for increasing diversity and inclusivity in the field, where is mathematics a refuge for you, where you don't have to worry about the negative side of humanity, racism, hatred, exclusivity? Where is even the nature of that question naive because there is no such thing as a refuge? How do you understand these things?
GOINS: I would definitely side more with the latter, that there is no refuge. I certainly don't consider mathematics to be a refuge at all. I think maybe when I was younger, in a very naive way, I thought that it was going to be a refuge, that it was a place where it was just all about the mathematics that you do, all about the equations. But I've realized now that there are people doing the mathematics, and people have their own flaws. In trying to get your mathematics out there, get it recognized, get it understood, that has to go through a human lens. So I do certainly understand that you have to be aware of that when you're doing math. When I was in grad school, I had a joke with my friends that I called myself the Black Mathematician to try to really emphasize that those aren't separate things. I can't be a Black man in America and be a mathematician, but I'm both at the same time.
As contradictory as that may sound or feel at times, that's just who I am in the way that I'm going to have to work through the world. I think when I was an undergraduate, I became very interested in mathematics for a very selfish reason. I didn't think of math as maybe a way to solve the world's problems, or to help out with the community that I grew up in in Los Angeles. I really just did it because I liked how pretty the equations were. I eventually came to the realization that a lot of the biases that I would see with people walking down the street, going into the stores were amongst the mathematicians that I was working with, still dealing with racism, dealing with people who have this historical notion that it's really just an older white male who can do mathematics, and nobody else can kind of fit into that mold.
When I started to see all of that, that's when I realized that I do have these, too, that I have to worry about working together, being a Black man in America and being a Black mathematician. Now, when I do mathematics, I think of the two of them as together. Whenever I work with my students, I don't just think of this as, "They're doing mathematics as this thing where it's just a very intellectual pursuit." But I certainly see it as, "They are humans who are doing this mathematics, and the humans doing the math are going to have to worry about the biases they get from other humans they work with." So to me, it's all together. You have to work with the whole package.
ZIERLER: To clarify, when you say there's no separating being a Black man and being a mathematician, can that be universalized to say that even if you're a white man, you might not be aware of it, but you also bring your own biases and culture to mathematics?
GOINS: Oh, yeah, most definitely. In math, nowadays, there's a term that's being used more and more. It's called humanistic mathematics. It's a term that was originally put out by Rochelle Gutierrez, who's at the University of Illinois at Urbana-Champaign. It's a very simple concept. The people doing math are humans. If you are going to consider doing math yourself as a career or even in class, you have to think about the humans behind who's doing the math. It doesn't matter if you are a Black man or a white woman, it all comes down to bringing your entire self to the mathematics that you do. That is a very different concept, I think, historically from the way people have viewed math. I'm not going to say it's different from the way people have done it, but from the way people have viewed it.
I think a lot of people do view math as this thing that you can do in a room by yourself, just working out the equations at a chalkboard, that there is no human component to it. You're just there to work out the numbers and the equations. In reality, it doesn't work that way at all. If you really think about it, science itself is a very communal kind of action. You have to worry about getting your publications out there. There have to be other people who have to referee those papers. You have to present your ideas at conferences. All of this comes down to the way other people view what you're doing. Ironically, when it comes to science, science only works because of the scientific method. Other people have to be able to reproduce your results. You don't just sit in a room and do it by yourself. Other scientists have to agree, "This looks correct." Somehow, we forget that when we're doing math and science. So I really do believe in this idea of humanistic mathematics.
Math as a Human Endeavor
ZIERLER: This is as much a philosophical as any other kind of question, in the way that we wouldn't think twice in art or in music that the individual's fingerprint, their emotions, their worldview are embedded in their artistic project–which is amazing because again, naively, you would think that math is so pure, it's so objective, it exists out there whether there are humans to connect to it–what you're saying is that fingerprint, our own heritage, the way we approach the world is our only access point to the math, just like our only access point to music or to art.
GOINS: Yeah, that's exactly right. I think one thing that's made science really great in the last 100 years or so is taking certain ideas, say, by Einstein, and really putting them into the popular culture. This idea of time travel, and relativity, and kind of what's happening with space time, I think has really encouraged people to think about science in a very different way. But it's still getting more people to talk about it amongst each other. It's not something where people just kind of do it in a room, in the dark, and then that's it. Mathematics, I think, will do better as a profession if it can find a way to get more into popular culture. There are certain theorems and results that I love, that are beautiful, and I try, when I can, to kind of explain to people what these ideas are.
I would like to see mathematics in general try to do the same thing, get some of these really beautiful ideas out there, just like art. I've always said I consider math to be more art than science. I am in it because of how beautiful and simplistic the equations are. I honestly don't care about practical applications or whether it'll solve the world's problems. I just love the equations for how beautiful and simple they are. That's what I would love to do, that's the way I would love to see math eventually go.
ZIERLER: I'll use physics as an anchor point because it's a world in which I'm much more conversant, and there's this very important idea, which specifically goes back to last summer and the murder of George Floyd. That is, it's not just that physics owes something to diversity, it's that physics needs diversity, that if we are going to solve the seemingly impossible problems of integrating gravity into the standard model or understanding dark energy or dark matter, we need, at a very elemental level, a multiplicity of perspectives because if we just have the same kinds of people attacking the same problems in the same way, by definition, we're not going to make progress. Does that basic framework work in math as well, would you say?
GOINS: It certainly does. Along these lines, a good friend of mine, Stephon Alexander, has this new book out, Fear of a Black Universe. I've been reading through it. He certainly puts out the exact same idea that you're saying here, that physics really has to embrace a diverse set of views, otherwise it's just going to be stagnant and might even die. Math is very much the same way. What usually happens in math is, someone comes up with a technique, and they use this technique to solve a whole series of problems. As they're solving these problems, they come up with conjectures of maybe statements that should be true.
But that's very much a closed system. You have these techniques, you then come up with these solutions, you have maybe a few more techniques that come out of that, you then have these questions, but then you hit a wall. You can't really go any further. The people in math like to say, "You have a hammer, and you're in search of a nail." You have this technique that seems to work really, really well, but at some point, you don't get any further. If you have someone who now is working in kind of their own silo, where they've done this, they have this technique, they then have this series of problems, and then they get stuck, once they look in the other person's silo, that's when real progress in mathematics happens. If you take a look at all of the big results that have come out at least in the last 100 years, you can take a look at people who have either won the Fields Medal, people who have won the so-called Breakthrough Prizes, they've all worked and been successful because they've tried a technique from a completely different set of problems in math. Somehow, they're using this diverse set of ideas that has to be introduced in a brand new setting, and then it works incredibly well. We in math know that.
We certainly do understand that once you have this diverse set of ideas, that's when the progress happens in mathematics. But for some reason, that still hasn't completely translated into, "Maybe this means that we need to have a different set of people working on the problems. Not just a new set of ideas, but perhaps individuals who are coming from different backgrounds to also introduce these new ideas." I think it's going to happen eventually. People are going to see that it's not just about the mathematical techniques, it's also about the humans doing the math that will cause math to realize that we do have to diversify, much in the same way as physics. We definitely need to have a different set of people.
ZIERLER: Now, I'll ask you to put on the sociologist's hat here. The things you're talking about are going to take a long time. It's going to take educating your colleagues, bringing up that new crop of undergraduate and graduate students. This is a long term proposition. On that basis, what are the things that seem immutable just about human nature? That even if highly educated academics run into these problems, it's like, "Well, if we're experiencing this in higher education, why should we have any hope?" What are those things about human nature where you're just hitting a wall, and it seems like we're just not going to make change? And where are those spaces where you are having these conversations and do see forward progress?
GOINS: I would say there are at least two walls math is hitting right now. One, we are very much in tribes. I think this is just human nature, we like to work with people that we feel comfortable with. This can come down to people who look like us, have similar backgrounds as us, speak the same language as us. That's just a human nature thing. It can even come down to something as simple as, as a Black male, I enjoy doing math with other Black males. Right or wrong, that's just part of human nature and the way things are done. That definitely leads to a slippery slope when it comes to doing math because then, you might have these tribes of people doing math, and again, it's this idea of not having a diverse set of views when it comes to working on math problems.
That's one thing that I think we as people are going to have to learn how to get around. Just questioning who's in the room, but more importantly, who's not in the room. The second thing is math seems to like this idea of a genealogy. I have an interest in working on certain problems. I may have an undergraduate advisor who then says, "Well, let's work together on some of these." This undergraduate advisor would then recommend, "You should go to grad school at this place where I got my PhD." So now, my undergraduate advisor has me perhaps working in the same area or with the same person who was his graduate advisor. Now, I'm kind of part of this very much locked-in lineage. Math people seem to like to do this quite a bit, and I'm not really sure if this is really a good thing to do. People like to say, "Who is your academic grandfather?" It's not just who you work with, but perhaps, "Who was your advisor's advisor?" Something like this.
And again, I think this is something that's very much part of human nature, us wanting to know who was part of our lineage. But again, I think that's going to be kind of a slippery slope. If you're so focused on saying that you're part of this lineage, that you know that you're part of this academic parentage, "Who was your academic grandfather/grandmother?" that, again, is going to lead into a stifling of creativity. But it's something that happens in math all the time. Now, with those two negative things, I think that there is a positive thing that is having changed happen. This idea of research experiences for undergraduates, or REUs . The National Science Foundation started these, I don't know, maybe around 20 years ago or so, and now, they really have exploded in the mathematics community. The idea of these is that it's a summer program that might last anywhere from six weeks to ten weeks, typically about eight weeks or so, where you bring in students to a certain school, and the students there just do research with other students and with a faculty member.
It's typically all paid for by the National Science Foundation. Working in these summer programs, the NSF encourages students from all different kinds of backgrounds. So these might be students that are at your fancy research institutions, like your Caltechs, or Harvards, or Princetons. They might also come from your small liberal arts colleges, like Pomona, like Grinnell College. They might even come from historically Black colleges and universities, or minority-serving institutions, or even women's colleges. You have all these students from all these different backgrounds that all are on one campus at the same time, throwing out different ideas and trying to work on these different problems, but they're all working together. Now, if you imagine having an undergraduate who's done this for four years, seen all these students from all these different backgrounds, that, then, gets away from the idea of having, let's say, tribes, students who are only working with other students who look like them, or even having these very stifled lineages.
Now, they don't have to worry about saying that, "My academic grandparents came from this certain line." Everyone's coming from very, very different backgrounds. I'm quite optimistic that because this has been around for so long, that the mathematics culture has changed quite a bit. You can see this even in the last ten years. I think if you give it another ten years, math is going to be a very, very different place.
ZIERLER: That's so exciting to hear. We'll have to stay tuned for that. A question we're all dealing with right now. As a mathematician, during the year and a half in the pandemic and the mandates of physical isolation and remote work, what aspects of that may have been productive for your research, really not going anywhere, and what areas, because, as you say, it is such a collaborative endeavor, were detrimental to the work you were doing?
GOINS: A couple of places I think, for me, it's been really great. One, you actually see mathematics everywhere now. That may not sound like it's true, but for example, when people first tried to talk about COVID-19, there was a question of, "How do you know how fast the disease is spreading?" And you actually had mathematicians on TV who were showing graphs, and talking about exponential growth, talking about the statistics of how to measure when people actually do have the disease, this concept of what's called R_0, the reproductive rate. I was loving it for the first six months. It was bad that you had to kind of stay at home, you didn't really know what was going to happen with the disease. But really, every night on the news, you actually saw mathematics being discussed.
It wasn't being discussed in the sense of just showing raw numbers and raw data, but really this concept of trying to understand the disease was purely a mathematical concept. People were trying to understand the mathematical model of how to determine or predict the future of the disease. So I thought it was great that we had the opportunity to have a national discourse on how to use mathematics to figure out where we would be as a country 12 months from then. The second thing that worked out well for me, in a very practical sense, math still happens. People are still doing the research. They're still going to give talks and presentations. But they realize that they weren't able to travel to conferences or schools to give their talks. What mathematicians have done in the last 18 months or so is, they've moved seminars online. Now, there actually are hundreds of talks, not just in the country, but all over the world, where everything's happening over Zoom. A lot of us math people have different websites, email lists, where we're just saying, "If you want to attend this seminar, here's the Zoom link." I can easily attend seminars in Germany, in Italy, in the United Kingdom all from the comfort of my computer.
In fact, at one point, I actually gave a talk in Scotland. I didn't even have to leave the country. I just gave it from the comfort of my computer. But the point is, it was a major conference happening in Scotland, virtually, at least, and I could give the talk there, but not worry at all about traveling. Now, I think, a lot of us in math are questioning the future of that. I think the idea before the pandemic was, "We have to travel to places if we want to talk to other people, have collaborators." We really are rethinking that, saying that we can do a lot of this online. The pandemic is really what caused us to do that. I think that's a big positive thing that's happened. Probably the negative thing is, math is not the easiest thing to really discuss, to present, in an online format. A lot of us still find it easy to be at the chalkboard, to actually write things down, to stand next to each other face-to-face and try to discuss things.
The online platform hasn't really been great for that. There's some software out there that attempts to mimic this, but it's really not the same as having two people standing together in the same room at a chalkboard. I think that we still need, as a mathematical community, to figure out how to get all of it to work. It would be great if we could find a virtual way that several people could be at the chalkboard, working at the same time. But until then, that's going to be the one thing about the math community that we all love doing, the act of being at the chalkboard together.
ZIERLER: Just as a snapshot in time circa November 2021, what are you working on right now? What's important to you?
GOINS: Mathematically, this idea of what are called Belyi maps and Dessin d'Enfants . Without really trying to explain the gory details of it all, I'm basically trying to draw graphs on the surfaces of things. Think of a soccer ball. If you have a soccer ball, it's actually a series of hexagons and squares that are all kind of sewn in together. They're kind of interwoven in a nice intricate way. But that's a nice object. It's really a drawing that I have on the surface of the sphere. That's one way to think of this. I would like to do something like that, but for more exotic surfaces. We call these Riemann surfaces in the parlance. But I really have been doing a lot of thinking of, "What are some of these objects? How can I draw them?"
And then there are, of course, other mathematical concepts that are associated to those. What's called the fundamental groups, also you have the automorphism groups. There are these certain functions that allow me to generate these things. They're called Belyi maps. I really am trying to figure out how to relate all of these together once I have these types of drawings, these so-called Dessin d'Enfants. I even have a student I met with earlier today I'm in the process of writing a computer program with, where once we're given one of these so-called Belyi maps, there's essentially a function that kind of encodes the way these things should be drawn that he has a program that should draw these in real time. About a year ago, the quickest I could draw them on a computer might take several hours, almost a day.
Now, he's found a way to draw these using just a mere few seconds. I'm hoping that we can now have some really interesting, intricate drawings but use the computer to put all these together. That's the big thing that I'm thinking about mathematically. Non-mathematically, I've been thinking if I can get more Black and Brown students in this area, this idea of number theory, algebraic geometry more generally. A lot of students, the way I was when I was a student, see mathematics as kind of a useless endeavor. I have to be honest about that. I think if you asked a typical undergraduate, "What does a mathematician do?" they would answer, "They teach college or high school."
That actually worries me because that in general is not true. Mathematicians, just like what we saw with the pandemic, can be out there in hospitals modeling diseases and how they're going to spread. They don't have to be in the classroom, just teaching mathematics. I've been trying to think of ways that I can really tell my students, at least, the different things that mathematicians do when they're not teaching in the classroom. But to kind of narrow it down even more for the area that I work in, not a lot of students, even the brightest students who take the most advanced classes, get exposed to number theory and algebraic geometry.
So I'm trying to think of ways to expose students to those areas to hopefully, eventually, diversify the field. Try to convince students to go off, get PhDs in these areas, then go out there in the world and try their best to work on these types of problems. But it is a complicated question, and it does have a difficult solution. How do you get students interested in these areas so they continue in them?
ZIERLER: This is such a great opportunity, like you said, not to go into the gory details, but to get mathematicians really to convey, as you said, that important question, what is it that mathematicians do? So my first question there is–and correct me if this is not the most fundamental binary in mathematicians–are you more in pure mathematics or applied mathematics?
GOINS: I'll say yes. It's weird that I think a lot of people think that mathematicians have this binary way of thinking, either you're pure or applied. I like to think of it as math combines a lot of different techniques. Really good math combines all of the techniques. When I was an undergraduate, I was lucky enough that I double majored in math and physics, but I was only a handful of classes away from getting a third degree in applied mathematics. I actually loved applied mathematics. It's just that for whatever reason, I just decided to kind of stop at math and physics. But even now, the work that I do combines all different ideas. Just to give you an example, sometimes when you're doing pure math–and I prefer nowadays to use the term theoretical math–that typically means that you're trying to prove something.
A question might be this. There's the concept of a prime number, a number that's only divisible by one and itself. You have two, three, five. The number six would not be prime because that's divisible by two and three, and that's different from one and six. What if I wanted to prove that there were infinitely many prime numbers? That's a pure math question. A pure mathematician, if you will, a theoretical mathematician, will spend their time trying to prove that statement. In fact, in a number theory class, this is something that you will prove, that there are infinitely many prime numbers. Once you have that, a question I typically like to give students is the follow-up question. "We know that there are infinitely many prime numbers. Find me a prime number larger than a million. Now, we know that there are infinitely many, so we know one exists. Write one down." Now, you might say, "OK, fine, what about a million and one?" Do you know that that's prime or not? Now, that question is an applied math question. How do you actually find this number? And can you write a computer program that can check that this is prime or composite? To me, these questions are all hand-in-hand. It doesn't really make sense to sit down and try to write a proof that says there are infinitely many primes because at some point, you actually need to find one. But in the same way, it doesn't make sense to write a computer program that just finds as many prime numbers as you want because you'll need to know if you'll run out at some point or if there are infinitely many.
With my research, I always combine those two concepts, the idea of theoretical math and the idea of applied math. Yes, I do want to prove things. But at some point, I need to actually write down examples. I do spend a lot of time thinking about computer programs and algorithms that would help me find the examples I'm looking for. Even when I work with students, I still tell them, "We're going to need to write a computer program at some point. We're not just going to sit with a pen and paper at the chalkboard to try to prove things. We actually do need to write a computer program that's going to find some examples." To me, it's one and the same. You have to combine the two.
ZIERLER: In the way you so elegantly answered, "Yes," to the binary applied or pure question, of course, the question is embedded in the administrative distinctions that even a place like Caltech draws, where there are different divisions. There's a Department of Applied Math and a Department of Pure Math. To what extent are those administrative distinctions problematic, given that this is the kind of progress that the field needs?
GOINS: I think in a place like Caltech, it's becoming more and more true that those divisions are arbitrary. Yes, there is an applied math division, but there is this new department that is essentially something like computational biology, which is a really crazy concept because it used to be, 100 years ago, you might have pure mathematics, you might have applied mathematics, which is more the computational side, you might have a computer science option that really doesn't worry about the computations, and then you'd have biology, and the four would never talk. Now, you have all four in one department.
And you even have faculty jumping back and forth between all four areas. I think that's going to be the future of science. You're going to have to combine all four. I can't imagine that a pure math department the way it is now is going to survive. Even here at Pomona, we've actually changed our name from the Department of Mathematics to the Department of Mathematics and Statistics. We just understand that in some sense, you have to evolve or die. We do understand that statistics is mathematics being used in many, many different departments. We as a college are also thinking about data science and what will happen with the future there, how that will be mathematics, and statistics, and computer science used in lots of different departments, the humanities and even, say, biology and chemistry.
I think this is what's going to happen more generally. The math departments that are very traditional and only want to focus on, "Let's teach linear algebra, and let's prove these big results," will not be the departments I think a lot of students will want to be a part of. I think a lot of these departments, as they're moving forward in the future, are going to have to think very much in an interdisciplinary way.
ZIERLER: You're saying, then, that mathematics is very much part of this broader academic trend of convergence, where these traditional walls that we place between academic departments are going to become less and less relevant or important?
GOINS: I think so. I think so. Now, don't get me wrong. There are a lot of mathematicians that are kicking and screaming that they don't want the change to happen. They very much want to keep their department in a very traditional sense, they just worry about the pure mathematics, they just have their blackboards, and they don't want any of that to change. Unfortunately, I think departments that are like that are seeing the students vote with their feet. The number of math majors is slowly decreasing, and the number of students who have an interest in going into statistics or computer science is fully increasing. I would love to see a math department very much like the way Caltech's thinking of things now, not saying it's math, but it's saying maybe computational or something or other, and it's a very general idea. For me, an ideal department might look like having mathematics, statistics, computer science, and data science all together in one.
Because I can tell you that with the work I do, yes, it is very much founded in trying to work through doing something in pure math. But I need and want students who know how to program. I also care about having a lot of data. I have another student right now, we're trying to form a database, and we're talking about how to actually pass information back into this database so we can use the information there to generate some other data that we need. That's more of a data science type of thing. To me, we need all of this together. It's not just going to be a pure math department by itself, but I really do think that the ideal department we're going to have in the future will be combining all of these together in one.
The Beauty in the Numbers
ZIERLER: You said before that what motivates you more than anything is beauty, elegance in the numbers, in the calculations, in the equations. Would it be fair to say, if I really tried to pigeonhole you, that you are a pure mathematician, but you recognize the importance of mathematical tools for applications?
GOINS: I think I got this when I was a student at Caltech. I really feel myself as a confused scientist who's really just trying to understand a couple of things. One thing I loved about my experience at Caltech was, students chose a major based on the problems they wanted to solve. I've never seen that anywhere else. I one friend in particular who wanted to invent an invisibility cloak. He was completely obsessed with the idea of an invisibility cloak. So freshman year, he thought, "What do I need to create an invisibility cloak?"
ZIERLER: I wonder if you might explain what an invisibility cloak is.
GOINS: Think Harry Potter. It's this idea that you have a coat or a garment that, if you wrap it around you, no one can see you. Now, this has been invented, so it does exist now in the real world. We didn't know this 20 years ago. We were all 18 years old, trying to figure all this stuff out. But the way that it works now I think is very much the way my friend thought of it then. To have an invisibility cloak is an engineering question. So he wanted to become an electrical engineer just to solve this problem of creating an invisibility cloak. Nowadays, my understanding is the way this thing is created is you have to worry about the properties of light, how light possibly bends if you take it, and it goes through a medium. Some if it's based on Snell's law, some of the stuff you learn in physics.
But this friend majored in physics and electrical engineering because he wanted to build an invisibility cloak. This is one of the things I loved about my time at Caltech, that you could talk to any undergrads, and each one of them had their own pet project, something they wanted to do, and they chose the major based on the project that they wanted to work on. For me, I got obsessed with what's called group theory. It's not the easiest thing to explain. It's essentially a set of axioms that you have to kind of form a certain mathematical structure. But the structure tells you the symmetries that a certain object might have. For example, if you're holding a laptop, then you can think of a laptop of a rectangle, and you might ask, "What are the different ways I can rotate around this rectangle to kind of bring it back into its original position?"
I can take the rectangle and rotate it around 90 degrees. Or I can take the whole rectangle and flip it upside down, that's another rotation by 180 degrees. Well, it turns out that the collection of symmetries I have number eight, and this is something that we call the dihedral group. There are a lot of these groups we introduce here in the theory, and they're all coming about from a very pure math standpoint by writing down this list of axioms, things that you want to be true. I was very much obsessed with, "What are these axioms? Why do you want them to be true? Can you generalize some ideas of group theory?" This is really what I was very interested in as an undergraduate. I realized that group theory is a study in math, but also a study in physics, in particular, things like quantum mechanics, and a study in chemistry because you care about properties of, let's say, lattices, or even properties of crystals.
I took group theory in math classes. I also took the group theory in physics classes. I took group theory in chemistry classes. It didn't matter to me what department I was in. I wanted to solve the problem of, what are groups? What is this idea of group theory? And that's really just something that I've kind of taken with me for the entirety of my career, that I have a series of questions I wanted to answer. I don't care how I'm going to get the answer. It could be writing up a proof in pure math, it could be writing up a computer program, it could be generating a whole bunch of data and staring at it, even running some statistical models to figure out, "Are there some patterns there that I need to find?" If it's going to help me get a little bit more insight toward that question, then I'm going to try it. So yes, there have been times when I will sit at a chalkboard and try to prove a theorem.
Or there have been times when I've sat there for hours, writing a computer program. Or there have been times when I've looked at things like almost four million data points, where I'm staring there at the data, and I've had to hand it to a statistician to ask, "Can you say anything about the distribution of the data here, so that you can maybe tell me something that I'm missing?" All of this, I've done in the past, just so I can answer a real, real simple question. What is a Belyi map? Or what is a Dessin d'Enfant . These, to me, are really simple questions I wish I were smart enough to come up with the answer to. But I'm going to use as many different techniques as I can to try to answer them.
ZIERLER: In the way that physics has a very well-developed, even teleological notion of where it's all headed, a grand unified theory, a theory of everything, however you want to call what all physicists are sort of working towards, is there a unifying concept in mathematics that mathematicians are also working toward?
GOINS: I would say yes, but I think it depends on the discipline that you're working in. The same way I think it's probably fair to say in physics that when you're looking at, perhaps, the grand unified theory, that's more or less a question, let's say, in particle physics or supersymmetry, you're trying to say you know what happens on the small scale, so you'd like to say, "This also applies on the large scale." You understand quantum mechanics relatively well, you understand electricity and magnetism, but how well does this fit into cosmology, what happens on the sides of black holes?" But I think if you work in astrophysics, perhaps even in astronomy, you don't really have those same questions of a grand unified theory. I get the feeling there that you're trying to maybe stare at this massive amount of data you have coming in, and you're just trying to understand more about what that data tells you.
I've never gotten the feeling that astronomers care so much about quantum mechanics, but I do get the feeling that those who work in quantum mechanics would like to know, "How many of these same laws do we see hold on a larger, more classical scale?" Mathematics is very much the same way. There are lots of different sub-disciplines that I think have their own questions and their own grand unification theories that they're trying to work out. The area that I work in, number theory, algebraic geometry, is very much influenced by what's called the Langlands Program. All of this was started in the 1970s by a Canadian mathematician named Robert Langlands, who really came up with a way of saying that some ideas that have been floating around for about 200 years might possibly make sense if we can prove a certain set of statements would be true.
Some of those, nowadays, we'd call things like Langlands reciprocity, but he mostly introduced very specific ideas that should say that they all should be related. Now, the way that this manifests itself, I would say, more for the popular culture comes about for people who've heard of the proof of Fermat's Last Theorem. This idea that there was the French mathematician back in the 1600s or so, Pierre de Fermat, who had this statement, and I'm not going to worry about repeating what it is, but he had a proof of the statement that he couldn't fit in the margin of his book. So people thought, "Well, he had a proof, but he didn't write it down. Perhaps it was lost all of this time." So-called Fermat's Last Theorem.
Well, in the mid-1990s, about '93, '94, there was a professor at Princeton, Andrew Wiles, who came up with a proof of this theorem. Some people say that the proof was maybe incomplete, he had to acquire the help of his former student, Richard Taylor to basically come up with all the details of the proof. But nowadays, the proof is accepted as being correct, and Fermat's Last Theorem is accepted as being true. Some of us like to call it the Taylor-Wiles-Fermat theorem because essentially, Wiles proved that this result is true, regardless of whether Fermat himself did have a proof but couldn't fit it in the margin of his book. Ironically, Wiles was not trying to prove Fermat's Last Theorem when he came up with the proof. He was trying to work through a specific instance of the Langlands Program.
Most people in popular culture don't know this, but those of us who work in the field actually understand Wiles is famous amongst mathematicians because he proved a specific case of Langlands reciprocity was true. That's really the big statement here for mathematics. So a lot of us do believe that if the Langlands Program is true, this series of ideas that Robert Langlands put forth, that if you can prove the following statements are all true, then there's a lot you can do with mathematics, we really have been pushing towards that ever since the 1970s, when he first put that out there. So I think it is fair to say in our area, in number theory, algebraic geometry, representation theory, there is a grand unification theory. It is this idea of the Langlands Program. But I do want to be careful to say that it is somewhat narrow in that it does only work for this area of number theory, algebraic geometry, representation theory.
Those who work in slightly different areas, perhaps in applied mathematics, statistics, they don't really have the same grand unification type thing. It's not even clear to me whether they have a certain program of things that they believe should be true or even a certain direction that they should try to prove to push the area along. But I can say in the field that I work in, it's very clear that this is kind of the big, big thing that all of us have been pushing towards for the last 50 years or so.
ZIERLER: I'm very curious to get your perspective on a debate that I know you're familiar with, and that is where some physicists criticize string theory for being so far away from observational reality that it's "just math". What is your take on the nature of the debate and the ability or non-ability of physics to be involved in the real world as we can see and measure it?
GOINS: I think a lot of this comes down to a very deep philosophical question of, what is physics? I was taught as an undergraduate that physics is a description of what you can see. Now, see, of course, doesn't mean you can see it with your own eyes. You can generalize it to say that it's something that's observable. You can conduct an experiment, you can figure out an oscilloscope that maybe can measure it in some sort of way. But there should be something you can observe by some device, by some machine. The question nowadays is, if you can't observe it, is it still true? It's not clear to me whether physics is going to resolve this any time soon because this is a fundamentally different way than physics has ever been viewed in the history of physics.
I think what happened was, maybe back in the 1800s or so, you had people such as Michael Faraday, James Clerk Maxwell. They did incredible work in having these beautiful experiments, but then also writing down these theoretical equations that could predict what the experiments were showing them. Even nowadays, electricity and magnetism, if you work out Faraday's laws and what James Clerk Maxwell had worked out as well, they are incredibly precise. They're precise, they're beautiful. Physics students study Maxwell's equations even to this day, and they are just a wonderful, very well-thought-out way of doing physics. About 100 years after that, let's say the early 19th century, really, the early 20th century, a lot of that changed based on experiments that people really couldn't explain.
You have the black body radiation experiments by Max Planck. You also have a lot of these thought experiments that Einstein was doing. You couldn't really explain these things. So people started to come up with really fancy mathematics. I'm still convinced that some of these young kids like Erwin Schrödinger and Heisenberg were just playing around with mathematics. Heisenberg was 31 when he got the Nobel Prize in 1932. Schrödinger was 46 when he got the Nobel Prize in 1933. They just happened to play with the math, and it worked. They were able to explain the experiments. They just couldn't really explain why the math was true. That, I think, is where physics really had a crisis, the early 20th century or so. There were a lot of brilliant physicists who were playing with mathematics, people like Einstein, Paul Dirac, and others, who just had beautiful math that seemed to explain the experiments, but then the math almost took on a life of its own.
In pure math now, we have these classes in linear algebra. Linear algebra deals with things like matrices, matrix multiplication, trying to do row reduction methods, and what have you. A lot of the ideas of matrices actually grew out of what physicists were trying to do with quantum mechanics back in the early 20th century. They needed a way to kind of explain all of these observables. So essentially, they just invented matrix multiplication. It was still infinite dimensional matrices, but they invented this to work. It was the mathematicians who kind of took on all of that, tried to codify it, make it a little more rigorous. But still, linear algebra kind of grew out of what the physicists were trying to do to more or less explain the experiments. This, I think, is really one of the issues that physics has to resolve, that there are a lot of beautiful of mathematics that have come out of attempting to explain the experiments.
But now, I think the mathematics has taken on a life of its own. I am a person who still believes physics should not be divorced from the experiments. In fact, this is the reason I decided not to become a physicist myself. I didn't want to spend all of my days just doing mathematics. I wanted to do math but still be able to be in the laboratory, running the experiments, seeing a lot of these real-time. It'll be interesting to me to see what will happen with physics over the next 100 years, whether the math at least of physics will get to the point where it matches up well with the experiments. But unfortunately, right now, the math has really gotten to the point where the experiments can't keep up. The level of accuracy that you need for these experiments is nowhere near what you need to match it with the math. That is a little bit troubling. I don't know if it's troubling for everyone, but for me, it is.
ZIERLER: The often-used pyramid metaphor where mathematics is at the bottom, it's the most fundamental, and then there's physics, and then chemistry and biology, what do you like about that metaphor, what's problematic about that metaphor?
GOINS: What's problematic about it is that it's hierarchical. I always worry whenever any system is hierarchical because then, the question is, if you have something that forms the base of a pyramid, are you thinking of it as below another subject or more important than another subject? Also, it doesn't really take into account how interdisciplinary a lot of this is, but interdisciplinary in the sense that they influence each other. For example, as I just mentioned, you could take linear algebra, this idea from pure mathematics. Yes, it is true that physics uses linear algebra, but linear algebra came about because of physics. So it's not clear to me whether it's fair to say that physics uses linear algebra, this branch of math, or if it's fair to say the math grew out of what the physicists were considering.
I think a lot of this is also happening in other areas. In math, we have this idea of what's called a differential equation. It's basically an equation that kind of explains solutions that you might have if you write down an equation from calculus. Well, in biology nowadays, you really are trying to understand perhaps how things grow, how infectious diseases spread. That can be described using differential equations, which is a branch of mathematics. I would argue that this area of math is inspired by biology as opposed to saying biology is using this part of mathematics. I really do like to think of all these areas as influencing each other, so it's not just that biology is built on math, but I would also argue that math is built on biology, that there is a symbiosis of them all working together.
That, I don't see in this pyramid idea, and that's what I worry about, that there really isn't recognition that we are all influencing each other. There are people who work in mathematical biology or mathematical physics who understand that one area can influence the other. It's not just the mathematics that other areas are using, but sometimes the mathematics is being influenced by these other STEM fields.
ZIERLER: A really broad question, and it's going to be one where we'll ask you to reflect all the way back to perhaps graduate school. What has been the role of computers in your research? What have computers allowed you to do, and to flip that question around, in what ways have computers constrained the research because of the way people rely on them and not their own artistic imagination, or however you want to understand that?
GOINS: I was very, very fortunate that I got introduced to Mathematica at Caltech probably the first month I was on campus as a freshman.
ZIERLER: This is Stephen Wolfram's program you're referring to.
GOINS: Right, Stephen Wolfram's program. Mathematica Version 2 came out in January 1991, and Version 3 came out in September 1996. Version 13 came out in December 2021. I just assumed Mathematica existed everywhere. If you wanted to do any crazy computations, there it is. I didn't quite realize that Wolfram was there at Caltech since when he invented it, and that if you're a physics major at Caltech, you're going to know Mathematica. I had no idea until after I left Caltech. But I've used Mathematica for everything since I was a freshman. It's been 30 years, and I still love using it. I think it's a wonderful, wonderful tool. I want to be careful though to say that it's a tool for exploration.
That's really the way that I see it. When I was in grad school, my advisor more or less gave me a question to say there was a guy who wrote a thesis at Harvard University back in the 1970s. There was a conjecture he was trying to prove. He wasn't able to prove the conjecture in general, but he was able to find one example of this conjecture being try by doing a lot of hard work to write down what's called a modular form dissociated to a certain Galois representation. Now, he was using computers back in the 1970s, which was even more impressive when you realize that he had to write everything to get all this to work. He couldn't use Mathematica. He really had to write everything from scratch. After he wrote his thesis in the 1980s, people came up with maybe another five or six examples.
But there were only a handful of examples of this conjecture being true. My advisor asked me, "Can you maybe prove this conjecture in a different way by perhaps finding this person's example from the 1970s, but using a totally different numerical technique?" His thought was twofold. One, if I can come up with a different technique, then maybe I can come up with more examples, perhaps even proof that there are infinitely many and not just worry about the six that were known up until then. Number two, maybe I can come up with a larger proof of the conjecture that wouldn't just rely on writing down more and more examples. Of course, for me to do this, I first had to write a computer program that could come up with one example. I spent a lot of time for my thesis just writing a computer program that would come up with this one example.
It wasn't reproducing the example from this guy from the 1970s. It was coming up with a completely different method. But I was able to do it. I do want to point out though that for my thesis, I spent a lot of time with Mathematica writing a computer program. I probably spent two years doing nothing more than just sitting in front of Mathematica writing this program. Of course, after I got the program written and had the example, then I was able to actually write a really nice proof to kind of generalize some ideas. But the point is, here I was in a pure math department, spending two years of my life as a grad student writing a computer program. So, I definitely saw it as an exploratory tool that I can get a better idea of what the general theorem should be.
That's the way I've always viewed computers, that it should be a good first step in writing down examples to get some intuition of what should happen more generally. I'll also say that I think of it in the opposite direction as well. Let's say that you do have a theorem, something that you prove. To me, if you know the theorem well enough, you should be able to write down a computer program based on the proof of the theorem that should give you examples. Like what I mentioned earlier, this idea of proving that there are infinitely many prime numbers versus finding an explicit of a prime number greater than a million. Well, if you really know the proof that there are infinitely prime numbers, that gives you a way to write an algorithm so you can actually find a prime number greater than a million. So there, the theory actually informs the computation.
But you still have to write a computer program that tries to do it. I've always thought of those as one in the same, always kind of hand in hand. It's not fair to say that if you write a computer program, you're never going to do any theory, and it's not fair to say that if you only care about theory, you're never going to write a computer program. I've always thought that one always influences the other. Now, you asked about limitations, and I certainly will say that the big limitation of computers is, you only have a finite amount of time to do the computation, and you only have a finite amount of memory to run the computation. This could be memory in terms of RAM, how much you can actually hold in the physical storage space while the computer's thinking about it, or even what's happening with the hard drive, physically how much you actually save to a disk.
But it's those physical limitations that mean that you're never really going to be able to compute everything. You will always have something that you won't quite be able to compute. That being said, it might come down to just waiting until you have a faster or more powerful computer that has more space, or even if somebody comes up with a fancier algorithm that runs just fast enough that the computer can compute what you want in the amount of time that you have allocated. But you are always going to be at the mercy of the speed or memory of the computer.
ZIERLER: Given the fact that we are in what seems to be a revolution leading to quantum computers, is there anything specifically that you're excited about that classical computing can't do that quantum computers might?
GOINS: My understanding about quantum computers is it really comes down to coming up with algorithms that a quantum computer can do that an analogue computer cannot. For example, when people were first coming up with things like the analogue computers or even the first digital computers, you really had to worry about very specific steps of how to add numbers together, how to multiply numbers together. For adding, we do it very much like the way that you're taught in elementary school, that you have the ones place, you have three plus seven, you put a zero, then you carry that to the tens place. But the point is that you're kind of doing it digit by digit. That's just the way that we naturally think of adding numbers. You add things digit by digit, and eventually you find what you care about.
My understanding is that Charles Babbage, Ada Lovelace, when they first came up with these first computers, this was the way that they thought of it, that the idea of addition was, if something could just do digit by digit, eventually you'll get things to work out. But now, of course, you have to worry about the allocation of how many digits you're allowed to store. Are you going to have an 8-bit computer or 256-bit computer? How many bits do you need to be able to do larger and larger computations? But still, the idea is that you're kind of doing it digit by digit to get it to work out. If you have a quantum computer, you can try to say, "What if we had an algorithm that doesn't add digit by digit? What if we came up with an algorithm that maybe uses this idea of not just a binary digit, but a quantum bit, a cubit, to actually do the computations?"
That, to me, is the exciting part. It's more the freedom of saying, "You're no longer constrained to what you're used to with analogue and digital computers. You don't have to worry about just adding things digit by digit and being constrained to the number of bits that your computer might have. Now, you can just be creative and come up with crazy algorithms that don't so much run faster but run differently." That's what I would love to see for the future of quantum computing, coming up with completely new ideas of how to do some of these computations. I'm sure that there are algorithms out there that people have that haven't even been invented yet. But that, to me, is the exciting part for mathematicians, coming up with something that hasn't been thought of because now, we're dealing with a computer that's no longer analogue or digital. It's a completely different beast that we've never thought of before.
ZIERLER: A question about the social side, the community of mathematicians that are important to you. Can you explain the origins of the project Mathematicians of the African Diaspora and your involvement in it?
GOINS: I'm actually a custodian of this project, and I took it over from someone else who started it almost 25 years ago. Scott Williams was a professor at SUNY Buffalo who started the whole project in the late 1990s or so. I believe the project went live in 1997. He's a Black mathematician, he worked in topology for the longest time. He would just go to conferences in his field. If he happened to run into another Black mathematician, he would make it a point to mark down that person's name, talk to the person, learn a little bit about their story, and he would eventually just create a webpage where he would talk about that person. He did this for about ten years or so. Going to conferences or other events, meeting people, writing down the information, writing up a biography, creating a page.
And he eventually created about 600 profiles of mathematicians and maybe another 300 or 400 pages of just stories from things that he heard from people. It was completely a labor of love. He got no money of right there. He just did it because he was genuinely interested in learning about other Black mathematicians, computer scientists, and physicists. Well, he retired in 2008, and I remember him telling us, maybe about 2005 or so, that he was going to retire soon, and he really needed someone to take over the pages. He didn't want this set of 1,000 pages to go away. This was at the Conference for African-American Researchers in the Mathematical Sciences, also known as CAARMS.
A lot of us Black mathematicians had known each other. I'd known Scott Williams since I was a grad student, and I attended this conference over and over again. I just remember Scott telling stories about people he would meet, people he wrote about in the pages, also saying that somebody really needed to take over these pages because he was going to retire. He did retire in 2008, and no one really stepped up to take on the pages. They just kind of languished for years and years. A good friend of mine named Don King, who's a professor at Northeastern University, would just tell me on and off over the years that he was kind of thinking about maybe taking over the pages and maybe trying his best to update them, make sure that we had new profiles that were being added, but he always said he didn't really know much about website and didn't really know where to go to even get the funding to do all of this.
Fast-forward, now, to 2015, when I became President of the National Association of Mathematicians. This is the nationwide organization of Black mathematicians. There was an event that we had maybe within the first year or so I was president, and I happened to be standing around chatting with Don King, and another friend, Asamoah Nkwanta, who is department chair in a historically Black college in Baltimore, Morgan State University. Asamoah had written lots of papers about Black mathematicians, so he was very well-versed in just the history of what's happened with Black mathematicians. He knew a lot of specific stories about people, and he was also very concerned with the future of the pages.
The three of us pretty much decided we were going to work together and try our best to update the pages. Now, neither of us had any experience in website design or even raising money to do website design. But we decided we were going to try it and do the best we could. I mentioned CAARMS, this conference for African-American researchers. The person who had created the website for that was named John Weaver. John's someone that we would see at the CAARMS conference over and over again. He wasn't a mathematician, but he had a lot of friends that would go to the CAARMS conference, so I got to know John pretty well over the years. That meant that the four of us decided we were going to get together and try our best to update the website. It took us about four to five years to figure out how to do this. It's a very complicated procedure.
We first had to figure out how to create a database. Scott Williams didn't have a database. He just had a series of 1,000 pages. There was no way to search, no way that any of them were linked. We had to take all of the content, put it into a database, figure out how to make the database searchable. Then, we realized that not all the information correct because Scott was just getting all of this from word of mouth or things he kind of pieced together. We had to hire students to go in and verify the information. Go online, try to find photos, email addresses, website addresses, rewrite some of the biographies in some cases, put all of this from scratch. We also needed to worry about raising money so that we could essentially pay for all of this. I would say that over the years, I've had to raise on the order of $100,000, and I had no experience in fundraising for these kinds of things. But I had to learn pretty quickly how to raise enough money so we could put all of this together.
After working hard on moving everything over to a database, hiring students who would update things, making sure we were adding in new names of people Scott hadn't added since about 2008 or so, I feel pretty comfortable with where we are now. I do have a series of students even today I'm working with who are looking to update the pages. I have eight undergrads from Pomona College, and I'm working with a colleague who has another five undergrads at Cal Poly Pomona. We're spending the rest of this academic year doing the same thing as before, updating the database, writing biographies, looking for photographs and even new names of people who are currently not in the database. It's sitting at about 800 names.
My ultimate goal is to take every Black American who's ever graduated with a PhD in the mathematical sciences and add them to the database. I'm estimating there are no more than 5,000 such Black mathematicians. The first got his degree, I believe, in 1923 or so, Elbert Frank Cox. So I think we can do this. It may take us another five or ten years. But I think it is possible to take everyone who's ever graduated with a PhD and add them here to this database.
ZIERLER: In your work in this project, what has been most satisfying in immersing yourself in this understanding that Black achievement in mathematics has this deep and rich history to it?
GOINS: What's satisfying for me is seeing the connections. I don't think that I really thought of all the connections, how all these individuals all kind of know each other and work together with each other. I'll give you an example. The second Black American to get his PhD in mathematics is Dudley Woodard. When he graduated from the University of Pennsylvania, he eventually went to Howard University, where he was the dean, and he started a master's degree program to kind of help other Black Americans to go get their advanced degrees in mathematics. When he started this program, there was a young undergraduate from Howard named William Claytor that he recruited to be in the very first class of the master's program. Well, Claytor eventually got his master's degree, and Woodard convinced Claytor to go off and get a PhD at the same school he got his PhD in math under the same advisor.
This mean that just a few years later, William Claytor became the third Black American to get his PhD in mathematics. Going down the line now, William Claytor eventually would go to a school in West Virginia, and he was teaching mathematics there at one of the local colleges. One of the students he had, you now know as Katherine Johnson, the woman who was in Hidden Figures. This meant that Katherine Johnson was actually being taught calculus by the third Black American to get his PhD in mathematics. There's this beautiful scene in the movie Hidden Figures where Katherine Johnson is trying to work out some orbitals, and she says she needs to know analytic geometry in order to resolve it.
Analytic geometry nowadays is called calculus. A lot of us believe that the calculus she actually learned was from William Claytor, the person who was the college professor who taught her back when he was in West Virginia. There's this beautiful connection of the second Black American to get his PhD in math, with the third Black American to get his PhD, with Katherine Johnson that leads everything up to present day that I don't think I really understood until I started to put all of this history together. This is just one of the things I love about history more generally, that there are all of these connections that you see. It just comes down to that you really have to understand the history, dig a little more deeply into it to see all these beautiful connections all laid out in front of it.
A History of African American Excellence in Math
ZIERLER: Perhaps there's one mathematician you have in mind specifically or maybe more as an overview of all that you've learned. But given that so much of this achievement in Black mathematics happened when obviously, African Americans did not have good opportunities in education, did not have good opportunities in being supported by professors, is there something that sticks out in your memory that just is so over the top impressive for what a Black mathematician has achieved in earlier generations?
GOINS: I would say yes. One who comes to mind is named Vivienne Malone-Mayes. She's someone I did not know personally, and she is, I believe, the fifth Black woman to get a PhD in mathematics. But what's fascinating about her story is that it's one of perseverance. I think a lot of the Black mathematicians that you read about certainly suffered a lot over the years. It's easy for us to forget that there were many schools in the country that forbade Black Americans from attending the schools. For example, the University of Texas's system really didn't let Blacks attend any of the schools until about the 1960s or so. A lot of colleges were this way. This is one of the reasons why historically Black colleges [existed] in the first place. Blacks were just not allowed to attend a lot of these schools. It was part of the state's charter, it was part of the statement there at the school. Vivienne Malone-Mayes was born in Texas, right around Baylor.
She decided to go as an undergraduate to Fisk University in Tennessee. There, one of her teachers was the third Black woman to get a PhD in mathematics, Evelyn Boyd Granville, who's still alive today, over 100 years old. The department chair at the time was a guy named Lee Lorch, who was a Jewish mathematician and very much an activist. If you study the Civil Rights movements from the 60s, you know that there were these freedom rides, people who were traveling from the North down south to help out white voter registration and what have you. A lot of the freedom riders wouldn't go directly to, let's say, places like Alabama and Georgia. They would kind of stop in Tennessee to get their acts together, figure out exactly what they were going to do because people were literally dying with buses being set on fire, people being dragged off the buses and beaten to death.
They had different classes in nonviolence. They were in Tennessee to kind of get people ready for what they were going to see when they went down South. Lee Lorch was one of the individuals who was very much involved with that. If you go to the Civil Rights Museum in Tennessee, there's a specific exhibit for Lee Lorch. When Lee Lorch passed away, there was a beautiful obituary written in the New York Times about all the activism he had done over the years. Remember, Vivienne Malone-Mayes was about 16 to 18 at the time, and these are her college professors. Third Black woman to get a PhD in mathematics and the indefatigable Lee Lorch. They eventually convince her to major in mathematics, stay on at Fisk to get her master's degree, and I don't know how they do it, but they eventually convince her that she should get a PhD in mathematics.
She decides that she's going to go back to Texas, where she's from. She's maybe her mid to late 20s. She first applies to Baylor University. Baylor, in general, has a rule, no Blacks are to be admitted to the school. So she gets a letter mid-1960s or so saying because she's Black, she cannot be admitted to Baylor University. She wasn't deterred. She applied for the PhD program at the University of Texas at Austin. She gets in, she's there in her classes. Unfortunately, there was a very well-known racist bigot named Robert Lee Moore who made it very clear he did not want Vivienne Malone-Mayes in his classes, and he didn't want any of his students to talk with her. So you see all these stories written by Vivienne Malone-Mayes and even people who knew her that said things like, when she was in grad school, she really wanted to work in this area of topology, but R. L. Moore would not physically allow her in the classroom.
She had to sit in the hallway to listen to his lectures. Also, a lot of her friends in grad school would go to one of these coffee shops in the area just to sit around and talk about math because this is what grad students do. Apparently, she wasn't allowed to go into the coffee shop with the friends because R. L. Moore told the students, "Don't let her in there." So you can imagine for anyone else, this would just destroy your thoughts of getting a PhD in mathematics. But she still made it through, and she got her PhD. In a really weird, beautiful twist of fate, the very first position she got as a faculty member was at Baylor University. Just a couple of years after she applied and was rejected for being Black, they actually rescinded all of that, and she came back as professor. So she actually was the very first Black professor in all departments that was hired at Baylor University.
That's one of these beautiful stories that you realize it was her mentors who encouraged her, "No, you go on no matter what because we fight for Civil Rights, so you have to do the same thing." And here, you have Vivienne Malone-Mayes, who did exactly the same thing. It's story after story you see like that when you actually are going through the history of all this. For me, it's really inspiring. This is why I really am inspired to tell more people about these stories, to learn more about the stories, so I can get more stories like this out there. But it's just remarkable, the things that you see.
ZIERLER: In the way that you've marveled at all of these connections in the history of Black mathematics, do you see in ways that you didn't before your involvement in this project your own intellectual heritage and connections for your approach to math, where that might come from culturally in the history of this field?
GOINS: I would say so. I think it's affected me in many different ways. When I was an undergraduate, I was very interested in history. I didn't quite major in history, but my senior thesis was in history. I spent pretty much the majority of my senior year in the history department. I even won the Rod Paul Prize, which is for the top student graduating in history for the work I did. So I've always wanted to get back to the roots of being in history. I just never imagined it would quite be in this way. But for me, it feels very natural to work on this project. Also, a lot of what I've seen historically helps me keep things in perspective with what's happening today. When I take a look at some of the mathematicians I've seen over the years, just in reading these stories, I then see some who, like Vivienne Malone-Mayes, were very inspired by their mentors, and they went on to have very successful careers. That means I have to think for myself, "Am I doing the right thing by mentoring my students? Am I doing enough to encourage them to also go on?"
I see, because I see it from a historical lens, the power of being a really, really good mentor. In the same way, I also see stories of individuals who are completely beaten down by the system, by racism, by being ignored by being shunned. In the same way, I have to ask myself, "What about the students who don't feel comfortable staying in mathematics? Am I being active enough to make sure I'm kind of eliminating some of those barriers, those negative experiences that students are experiencing that are driving them away from the field?" So just by looking at the history and these stories, it's helping to inform how I think about what's happening in the field today. I really have to be careful because I realize that I don't have all the answers. But at least in seeing the stories, I think it's helped me to ask the right questions.
ZIERLER: I'd like to ask about some key funding sources that are most important, both for your research career, but also in the way that you want to make mathematics more diverse and inclusive. So let's start first with the National Security Agency. Of all agencies, I'm curious, why is the NSA interested in supporting what you're doing right now?
GOINS: The NSA is certainly interested in the outreach of doing mathematics. I had a graduate fellowship where I actually worked for NSA for a couple of summers. I view NSA as a place that just has a lot of employees who love mathematics. I do realize that it can be viewed in a very controversial way. But really, the people I work with, I think, are very conscientious people. They certainly do understand the consequences of the math that they do. But also, in general, they really, really love mathematics. There are different ways in which you can get funding from the National Security Agency.
The way I've gotten funding the last several years is from their REU program, this research experience for undergraduates. NSA doesn't really like to give funding for, let's say, security research. Because kind of the feeling is, they do it, they do it well. They're not going to pay other people to do security research. Instead, they prefer to give money more for enrichment. More or less, they count this as outreach. So I appreciate having funding from NSA so that I can expose students to the beauty of doing mathematics. That's the whole idea of getting funding for an REU, just so I can expose it to them.
ZIERLER: And the National Science Foundation, on many programs, has been such a strong supporter of your efforts on so many levels to make mathematics more diverse and inclusive. Can you tell me about the origins of your partnership with the NSF and what they've allowed you to do?
GOINS: Definitely. They've allowed me to do quite a bit, but I'd say from very different points of view. Of course, there is the REU, the funding that I've gotten from the NSF for this research experience for undergraduates. It's the same concept as with the NSA, very much for outreach. There, you're just trying to expose undergraduates to the beauty of the subject. I've felt very fortunate in getting funding from NSF in that sense. Also, I've gotten funding from the NSF for running conferences. One of the ideas is that you want a way for undergraduates to present the work that they've done in the past. When I was president of the National Association of Mathematicians, we received funding from the NSF to run what we call Math Fest. This is an activity that takes place over about two and a half days that really is meant for undergraduates, specifically undergraduates from minoritized groups, but I'll say even more specifically, undergraduates from historically Black colleges and universities, to give talks, presentations on the research that they've done the summer before.
What's beautiful and remarkable about NAM's undergraduate Math Fest is that you might have on the order of 20 or so Black and Brown undergraduates all talking about mathematics research. This doesn't happen anywhere else on the planet. But these are definitely beautiful, high-level research projects. Some of it can be theoretical math, some of it might be statistics, it might be applied math. But it's all mathematics. They actually don't really have faculty giving talks at this conference. The idea is that it's really for undergraduates, by undergraduates. Primarily, you have on the order of 100 or so undergrads that attend this conference, another 20 or so undergrads that present talks, maybe another 15 or so undergrads that present posters. But it's all about undergraduates presenting to other undergraduates.
And I really love the fact that the National Science Foundation understood the importance of this and was willing to help fund it. What I'll say more generally is that it certainly feels good to be supported by this government agency in different points of view. When I'm doing the REU, that is funding for research. There, it's very much about saying that we want to not only encourage undergraduates to learn about the beauty of mathematics, but we also want to expand the knowledge of mathematics itself. When you're dealing with the conferences, that's more for undergraduate education, if you will. There you really are giving undergraduates the opportunity to present on what they already know. Of course, as we know, whenever you give a lecture on something that you think you know, you get to know it better.
I love the fact that we have funding there from the NSF in a very different point of view from the undergraduate education so that undergraduates can present to other undergraduates. It's just been really great that I've gotten funding over the years in very, very different points of view but all that kind of put forward this math.
ZIERLER: Your wonderful essay, Three Questions: The Journey of One Black Mathematician, what are those three questions, and why did you frame the essay in such an interesting way, where you posed these questions and wanted to submit them outward for the community to think of themselves?
GOINS: That piece was really meant to be an introspective think piece. I have to admit, I'm a big fan of The Walking Dead, and really, the questions come from something that one of the protagonists, Rick Grimes, would say. The Walking Dead is the story of this dystopian future where zombies have taken over, and humanity has completely fallen apart. When you're kind of walking through the woods, you don't know who you're going to meet. You don't know if it's going to be someone storming for food who really needs help, or if it's going to be someone who might be out to kill you. Rick Grimes had this rule. Whenever he would meet someone, he would ask three questions.
And the questions at the time were, I believe, "How many people have you killed? Why did you kill them? Would you kill again?" I don't remember the exact three questions, but it was something where he was asking this person he would meet, essentially, "Are you a good or bad person? Can I really discern who you are based on how you answer these questions?" That's the general idea of this think piece. Let me see if I can really remember what the questions were. In this article, I ask the question–this was more for myself–"How many Black students have you admitted in your department? How many Black faculty have you hired in your department? And why?" So the three questions, for me at least, were meant to say, for the department I was in, because I was there at Purdue University for 14 years, "How many Black undergraduates, how many Black students, do you have in the department?"
I was really more focused on the number of Black PhD students, although I could've asked more generally what was happening with Black students all over campus. I wanted to know how many Black PhD students we'd had historically in the department. That meant I had to go through some records and do some history to try to figure out, of all of the students Purdue has had in the entire history of the school giving out PhDs, how many were Black? I think at the time, I came up with the number of seven, which really shocked me. But I don't really think I was expecting a [specific number] one way or the other. I think it just surprised me that the number was seven because Purdue graduates on the order of about 25 every year. That means if you round the numbers, maybe the department's been around for about 50 or 60 years giving out PhDs, that there may be close to about 1,000 or so PhDs out there in mathematics from Purdue University.
Hearing that there were just seven total in the history of department, for me, was shocking. Then, I decided to ask about faculty. Very similar question. How many Black faculty had the department ever had in the history of the department? I knew in the 14 years I was there, the Math Department had only hired one Black faculty in those 14 years, and that was me. So I wanted to know, before me, how many people had come. Again, I don't remember the exact numbers. It might've been something like three. Again, the number of Black faculty was very, very small. For comparison, there's around 100 faculty in the department now, so if there were only three total out of close to 100 years of the department, that was also very surprising.
The third question was not so much a quantitative question, asking how many. It was more qualitative. Why? Why is it the case that there are only seven? But that really is a double-edged sword because I wanted to know why in a bad sense of, "Why so few?" But also why in the good sense of, "What had we done right in that we had attracted these students or faculty?" Again, it was really a think piece. But I put this out there more for faculty at other schools to ask the same question. If you look at your own PhD department or even your own undergraduate institution, how many Black students do you have? If you look at the faculty that you have, how many Black faculty do you have?
And then, instead of asking the quantitative question, asking more of a qualitative, why? Is there something that you're doing right to attract all of these students, more like what I was asking here at Pomona college, versus something you're doing wrong that might be driving them away? Really just being very introspective about all of this.
ZIERLER: The last topic I'd like to engage with you for today's session is one that's very much still current events at Caltech, and that is the decision to rename some of the buildings that have been associated with professors and benefactors who, of course, were associated with the eugenics movement. To put this in historical context, when you were a student at Caltech, of all of the problems that you might have dealt with, from micro-aggressions to more overt problems, was the fact that the tallest building on campus was named after Millikan something that was specifically problematic for you? Or was that more of a general issue, and it wasn't specifically on your radar back then?
GOINS: Ironically, that wasn't the key issue, but there was another issue that was a key issue that I still want Caltech to address. I can't say that I was aware of Robert Millikan and his work with eugenicists in particular. I've always worried about putting men's names on buildings literally as a monument to them without being very questioning of who they were as individuals. One thing I learned when I was an undergraduate kind of doing the research of minorities at Caltech is, the curious meeting of William Shockley and Grant Venerable. Now, Grant Venerable was the first Black student to graduate from Caltech, did so in 1932. But if you take a look at the yearbooks going way back when, Grant Venerable and William Shockley were in the same class. Now, William Shockley, a lot of us as physics majors, know because he would go on to win the Nobel Prize because he invented the transistor.
The transistor is ubiquitous in all of electronics today. You can't run a computer, you can't run a laptop, you can't even run a watch. In fact, you can't even run your car these days without the transistor. Now, I don't remember if Shockley's name was literally on any of the buildings at Caltech. But certainly, being a physics major, you're very much aware of this guy who has his undergraduate degree, who got the Nobel Prize. He's a big, big name in physics. When I was an undergraduate, I remember turning on television, watching PBS at one point, and there was an old, old interview of William Shockley, maybe in the 1970s. But he was discussing a little bit about his philosophy on life, science, what have you.
The interviewer at one point asked him how he invented the transistor, what it was like to win the Nobel Prize, and what have you. Then, the interviewer eventually went to his thoughts on current society and where he thought things should go. Here was this 19, 20-year-old Black kid in Los Angeles, finishing up my degree at Caltech, watching this older white guy on television talk about how he thought he felt bad for Blacks because they were mentally inferior. He was completely convinced from their lack of social mobility, from their lack of entering colleges and universities and getting degrees, that this was just empirical proof that Blacks were inferior, and he really wanted to do something to help out Blacks. I could see that he was trying to approach this from a very kind point of view, but also, he was approaching this from a very openly racist point of view.
That more disturbed me than I think anything that I've seen about Millikan because that was a direct lineage for me. Seeing this guy who had a Caltech degree that Caltech hyped up as one of its great alumni who had a Nobel Prize, who had worked on something that was so ubiquitous in everything that we see in everyday life, but yet seeing that he had such horrific views that were all right there for the world to see. Knowing that he was a classmate of the very first Black alum from Caltech was also very jarring for me to kind of see those two juxtaposed. I've always wanted to delve into that a little bit deeper because it's not clear to me that Shockley was even aware that even though he said he had all this empirical proof that Blacks were mentally inferior that his classmate was a Black student. I just want to delve into that a little bit deeper. I would argue that yes, Caltech was doing the right thing at the very least in questioning the names for the individuals that they have on their buildings.
But I think it would be better for Caltech to really delve a little bit more deeply into some of the beliefs that some of these individuals had, to really question why it is that they would take the names off of buildings. That, I think, is going to be a little more informative to individuals because right now, I think a lot of individuals have this knee-jerk reaction of, "Well, we live in a cancel culture. We're just taking the names down just because people think it's the wrong thing to do." I would very much like to focus a little bit more on what exactly these individuals said and believed so that more in the Caltech community would really understand why some of this is problematic.
ZIERLER: Were you involved in some of the debates in 2019 and 2020 that led to the creation of the Renaming Committee? And did you have the opportunity during these discussions to make this point that you're making to me now that there needs to be a more expansive look at the way Caltech understands and celebrates some of its most prominent figures in history?
GOINS: I was not. I think I just read about it like the other alumni did. I remember when the article in the LA Times came out from this one alum, who really tried to put a lot of the information out there. I remember tangentially hearing about the conversations at Caltech. I think I remember hearing when this commission was formed. But I wasn't formally involved with any of that. Here at Pomona College, we're actually having our own set of discussions about all this. Ironically, the building I'm in now, where my office is, was named Millikan Labs. Same Robert Millikan. Before I got here though, back in 2018, there already had been a lot of discussion amongst the faculty, the students, and the alumni about changing the name of the building.
And by the time I got here, the board of trustees had already voted to take the name off. There was more discussion of what they were going to change the name to. We actually did change the name of the building about a year ago, right about the time the discussion at Caltech was starting to happen about changing the names. Now, we actually call the building Estella Labs after, I believe, the granddaughter of one of the donors of the buildings that we have here in the Science Complex. But I can tell you that there was a very similar discussion happening here at Pomona.
That discussion, though, was a little bit more on, "Can we think a little bit more carefully about who the buildings are named after, perhaps, going back to see what it is they believed and did?" I know there's a more general question of the process of removing names on buildings, if that is something we want to do. But I can tell you that at least that discussion of having Millikan removed from the physics and math building was something that happened before I got here. So really, when I got here, it was already a done deal. I found it really interesting that while Caltech was starting the discussion, Pomona had already finished it and moved on.
ZIERLER: In the way that you're approaching this from a deeper level, my last question for today–and it's one that is really of paramount importance in the way we go forward. The one issue, as you say, is, there's this debate between maybe some benefactors or senior faculty that this is just cancel culture, and there are graduate students who say, "Take these names down yesterday." That's the debate that we're in the middle of right now. But the question moving forward and the one that's so important to get right from the beginning is, how do we ensure–and by we, I mean not just Caltech, but higher education, because this is something that's happening all over the place in the United States–that in taking down the name of somebody with this problematic past that it's not just a gesture, that we've done this gesture, and we can pat ourselves on the back, and ironically, maybe not do the harder work that you're focused on? How do we ensure that this is the beginning of a process and not the end of one?
GOINS: That's definitely a difficult question. I personally have always been a fan of history. I've learned, just by studying history, that there are a lot of times that you don't want to shy away from things, and you also don't want to sweep things under the rug. You do want to shine a light to understand as much as you can. For example, I'm certainly a big fan of maybe not having monuments for people, but having displays in museums. I am very much in this idea of making sure that future generations know what's happened in the past for the good and for the bad. Having a name on a building or having a monument is tricky. Because of course, as humans, we get to be very finicky. It could be that one generation really appreciates someone or some idea for years and years, and it might be that a later generation thinks of that very differently.
I don't really know if I have an answer in really trying to figure out how to deal with this generational divide. For example, here in the state of California, growing up, Columbus Day was a big thing. Now, people have replaced Columbus Day with Indigenous Peoples Day. What I like about that, at least there's a discussion of what it meant for a person to discover a country. There's a question of what exactly Christopher Columbus did. I love that from a historical point of view because now, we can delve deeper into that and just focus on the facts of what happened. Whether or not you think he was a good person is a judgment call you can make later. But I do like the idea as a historian of looking at that more carefully. Similarly, really understanding more about Native American cultures, what we know about the lands here in Southern California.
Again, just learning a lot more about the history. But this question of whether or not we commemorate Christopher Columbus on this day, I don't really have a good answer to. Generation after generation, there's going to be a different thought of that person, of these people, and that person may just fall out of favor. It might just be the way the generation views it. I wish I even had a better answer when it really does come to how buildings are named, especially in a place here like Pomona.
I know there are a lot of rules, specifically in the state of California, about how buildings are named, how names are removed from buildings, what happens if someone gives money to a building and wants their name put up on there versus the school deciding that the name's going to be taken off. I do understand from a legal point of view, that's a very complicated thing. All that I can say as a historian is, I really just appreciate the concept of learning as much as you can about that person that you might possibly name the building after.
ZIERLER: Well, Edray, this has been a phenomenally interesting and immersive conversation about the big questions and areas of research across your career and life. In our next conversation, we'll go all the way back to the beginning and get the story of your family origins and your childhood. So thank you so much. We'll take this up next time.
[End of Recording]
ZIERLER: OK, this is David Zierler, Director of the Caltech Heritage Project. It is Monday, November 8, 2021. It's my great pleasure to be back with Professor Edray Goins. Edray, wonderful to see you. Thank you again for joining me.
GOINS: It's great to be back.
ZIERLER: In our first conversation, we tackled the big questions as they relate to your commitment to research, to teaching and mentorship, and to your commitment, of course, to diversity and inclusivity in mathematics. Today, what I'd like to do is take the conversation all the way back to the past and your personal journey. Let's start, first, with your parents. Tell me a little bit about them.
GOINS: Well, my mother is originally from Texas, and father's originally from Chicago. I guess to go back a little bit further, back to their own parents, they were both products of the so-called Great Migration that happened with a lot of Black Americans between World War I and World War II. My understanding on my father's side is that his father was a minister who lived in Louisiana. He eventually moved up to Chicago. That's where he met his wife. On my father's side of the family, there's something like 12 brothers and sisters. My father's father passed away when he was very young, I think when he was maybe 3 or 5 years old. So he never really knew his father. My father's the second-youngest of all of his brothers and sisters. In fact, I think he's the youngest.
He was part of just a very, very large household. Most of his siblings did not go off to college. I know he himself went off to the Vietnam War in the early 1960s. When he came back, he really did not want to go back to Chicago, so he ended up moving out to Los Angeles. My mother, on the other hand, grew up as a single child in Texas. She actually grew up in Marshall, Texas. But that's kind of Eastern Texas, almost Western Louisiana. It was really just the three of them growing up. It was my mother, her father, and her mother. Her father moved out to Los Angeles in 1942, somewhere around there. Right about the end of World War II. Because essentially, Blacks couldn't find any employment in that part of Texas. Segregation was just the law of the land back then.
A lot of Blacks moved out from that part of Texas to Los Angeles, and this was really part of the family that I grew up with. Her father moved out to LA I believe a year later. The father, then, called for my mother's mother and my mom to come out to Los Angeles. They moved out, I'd say, 1944, 1945, somewhere around there. Since there were so many Blacks that had moved out from Eastern Texas to Los Angeles, there was a huge community of folks that all pretty much knew each other in Texas when they moved out. My mom was only about maybe 6 years old when she moved out from Texas. So pretty much everything she knows is out in Los Angeles. But I'll say that all the relatives that she grew up with, aunts and uncles, godparents, what have you, all actually knew each other from Texas. It's really kind of strange.
They moved out to the largest, oldest Black Baptist church in Los Angeles. This is all where the history gets very, very interesting. A lot of Blacks who moved out to LA were not allowed to have bank accounts, they were not allowed to live in certain places in the city due to housing covenants. A lot of people could not afford their own cars. So that meant that the churches weren't just this religious institution that people think about. They really were the hub of all of Black life. For example, the church that I grew up in had its own credit union. Because Blacks moving out to Los Angeles didn't have credit cards or bank accounts, so they needed some way to keep track of their money.
The church was a way to do that. In terms of finding places to live, if you take a look at the history of Los Angeles, there are a lot of places in LA that, by law of the city, were not allowed to either rent or sell to Blacks. Which meant that a lot of Blacks lived in a very concentrated part of downtown Los Angeles. Central Avenue District right there in downtown LA. So when they wanted to find places to live, when they wanted to have bank accounts to do things, everything was very central to the church. That meant when I was growing up in the 1970s, I really saw a lot of this. I had a lot of friends of the family who had moved out to LA in the 1940s. The very first places that they lived were all in this concentrated area. So not only literally did they live together, work together, and go to church together, but this was their lives.
I say all of that to say that my mom grew up in this area where even though she was a single child, an only child, she had a very strong extended family. That extended family was all part of the church that I grew up with out there in Los Angeles. She and my father met somewhere in the mid-1960s or so. I was eventually born in 1972. My brother was born two years later. But really, everything was right there kind of in Los Angeles. I can't say that I knew my father's side of the family very well growing up. He did have a couple of sisters who had moved out to Los Angeles who I knew pretty well. But in terms of the majority of his brothers, sisters, all of the cousins, grandkids, and everybody else, they were all in Chicago, and I didn't get to know them at all until I was much, much older.
Let me maybe say a little bit about what my parents did in terms of their employment. My mother was a teacher, just like her mother before her. So my mom taught either 1st grade or 3rd grade for the majority of her career. She worked in Inglewood, which was right on the border of Los Angeles. I never really saw the difference between Inglewood and Los Angeles proper because it was so close to where I grew up that half the time, I was in LA, half the time, I was in Inglewood. I just never thought about the differences between the two. So we grew up not too far away from where she worked. She worked for Los Angeles Unified for a few years, but I want to say of maybe the 33 or so years that she was a teacher, she really taught in Inglewood Unified School District. My father, on the other hand, worked as a technician for IBM.
You may remember that before we had these fancy kinds of printers, you actually needed to have a copier, and this copier meant that you had to have paper that went through it, and random things could happen. Of course, the copier could break down. You had to have a specialized technician to come out and fix it. He eventually got trained to fix some of these computers. But these weren't computers as we know now with fancy hard drives and USB drives. They literally had hard drives that were maybe 12, 15 inches in diameter. So he also had to worry about soldering in the microchips to make sure everything was fine. But you had technicians who were on daily call to go to business after business to fix all of these things. He would drive around, if not in his car, then on his motorcycle, in random parts of Southern California every single day. Because he would just get called for this specific company to go fix this.
He might be in Beverly Hills one hour, San Diego another hour, San Bernardino another hour, just constantly moving around, fixing item after item. So they were very different people. My mom, I would say, was more into the finer things in life, for lack of a better way of saying it. There at the church that I grew up in, they were very much into listening to a lot of classical music. So in terms of playing music there at the church, they were very much into things like opera, Handel choirs, singing just a lot of very classical songs and pieces. My father, on the other hand, was more of just a guy's guy. He would like to spend the evenings kind of hanging out with his guy friends, having a beer, that kind of thing.
I kind of grew up more understanding my mother's side of things, which meant she was a teacher, just like her mother, she played classical piano, just like her mother. She actually got her master's degree in Organ Composition and Music Therapy from USC. My father, on the other hand, went to LA Trade Tech, but he doesn't really have a college degree. I think he was there for a few years. He might have a technical degree. But he never went to college. My mom was supposed to go off and get a PhD. She was on track to. She got sick. She had an accident where she got burned when she was finishing her undergraduate years. She never went back. I know that the family really wanted her to, but she decided not to go. Whereas on the other hand, my father really had no interest in going to college.
They were very different people. But I'll say that a lot of the way that I am now was kind of a merging of the two. They separated when I was younger. They started to live in different houses when I was around 4 years old, maybe even younger than that. They officially got divorced when I was around 15 years old. Right about the time I was starting high school, 15, 16, is when my father remarried and moved back to Chicago. So he was around to see my high school graduation and me graduating from college. But still, I kind of grew up in a household mostly around my mom and seeing my father every now and then.
ZIERLER: Some foundational questions about the origins of your family moving out to Los Angeles. Obviously, this is much before your time, but in the stories that you heard, what were some of the industries or sources of opportunity that compelled families like yours to move from places like East Texas to Los Angeles?
GOINS: A lot of the professions that people had were more trade kinds of professions. The women were certainly into being teachers. That was primarily what the women did. Everybody was either elementary school teacher, high school teacher. Some would eventually become principals and what have you. But that was very much what they did. The men, on the other hand, might've been into construction work. That was a big one that a lot of the men did. Some of them were in the Los Angeles County Probation Office, so they were very much into being truant officers, probation officers, what have you. Not many were teachers. Only a handful. But the ones who were very successful either became bankers, lawyers, or doctors.
But it was very much kind of one of those types of professions. What I learned is, a lot of the ways people got into these were by people they knew. For example, if you wanted to get into construction work, it was all a matter of knowing somebody else who was in construction work. You learned the trade and eventually got into it. Another thing, especially for the men, is, they understood that they were going to be kind of held back because of segregation. So they were very much into working in offices that were very progressive in Los Angeles. My understanding is that the probation office that Los Angeles County had was very much an integrated office. They understood that they wouldn't have been held back for different positions that they wanted to eventually go for.
I know that for the women, my mom always told me that being a teacher in Los Angeles County was very tricky back in the 1960s. There, if you were unmarried, it was relatively easy to be a teacher and do your own thing. But as soon as you got married, things became very tricky. I believe there were times where you had to either resign your position, or you maybe had to move to a different office, a different county. It was very tricky if you got married to be able to keep your position as a teacher. I know that it was very different depending on the profession. But certainly, people were choosing the professions when they moved out there in the 40s and 50s based on who they knew, the lack of hindrances that they might have.
But it was a very tricky thing. Now, my mother's godfather, who was essentially one of her parents, because she had, like, two, three different sets of parents, depending on how you count, would always tell me that there were basically no opportunities when he was in Texas. It definitely wasn't like, "You have to choose whether you want to be a construction worker or probation officer." He made it very clear, there were no opportunities at all. If you worked in Texas at the time that he was growing up, he knew that he would have to be a porter on a train or a ditch digger. But he basically made it very, very clear, there were zero opportunities. That really stuck with me. When he said that he was moving out to Los Angeles–and it definitely wasn't a matter of moving out to LA so that he could have a fancy job and a really nice house.
He made it very clear he was moving to LA because he didn't have a choice. Either he moved to LA, or he'd have zero life whatsoever. He said that he knew it was taking a huge risk. He didn't really know what life was going to be like in California. He just knew that there was no way he was going to live a life under Jim Crow South in Texas in the 1940s. So he moved and never wanted to go back.
ZIERLER: Of course, segregation played a big part in the lack of economic opportunity in places like Texas. It's so jarring to hear you talk about restrictive covenants, not being able to open up bank accounts. Was your family clear-eyed, or was there a certain naivete about what kinds of racial politics existed in Los Angeles before they arrived?
GOINS: No, it was very clear. But I think it was understood everywhere in the country, it was like this. Moving to LA, you knew that you had to navigate a very different system, but again, they all kind of went to the same church. I think the way they said it was, they were in Texas. They knew that there was a Black Baptist church where people were going to, so they simply went to LA, right away became members of the church. Again, this wasn't a religious thing, it was more just how you networked to understand how to learn about all these housing covenants, restrictions with banks, and so on and so forth. When they moved to LA, they learned right away, "These are things you can do. These are things you cannot do." And once you kind of knew the rules, then you would kind of learn how to navigate through it all. But they knew from day one, literally, when they got to Los Angeles, "This is life. This is the way it is."
ZIERLER: What stories did you hear growing up about your family's experiences during the 1960s? The early part, during the Martin Luther King years, or the later part, particularly in 1968, when things were violent and very scary in parts of Los Angeles?
GOINS: I heard story, after story, after story. The first one that comes to mind is the Watts riots. It was 1965. LA has always been a very segregated city. I don't think a lot of people want to admit that, but it's always been this way. My mom and her parents moved out to a part of LA where they were only allowed to live in the Central Avenue District. Essentially, right now, what's the very compact area of downtown Los Angeles. We're talking around Central Avenue, just east of the West Adams District that a lot of people know the affluent Blacks would live in. But they wouldn't go below, I'd say, maybe about 20th Street if you're kind of heading south from downtown Los Angeles. Literally, the housing law said you were not allowed to move down that far south.
By about the 1960s or so, you had cities like Inglewood, who were known to have sundown covenants. What that means is, if you were Black and in the city of Inglewood, you better not be in the city after sundown because anything can happen to you. You hear about a lot of these things in the Midwest and in the South, but you don't really think that a city like Inglewood actually did have these sundown covenants. At the time, it was called an all-American city because it was predominantly white. Actually, Pepperdine University used to be in that part of Los Angeles. Not in Englewood, but very close to that part of Inglewood. It was a very white, affluent area in the 1950s, early 1960s or so. There was a lot of white flight, where whites, especially college professors, moved out of that area. Eventually, by about the 1970s or so, Pepperdine moved over to Malibu.
A lot of people don't know that it was in that part of Los Angeles. This meant that a lot of Blacks were now moving from this kind of restricted area in downtown Los Angeles out further south to areas like South LA and Inglewood. This is kind of what my mom and her parents did. They moved from the Central Avenue District, where I think they had a one-bedroom apartment for the three of them, and then they moved out to a nice two- or three-bedroom house right there on the border of where Inglewood was. I actually grew up in that house, the same house that my mom grew up in. It was only two or three miles away from where Pepperdine University used to be.
My mom would tell me when she was growing up in the 1950s in that area, and by about the time that she was in high school in the 1960s, she knew that there were college professors living up and down that block, these white affluent college professors. They eventually passed away or moved away. But I certainly understood the history of that area there. Now, fast-forward to about 1965, when the Watts riots happened. I think there was a lot of resentment about how the neighborhood was changing. But still, a lot of Blacks were feeling that they didn't have any power over where they lived. When the LA riots or the LA uprising happened in the 1990s in Los Angeles, there was a lot of animosity between the Black residents and the Korean store owners. My understanding is that in the 1960s, when the Watts riots happened, it was very similar.
There was a lot of animosity between the Black residents and the Jewish store owners. I specifically remember my mom telling me that right about that time, she was finishing high school, and she says that she remembers that when the Watts riots started, the National Guard came into the city, and they were trying to figure out what to do to quell all of the violence. She says that she remembers a tank rolling down the city streets one of the nights during the riots. Again, this is the same house that I'm growing up in, and I'm trying to wrap my head around this idea of a tank rolling down the city streets. Because these streets really aren't that big. But she told me this was the way the Watts riots happened, that it was just kind of a scary time. It was a feeling that people wanted the world to listen because people were very unhappy, but also this is just what happened that really resonated with me.
I remember asking her about all of these when the LA riots happened in 1992 or so. I really wanted to know what the comparison was. It was really scary to think it was almost exactly the same situation. Here we were, some 27 years or so later. It was exactly the same kind of animosity. Another one of the stories that they would tell me was about when Martin Luther King was assassinated. This was just a few years later, 1968. The way my mom would tell the story, and she still does to this day, it was in April of 1968, and she had just gotten off work. She remembered this day well because it was April 4, and it was her father's birthday. She had gotten the birthday cake together, and they were going to have this big celebration.
They get there to the house, they turn on the news, and they realize that Martin Luther King had been assassinated. What I also learned at the time was there were a lot of people, especially people her age, in their late 20s or so, who really wanted to be involved with the Civil Rights movement. Remember, the church I grew up in was a central hub of activity in Los Angeles because of how many Blacks had come out to the city. Martin Luther King would come to the church to give talks and rallies. You'd have many people, James Lawson and others, to come by the church to talk about what was happening all around the country. It was a central hub. It wasn't something that was far and removed. There were a lot of people who were very, very active. My mom would tell me that a lot of the younger people really wanted to be involved with the movement.
It was their parents who were scared to death about having their kids go off to the South and do this. They were very well-aware of people being killed, being lynched, being set on fire. They knew all of this was happening. Of course, they didn't want their kids to go off into all that. But my mom made it very clear that a lot of the youth involved with the church in their 20s really wanted to be involved. So they were following all this very carefully. She said that when Martin Luther King was assassinated, it just kind of let the air out of the sails of everybody who was really involved. She did say that a couple of days later, I guess there were maybe some stores that were set on fire in Los Angeles. I know there was a lot of uprising in other cities, Washington DC, Baltimore, what have you. But I know there was just kind of an unease that happened in Los Angeles at the time. Those are just a couple I remember she would tell me from the 1960s.
ZIERLER: What about community relations with the police in the way that that, in 1992, was such a major source of tension? Did you hear stories about that in the 1960s as well?
GOINS: Oh, yeah. Yeah, definitely plenty of stories. Let me say, it depends on who's telling the story to see what perspective you're going to get. Remember, the area that I grew up in was very much about self-governance, Blacks helping other Blacks, this whole thing of the church helping out with the community. That meant that the Black Panther Party was very, very popular in that part of Los Angeles. Now, those who are listening to all this, let me first back up to say, when I think of the Black Panther Party in that part of LA, I'm thinking of the programs that they had in Oakland back in the 1960s. This meant that they were very much about kind of working with the community.
They had breakfast programs, free lunch programs. They were doing a lot to make sure that the community wasn't going without things. If there was someone homeless, they would just work to, say, set up a homeless shelter or a food distribution center. They were 100% about, "Let's work with the local community to get things done." In the same way, the Black Panther Party was very much about, "We don't trust the police," because they were coming in, beating people up, harassing them in police stops, all of these things. There was a general feeling of, "We really don't trust the police because they're not helping our community, they're harassing our community."
Also, I remember my parents telling me that in the 1950s, early 1960s, when Ronald Reagan was governor, he was very much about anyone on the street can own their own guns. So it wasn't kind of a crazy thing for people just to have their guns just to kind of protect themselves. I had a lot of relatives who told me that even when they were in college, it was just kind of the thing to have your own gun. You didn't necessarily advertise it, but back in the 50s and 60s, that was just something that people did. This was if you were Black and really didn't trust where you were, your surroundings. Hearing all of that, I got this image growing up of the Black Panther Party was 100% about protecting the community, not just by having a gun, but also saying, "If someone's homeless, someone needs help, we're going to do whatever we can to help out the local community."
That not only happened in Oakland, it also happened in Southern California. When there were shootouts with the police in Los Angeles, I would hear my family kind of say a very different side of things. It was more saying, "Yes, we understood that the Black Panther Party was helping out the community in Los Angeles. Yes, we understand that they were a little bit on the fringe in how they were openly flaunting having guns out in the streets. But when the shootouts happened, that wasn't really so much of a surprise. It was more kind of being upset that the news told one side of the story, but the Black community thought a different side of the story." I do remember growing up, starting, when it comes to relationships with the police, hearing about the Black Panther Party, and the shootouts that happened in Southern California, and the fact people were really saying they didn't trust the police to the point that almost everybody had a gun. It didn't really matter who you were.
Almost everybody had a gun at one point or another. Now, fast-forward to, let's say, the 1980s. This is when I was growing up, about elementary school or so. There is a TV show called Snowfall, I believe on FX, where they try to talk about what happened in Los Angeles in the 1980s. Essentially, the show tried to say, when crack-cocaine hit the scene, things went really crazy in LA. I definitely remember being in elementary school or junior high school, having all these conversations about what crack-cocaine was, what it was doing to the community, how people were all of a sudden going crazy about wanting to break into other people's houses just to get a fix, how the police were doing drastic things to kind of cut down on all of this.
I remember the conversation about what's called the batteram. This was this battering ram that was put on the edge of a tank so that tanks could now knock down people's door, so the police could get inside. There were rap songs at the time talking about all of this insanity that was happening with the police just raiding people's houses and what have you. Now, remember, I'm 10, 12, 14 years old hearing all of this. When you're that young, hearing about how the police are ripping apart the Black community in Los Angeles, it doesn't really give a whole lot of trust and respect that you have for the LAPD. Ironically, growing up, I knew about Mayor Tom Bradley. He was the mayor of Los Angeles who became very well-known because he was, I believe, the first Black Police Chief of the LAPD.
He was very well-beloved to the Black community. I remember meeting him several times growing up at different events the church had run, different events there in the community. But then, you had somebody named Daryl Gates who became head of the LAPD, and he was loathed by Blacks in Los Angeles. Just kind of the general feeling was, if anybody could be any more racist, we couldn't think of who they were. The 1980s or so, because of the crack-cocaine epidemic, because of things like the batteram, because of even things like the chokehold that was coming out of New York City, there was more, and more, and more distrust with Blacks in the LAPD. When you put all of that together, we're talking about what happened with the Black Panthers in the 1960s, all the distrust through the 1980s, when everything finally came to a head with the four police officers who beat up Rodney King in 1991 or so, it was almost like we could see all of this coming, and we definitely hate the police.
It was just kind of this very, very long buildup to the early 1980s or so. But I can tell you that it was just decade after decade of a lot of us growing up in LA, seeing all of these things happening year after year on TV, in movies, in rap songs, and what have you that there was just absolutely no way that anyone Black in LA would have even the smallest modicum of respect for the police.
ZIERLER: Did you hear about the Vietnam War from your family growing up as well?
GOINS: Yes and no. It was something that existed, but they didn't really talk about it too much. My father actually was in the Vietnam War. But he never really spoke about it. It's only been within the last maybe 15 years or so that he's actually said anything about the Vietnam War. The only thing I can really say that I heard from him was, he had mixed feelings. Which doesn't surprise me, based on what I've heard other Blacks say about the Vietnam War. He would say that being in the Marines, he definitely felt this sense of camaraderie when he was on the battlefield. But he said that as soon as they got off the battlefield, went into the bars or whatever, he felt the segregation and racism all the time. I know even now, he's very hesitant to talk to people about what he went through. He's only mentioned that he's had a few friends who got shot and killed, he definitely saw death over there, but he doesn't really talk about it much, except just to say that the country is a very, very racist country. Even though he was there, and he did his time, and he was around folks supposed to be fighting together, all of that is very idealized. He will say that he felt very much the sting of racism when he was there.
The Story Behind the Name
ZIERLER: When we come up to 1972, when you enter the scene, first question there, your name, Edray, is unique. Is there an origin story there?
GOINS: Yes, there definitely is. I don't remember the exact story from my parents. I think it comes down to my father's name is Nimray, and he wanted at first to name me Nimray, Junior. The problem with that was, he has a lot of brothers and sisters out in Chicago, and I think one of his brothers had a son, and this son apparently is named Nimray. He was worried that there were going to be too many Nimrays going around, and they would be confused as to who's who. Even now on Facebook, this guy who's named Nimray, I sometimes have to be careful whether it's my father or this cousin. But still, there's another guy out there running around with the name Nimray Goins. My parents spoke, and they had to come up with a name that would honor my father but be a little bit different. My mother's father's name is Edmond. What they decided to do was take the Ed of Edmond and the Ray of Nimray, and they combined them both together to be Edray.
That's where that comes from. Now, to add to that story, remember that my mom had several sets of parents when she went out to Los Angeles. Her godparents were probably the closest to her. Apparently, her godparents were good friends with her biological parents before she was born over in Texas. When she was born, it turned out that the godparents never had their own biological kids. So really, she had two very close sets of parents who did everything for her for birthdays, holidays, what have you. My middle name, Herber, actually comes from her godfather's middle name because his name was William Herber Dailey. No T. I have no idea will have his middle name has no T. It's not Herbert, it's Herber. I like to tell everyone that my name really comes from all of the men in my mother's life. The Ed from her father, the Ray from her husband, and the Herber from her godfather.
ZIERLER: Do you have siblings?
GOINS: I do. I have one brother who's two years younger. His name is Dwight Naamon Goins. Dwight was my father's father's name, so my grandfather's name. Naamon is all kind of the inside joke with my father's siblings. Apparently, because my father's father was a minister, all of the boys have names that start with N-I-M, and all of the girls have names that start with N-A-A. My father's name was Nimray. He has brothers named Nimshem Nimrod. He has sisters named Naahath Naakou. I don't know how exactly how they worked all this out, but my brother's name is Naamon, but it's supposed to be kind of along those lines.
ZIERLER: Did you have nicknames? Or did you always stick with the formal Edray growing up?
GOINS: For the most part, I'd say up through college, I stuck with Edray. There was occasionally someone at the church who might've remembered my father, who might've called me Little Ray, just because they kind of knew that at some point there was discussion of naming me after my father. But that was rare. Everybody called me Edray growing up. When I went to college, though, that's when my name started to change a lot. People had various variants on my name. When I started college, it turned out that there was another Black guy from LA whose name is Dr. Dre. So people used to call me Dr. Dray when I went to Caltech as an undergrad, and that's kind of a name that stuck amongst a lot of people. When I eventually left undergrad and went other places, people formally started to call me Edray, Professor Goins, what have you. But there's still a good number of people who remember me from my undergrad days at Caltech who still call me Dr. Dray.
ZIERLER: When your parents separated, did you remain close with your father? Was that possible?
GOINS: Not really. I was always close with my mom. I would say unfortunately, I never really knew my father. I knew of him. There were times we would hang out and chat about things. But because my parents separated when I was around 5 years old, they lived in houses that were only about a couple of miles apart, so I would see him maybe once a month or once every couple months growing up. But by the time he left back for Chicago, when I was at 15 or 16, I really didn't talk with him much after that. We'd see each other once every two, three years. We might talk on the phone once every six months, once a year or so. It wasn't until I moved to the Midwest in 2004 that he was right there in Chicago, I was in West Lafayette, about two hours south, that I would then see him about two or three times a year, and that's when I got to know him much, much better.
ZIERLER: Did your mom remarry? Or did you have a different father figure in your life growing up?
GOINS: No, she never remarried. The closest I had to a father figure was her godfather. I'd sometimes call him my godfather. My mom was about 33, I think, when she had me. He was maybe in his 30s when she was born. Even though he was about 60 years older than me, I really considered him to be like my father. We got very, very close. Actually, he and I got closer than my mom and I ever were, so we got very, very close eventually. I think it's because of the way we saw the world. It's that, and also as boys are known to do, he would give me advice growing up, I would kind of push back and decide not to do things. There was a while, maybe two or three years, I didn't want to talk to him because I kind of felt that he didn't understand what I was going through. I'd say probably by about the time I hit maybe age 40 is when I realized that he was right with everything he recommended that I do over my life. We just got very, very close. Now, he passed away about eight years ago. I would say probably for about the last five to ten years of his life, we were very, very close. Pretty much talked about anything and everything. We came to the realization that even though we're very different people, we understood what made each other happy, and I think we respected each other for that.
ZIERLER: If there is a genetic source of mathematical or scientific ability, and I'm not saying there is, is there anybody you can look to in your family as a connection for the gifts that you would realize you had later on?
GOINS: That, I've been asking my whole life. I don't know. I'm not really sure. I know that my mom hates math. Even though she was a 1st grade teacher, 3rd grade teacher for a while, she said she always hated math. She could barely do multiplication tables, but she didn't want to do anything more than that. My father doesn't do any math at all. He went to LA Trade and Tech, so I don't think he's ever taken a math class at all in his life. Even on top of that, I think he might be the only of his brothers and sisters to even finish high school. I don't think that any of his brothers or sisters actually finished high school. On my father's side of the family, even when it comes to higher education, there was really no interest there. I definitely don't know of anyone who had an interest in math or science.
On my mother's side of the family, my mom has mentioned a couple of times that her father seemed to be pretty good at numbers. But as far as I could tell, he never finished high school. My mother's mother was an elementary school teacher. She finished college. She graduated from an HBCU there in Texas. But also, I don't think that she had any interest in mathematics or science. So there's a possibility maybe my grandfather on my mother's side might've had some kind of proclivity for doing math. But I can't tell if anyone in the family had any interest whatsoever in math and science. No one that I can come up with.
ZIERLER: And either from your family, your teachers, or yourself, when was it first understood that wherever it came from, you had these abilities?
GOINS: It was clear at a very, very early age that I was precocious. I think everyone in the family would say that. My mother was an elementary school teacher, and her mother was an elementary school teacher, and they were both very big on getting me to read at an early age. So I have early memories of maybe 4 or 5 years old of my grandmother sitting there with me, just reading. By the time I went to kindergarten, I think they said that I was reading at maybe a third-grade level. I just remember reading all the time. Whatever I could get my hands on, I would just read and read. I'd say by the time I made it to the 1st grade, it was clear that I did have a strong interest in science and the world around me.
The problem was, there weren't a lot of teachers who knew anything about science, which really meant that my mom spent time just buying me books. I was pretty lucky, and I believe this was when I was roughly in the 1st grade. It might've been 2nd grade or so. NASA had decided to relaunch its space program, and they had a launch of this brand new thing they called the Space Shuttle. Now, before then, I can't explain why, I was obsessed with learning about being an astronaut and learning about spacecrafts. The way some kids can rattle off names of dinosaurs, I could rattle off what was happening with the Mercury program, the Friendship VII, all these things with the Soyuz spacecrafts that would've happened back in the 60s and 70s. I could name all of those.
That was just my obsession when I was in 1st grade, 2nd grade, knowing everything I could about the space program. When there was an announcement that there would be this brand new Space Shuttle program coming out in the 1980s, I just had to learn more about it. There actually was a summer science program held over near USC. It was actually in Exposition Park. The idea was, for extra money, parents could pay to have their elementary school kids take these classes over the summer. It was all part of the Museum of Science and Industry right there in Exposition Park. I don't even remember how my mom heard about this. I just know for several summers when I was in elementary school, I would beg her to let me go to this Science and Industry set of classes.
One of the most influential sets of classes for me was building model rockets. This was the first time ever in my life I wasn't with the elementary school kids. I was with totally different kids from all parts of Los Angeles. Some were Black, but the majority weren't. They were white and Asian kids who were all living in Los Angeles. But we had these incredible teachers who just let us explore. Remember, we're talking 8, 9, 10 years old. What they're saying is, "We're going to spend the next couple of weeks, and we're going to build a model rocket." I had absolutely no experience doing that beforehand. But remember, I'm obsessed with the space program, so I understand all these things with the model rockets. Literally outside of the building where we were working, I believe there was a Saturn V rocket.
I knew that it was a Saturn V rocket because I was obsessed with these things. Literally, going to this every day over the summer, I would see the Saturn V rocket outside of the building, and then I would walk into the building, where I was actually building these model rockets. Now, the teacher was somewhat conservative in saying, "Here's how you build a model rocket. You have these little booster packs you put in, you have to worry about building the cardboard tube, putting in a parachute so that when the holding wants to land, you can catch it, using spray paint to make it look nice, worrying about the aerodynamics by placing these wood fins on the sides so that the thing would go up straight. We would spend a lot of time talking about the physics of how all the stuff was going to work.
Well, as boys are known to do, we got very competitive with each other, and we learned that you could build a very simple rocket that has one booster pack, you light it off, it goes up so far, the parachute goes out, you catch it, then you go onto the next one. The teacher mentioned there was something called stages to a rocket. Now, I understood that there were stages from what I had learned about the space program. I didn't know you could build a model rocket that had stages. What that means is, you might have one cardboard tube that has one of these booster packs in there. But then, you have a second cardboard tube on top of that so then when the first one is done and has used up all of its fuel, it then ignites the second stage of the rocket, so the rocket could go up even further. Those were very, very complicated to build. My friends and I would kind of talk a little bit to each other about what all of this meant and what was happening.
One of my favorite memories of this whole program is that there was this one kid, and I don't even remember where he was from, who was convinced he was going to build a three-stage rocket, and this thing was going to be the most fantastic thing any of us had ever seen. So my friends and I were all huddled around this guy who was building this very complicated, three-stage rocket. He spent the whole summer working on it. At the end of the summer, of course, part of our graduation, we went up and launched the rockets, where the idea is that we'd spend the whole time building it, launch it, catch it, take a photo with friends, and everything would be great.
Unbeknownst to the parents, my friends and I were all waiting for this one guy to launch his three-stage rocket. Of course, the guy was very proud of himself because he had spent all of his time working on it. Most of the rockets were maybe about a foot, a foot and a half in height. This guy's rocket was probably about three feet tall. It was this massive thing he had spent weeks working on. He ignites the first stage, takes a step back, lets the whole thing launch. In an ideal world, when you launch the first stage, it goes up maybe about 500 feet, and then the second stage launches, it maybe goes up another 500 feet, then the third stage launches, it goes up another 500 feet, and then it starts to fall back down to earth. All of this would've happened within a span of ten seconds or so.
When he launches the first stage, it goes up maybe 500 feet, and the guy didn't take into account that it wasn't well-balanced. So the rocket goes up, but then it starts to lean to the side after the first stage goes out. That's when the second stage ignites. Now, instead of going straight up, it goes to the side 500 feet. Now, this thing is shooting at probably 60 miles an hour at this point. Remember, it's doing all of this in less than a few seconds. Since it's turned off to the side and gone off another 500 feet or so, now the rocket starts to turn downwards because it's not weighted very well, and the third stage ignites. Now, again, it's going full speed, but now it's pointing down to the ground. Of course, it hits the ground and shatters into a thousand pieces. I think the parents were kind of horrified because all of this has happened within fractions of a second, less than ten seconds or so.
And people were kind of scrambling to get out of the way because this thing had just smashed into the ground at full speed. We as the students basically gave this guy a standing ovation. This was the greatest thing we had ever seen. Granted, it's a complete disaster that he has no rocket at all to show off for all this work over the summer. But that image was what sold me for life on being a scientist.
ZIERLER: When did you first interact with computers?
GOINS: This is a story in itself. I first really learned what a computer was probably in the 4th grade. There were gaming systems starting to come out right about then. We're talking early 1980s or so. Atari had come out with one of these gaming systems, I believe Coleco had ColecoVision. You heard people talk about this game Pong, where you have these two bars on each side of the screen and this little ball that bounced back and forth. That was my first introduction to what a computer was. We bought one. We had to turn to channel 3 to watch all this stuff. I was more interested in how it worked. I wasn't so interested in trying to play the game. It was such a simplistic game, it wasn't anything interesting. Now, when I went to junior high school, the school, I really don't know why, had these Apple II computers. They were Apple IIc. Now, the Apple IIc was not a great computer.
Nowadays, people take it for granted, you turn on the computer, you can type in things for programs, turn off the computer, and you can walk away. When you come back and turn on the computer, everything was there. This was not the way those first computers were. When you turned on the computer, you had these five-and-a-half-inch floppy disks, you had to put them into the computer, save everything on the floppy disk. Because if you turned the computer off before you saved it, everything was gone. There was no memory to save all of this. But in the 7th grade, we had a computer class where we were supposed to learn how to program on computers. That isn't the reality of what happened. It was more we were sitting there in this room, and the teacher didn't really know what he was doing. Because literally, computers were brand new. This was the first year this school ever even had computers. But remember, my mom was constantly taking me to the bookstore because I just had to read everything.
I remember going to probably Borders Books–I don't remember if it was Borders or Barnes & Noble–but at the time, the way you would program was, you had these books of programs. The way you'd program was, you'd take a page out of the book, you would type it into the computer, and then wait and see what it would do. I had several of these books of programs I would bring to school with me every day, and every day at the start of class, I would go in, type in one of these programs to see what it would do. Then, I might save it, but then class was over, I'd move on to the next class. So I was the best programmer in that class. Anything that you wanted to do on the computer, I knew what to do because I had this book, I was writing things every day. We even had a computer club after the day was over where the computer teacher would just let us sit in the room and do whatever we wanted to for hours.
At the time, Basic was the program everybody would use. I got obsessed with this other program called Logo. Logo a good way of how to do graphics. Remember, this whole thing of Pong. I wanted to know how to do the graphics in Pong. In a sense, by day, when I was in class, I would learn how to do basic. But then, in the evening, with my friends in computer club, we were learning how to do Logo. That was my life in 7th and 8th grade. I was just programming all day. My mom told me this part of the story later that I didn't know. Because I was constantly writing these programs every day, I would just save them on the floppy disk and not even think about it. Apparently, after I would save them on the floppy disk, I would leave the computer on because the teacher would always say, "Leave the computer on," because the next class would be coming in in a couple minutes.
This teacher would take the programs that were still there on the computer screen that I had written, he would save them on his floppy disk, and then he would use those to teach the computer class the next class period. Even though he was teaching nothing during my class period, he was still using my computer programs to teach the next class period. I didn't know this for years. It didn't bother me. I just thought it was funny when my mom told me years afterwards.
ZIERLER: Being in the computer club, being good at math, was the term, in the positive sense of the term, nerd, something you embraced as your identity? Or did you want to keep that at bay because that might not have been the path to popularity?
GOINS: For one thing, I wasn't good at math. I definitely was not good at math. I really liked computers. I really liked being involved with student leadership when I was in junior high school. Math, I was actually getting Ds and Fs in. I was not doing well in math at all.
ZIERLER: There's an inspiration story for you. [laugh]
GOINS: I know, it sounds really weird, but when I was in 7th, 8th, and 9th grade, I had no interest in doing math. I did not like math, I couldn't stand my math classes, I hated my geometry class. Math was actually the class that I dreaded going to the most. I really, really did not like math.
ZIERLER: Let's stay on that for a second. What does that say about you, and what does it say pedagogically about how math was taught to somebody who clearly had innate mathematical untapped ability?
GOINS: Well, for one thing, I definitely think it shows that if you have the wrong teacher, you can stifle math talent. I realized that early on. I genuinely hated math almost entirely because of the teachers. I'm not going to say that I didn't understand there were applications to this or what it was good for. That wasn't it. It was more the teachers either didn't explain it well or didn't explain it at all. A lot of my classes, the teacher might go to the chalkboard, they might explain a little bit, they might work out one example. Then, they would say, "You students go work on it on your own and figure it out." I remember at one point, it was maybe an algebra class, we were learning how to do square roots kind of by this general idea of generalized long division. This really weird method where you basically use long division, but you modify it a little bit, then you take square roots of numbers.
I remember one day the teacher doing an example in class, and then she said, "Now, you all work out the rest of these problems." I remember sitting there in the chair not having any idea what to do, just being completely baffled. This made no sense. I didn't understand why this worked. I couldn't figure out from the example she had done the more general steps. I also remember that because we had a classroom of 40 students or so, I couldn't ask her a question because she was always off in another part of the class trying to ask people things. I remember spending that entire class period being stuck, not having anybody to talk to, not being able to get any help, and then the bell would ring, the class would be over, time to go to the next class. Just feeling frustrated class, after class, after class, not being able to know what I could do or how to get any help with it.
I understand that, and I appreciate that now, when I see students who say things like they don't like their teachers, or they have really bad teachers. I definitely am not saying that I'm the world's greatest math teacher, but I'm saying that I definitely understand that when students say that, and I try to remember that when I hear students saying things like they don't like math because of the teachers that they have.
ZIERLER: Having 40 students in a class, overly crowded classrooms, is classically a symptom of an underfunded school. Just socioeconomically and racially, what were the demographics of your school?
GOINS: Well, the junior high school that I went to is Audubon Junior High School. It's actually right there in the middle of the Crenshaw District. It's interesting. The school was probably 98% Black. The other 2% was Latino. I'd probably say Mexican-American heritage. All of the teachers except for a handful were Black. The principal was Black. The vice principal was Black. So it was very, very much a Black school. It was also in an area where even now in Los Angeles, it's considered to be kind of the hub of the Black community. There was a lot of sense of pride, a sense of community, a sense of activism there at the school. I'll say that racially, it was an interesting situation. It was very much a school that was rooted in cultural identity and also, I'll say, cultural activism. That's, I think, what helped me to really submit who I am today, really kind of saying, "You can help your community, and you can be a part of your community."
But I loved the fact that we were right there in a predominantly wealthy Black neighborhood of Los Angeles. West Adams, back in the day, was considered to be kind of the upscale Black part of LA. But really, the Crenshaw District, where people were living up in Baldwin Hills, really was the upscale part of Black Los Angeles in the 1980s. That's where my junior high school was, right in the middle of all of that. But also, when it came to getting help from the teachers, or at least moral support, the teachers were there for the most part. But you are right in that when it came to this very general idea of a school in Los Angeles Unified School District, the school certainly was underfunded, and I feel like in a lot of ways, it was understaffed. But it was definitely very frustrating that we had so many students in the classes that the teachers couldn't really help us. I think the teachers wanted to. But there's only so much you can do in a short class period.
ZIERLER: Obviously, the story turns around at some point, and probably some point soon. When did you go from hating math and getting Fs and Ds into loving math and excelling at it?
GOINS: It's kind of two parts. My mom was very active in my education over all the years. Because she herself was a teacher, she appreciated parent-teacher conferences, so she was there at the school all the time. All of my teachers knew her, the principals knew her. Everybody knew her very well. When she saw me getting Ds and Fs, she knew something wasn't right. She immediately went to some friends at the church to ask some of the engineers who worked around there if they could help tutor me and talk to me about things. Ironically, we were actually just talking about this story last night. She found a Black guy who worked as an engineer for JPL and asked him if he would tutor me because she could see I was there in the 9th grade struggling with these classes. The guy came by to the house one day, and I do remember this. He wanted to sit down with me to kind of ask me about how I felt about my math class, he wanted a copy of my math book so he could look at it, and he asked me to work out one of the problems I was doing there in class.
Apparently, he realized that I actually understood a lot more about the problem than I was willing to let on. It's just that I didn't know when to stop. Apparently, I was working through the problem, I would come up with an answer, but then I was so creative that I would start to do some other things with the answers. I would start to write down something that the teacher would think was gibberish, and then the teacher would mark it wrong. Once this guy understood that, he then told my mom she should sit down with me to make sure that once I've answered the question, stop, box the answer, move on to the next one. Once I did that, I started getting As in my classes, and it wasn't an issue.
ZIERLER: Walk me through that. What does a problem look like where you didn't know when to stop and kept on going? And here, this gets me to our earlier conversation, where clearly, there's an artistic element going on, where it's maybe like jazz or improvisation, where you're just going off and doing your own thing unbounded.
GOINS: I wish I could tell you what it looked like for the math classes because I just don't remember. I just remember being in algebra, where we were supposed to work on certain problems. I wasn't really clear what the teacher wanted us to do. I could mimic what she did in class, but it wasn't clear to me where to stop. So all I can say is, there might've been a problem, like this idea of taking the square root using long division. It might've been, "Work it out to one decimal place," and maybe I worked it out to four decimal places. That's all I remember, one of these problems where I could keep going, and keep going, and keep going, but I just didn't quite know when I was supposed to stop. I don't really remember in all the details of any of these specific problems that we had when that came up.
I can tell you more for contrast, the classes where I loved them were ones that were very much open-ended. Ironically, the classes I loved the most in junior high school were my English classes. I had two teachers that, to this day, I think were the best teachers in the world. One of them was this old-school English teacher. Actually, she was white, even though this was a predominantly Black junior high school. She would force us to diagram sentences. I didn't even realize that nobody does this anymore. But she spent a lot of time saying, "Here's a sentence. Let's break out what the adjective is, what the verb is, the subject, the object." And I just fell in love with all of that.
I felt like I got a really good appreciation of how English worked. I had another teacher, also a white teacher, who had us read various books, but then she let us be as creative as we wanted to on the books. One of the books we read was To Kill a Mockingbird. Remember, this is a predominantly Black junior high school. I had never heard of this book by Harper Lee before. But what the teacher had us do was in class, read aloud sections of the book. Then, when it was done, we watched the movie. For the listeners here, the book is essentially about a white lawyer in the South who has to defend a Black man who's been accused of rape. It's pretty clear the Black man never raped the woman. But the town has blinders on, and they're out for blood. The book isn't really about that. It's about the consequences of trying to do the right thing in a society that will vilify you for it.
The main character's this guy named Atticus Finch, this white guy, who lives in a pretty nice well-to-do house with his daughter, Scout. He wants to do the right thing, but he realizes that the town is completely against him, they're not happy with him, and he has to kind of tell his daughter, who was roughly our age when we were in junior high school, "Unfortunately, this is racism. This is just the way things are. Chances are, I'm going to lose this trial, and chances are, this Black man is going to die." He's very clear to his daughter, "Unfortunately, this is just the way the world is." That book was one of the first times that I really saw race from a white person's point of view. When you're growing up in a Black neighborhood, you learn about Martin Luther King and about the Black Panther Party, and you learn about race and what it means to be Black in America.
But this was the first time I saw race from what it means to be white in America. My friends and I spent a lot of time discussing this book, what were the consequences, and what would this really mean if we were to go to a school that was not 99% Black because we didn't know. This was the way that the neighborhood was. The teacher would ask us, "Come up with creative ways of expressing what you think about the book." My friends and I got very, very competitive. One week, for example, someone decided that they would just do a drawing to depict one of the scenes. The next week, the person wanted to outdo that. Then, they would sew or crochet a doll that would kind of show one of the characters from the book. I made it a point to go later on in the semester, because I wanted to blow everybody away. I was that competitive. It took about a month for me to do this. I wanted to recreate the courtroom scene, where Atticus Finch is essentially trying to defend this guy.
But I wanted to have the entire scene laid out. I had a box, it was probably about one and a half by one and a half by three feet long. I had actually had Styrofoam balls to make up all the different characters. We actually had the chairs set up. We had the guy who was on the stand. I wanted to make it a point to do the gallery in the back of the courtroom where the Blacks were allowed to sit. Because of course, they weren't allowed to sit in the main part. They were only allowed to sit in the back in the gallery. I spent a month working on this. This was my baby. I didn't want to tell anyone at school I was doing this. I walk in with this big box, almost as big as I was at the time, and of course, that got the respect of all of my friends. But it was me being creative like that. That's what I loved about my English class.
Yes, it was English, but we could all show off our artistic sides. That's really what caused me to love being in junior high school. I didn't understand the artistic side of mathematics until college. But being able to be artistic and just being an intellectual. That's what really caused me to love those classes.
ZIERLER: You talk about To Kill a Mockingbird. What about television and what you learned about race from watching television? For example, The Cosby Show, the way that that portrayed a very unique type of Black family life.
GOINS: The Cosby Show was a very big show, not only in my family, but also amongst my friends. I guess it's weird because I never knew how The Cosby Show was viewed in other parts of the country. At least where I grew up in Los Angeles, it actually was a pretty well-to-do area of Los Angeles. There were people I knew who, of course, were in gangs, in very poor neighborhoods. But there were other people I knew through the church who were very, very well-to-do. For example, the first Black Surgeon General of the country, David Satcher, was a member of my church. I actually remember seeing him around the church, and somebody mentioned at some point that he got some big promotion, he was moving to Atlanta. I didn't know anything about that. Then, years later, I realized it was because he was becoming the Surgeon General.
That's kind of what I grew up with, these people who were very well-to-do, very prominent, but also people who were somewhat poor and having a hard time. When The Cosby Show came out, I could relate to that world. You had Blacks who were very, very well-to-do, and they had kids who were doctors and lawyers, going off to these fancy schools. I think for me, the difference was, it was the first time I saw this on television, but it wasn't the first time I'd seen this in everyday life. Ironically, the part that impressed me the most was what he thought about Black colleges. Growing up, I certainly knew a lot about Black colleges. Almost everyone I knew either went to a Black college or graduated from a Black college. That was kind of kind of standard. Again, it was the first time I ever saw it on television. That's kind of what shocked me, hearing people talk about Hillman and these places because all of us knew that they were thinly veiled descriptions of Morehouse, Spelman College, and being in Atlanta.
When I went off to college, I spent a lot of time thinking about that lifestyle of going off to a Black college. Most of my friends from high school who went to college ended up going to Spelman, Morehouse, and other schools that were there in Atlanta. I would always think of this idea of, "What if I didn't go to Caltech for college? What if I went to one of these historically Black colleges in Atlanta? Would my life be very similar to what I'm watching on television?" One thing in particular that really struck me is, there's an offshoot of The Cosby Show called A Different World. A Different World was my life. That's really the life that I wanted to have. There was one character in the show named Dwayne Wayne. Dwayne Wayne is this very nerdy character who was a math genius. In the show, they specifically showed him as this weird, nerdy guy who was always sitting in the math classes, always the first one to answer the problems. When he wasn't in the math class, he was tutoring his friends in math. He had these cool sunglasses he would wear all the time, this weird hairdo.
ZIERLER: The ones that flipped up.
GOINS: Yeah, the flip-up sunglasses, that's right. But that's who I wanted to be. I wanted to be Dwayne Wayne. But again, that was the question. If I had gone to school in Atlanta, the Hillman wannabe, essentially Spelman and Morehouse, would I have been Dwayne Wayne? That was my vision of myself the whole four years I was an undergrad. It's kind of hard to explain that because I don't know if anybody from Caltech really understood that that's the way I saw myself, in seeing Dwayne Wayne on A Different World. But it made a major impact on me. Even to this day, it made a major impact.
ZIERLER: To go back to your tutor at JPL, did that plant a seed that Caltech was a special place, particularly because of your earlier interest in rockets and space?
GOINS: It actually had happened before that. I mentioned that my mom's godfather was very influential in my life. Well, we had this family tradition, where the godfather was very active in the church. He's one of the first people that kind of founded the church when he got there in the 1940s and was always very big on the financials and everything with the church. The way the church would work was, we would have the first Sunday service at about 8 o'clock in the morning. There'd be Sunday school, which would be about 9:30 to 10:30. Then, there'd be a second church service about 11 am. Well, the 9:30 to 10:30 was a thinly veiled way in which the elders of the church would have time to kind of debate where the church was going, what the church was doing. It was supposed to be someone leading discussion from some passage in the bible. That was almost never the case.
Years later, I realized that there might be one person kind of talking about something from the bible. But then, it would get into something practical. It might be, "Well, let's discuss what's happening with police brutality in the neighborhood and how the church should be more involved with this." That meant that when it came time for Sunday school, it was a stratified series of classes. Those who were in elementary school would go to one class. Those in the 2nd grade would go to another class. There was the young adult class, which would be for anyone, say, in college. Then, there would be the seniors, which were the elders of the church. This was the class my mom's godfather would go to. My mom's godfather didn't live that far away from where my brother and I were growing up.
Maybe ten minutes north of where we were. He made a deal with my mom that Sunday mornings, he would drive to my mom's house, pick my brother and myself up, drive us to Sunday school. We would go to our classes, he would go to his senior/elder discussion class. Afterwards, my mom would meet us there at the church for 11 o'clock service. We'd be there, and then we'd all drive back home. At least once a month, though, my godfather and his wife would make it a point to take us to dinner in Pasadena. We went to this place called Beadle's Cafeteria. I don't even know if it's still around now. This is what we did every month for I don't know how many years. Remember, I'm obsessed with the space program at this point. When I heard the word Pasadena, I knew that Pasadena was involved with JPL and this place called Caltech.
I would make it a point every month we would go to Pasadena for Beadle's Cafeteria to ask my mom's godfather, "Can we just drive past Caltech?" I would say probably starting in the 6th or 7th grade, my dream was to go to Caltech. Everybody in the family knew this. I would not shut up about it. That's what I wanted to do from 7th grade on. That seed was set. I can tell you that I got an application to apply to Caltech in the 12th grade. I still remember being ecstatic that I got the application because again, for years, I knew I was going to go there. I applied, I got in, and I still have the acceptance letter to this day because of how much it meant that I got into Caltech.
ZIERLER: In high school, we covered your interest in English, your early non-interest in math. What about science and physics in particular? Were you turned on to science at all in high school?
GOINS: I got very interested in physics when I went to high school. I'm not really sure exactly how it started. Certainly, my interest in rockets and the space program eventually moved over into physics. I think I got more interested in how rockets worked as opposed to trying to be an astronaut. There was a program in LA called MESA. This is Math, Engineering, and Science Achievement. It was actually a program that was supposed to be set for minority high school students who become more interested in the sciences. I got involved with the MESA chapter at my high school. I eventually became president of my MESA chapter. They had a few activities that would happen once a year. I think it was maybe at Cal State LA. They might have one day of MESA activities. Now, there were a lot of activities that would happen during MESA day. One of them would be a math contest. You could just show up in a classroom, solve math problems, and just do that for an hour-long exam or so.
The big one, though, was the egg drop contest. The idea would be that you would take an egg, you'd have to drop it in some device from a three-story building, and whichever eggs would survive this drop would then make it to the final round. It wasn't so much how to get the egg to not break, it was more trying to figure out what you should build to make sure that the egg wouldn't break. It was really interesting seeing the very creative ways people were doing all these various egg drop contests. I remember one year deciding that I was going to enter this contest, and I had this really elaborate way of combining toothpicks, and at some point, I had kind of convinced myself that if you take toothpicks but then have a very large figure, the surface area should be enough to kind of crumple and take care of the egg, but then also if you take the toothpicks, put glue around them, and put the glue in the oven, then the glue will harden in such a way that it will work out really, really well.
Turned out that that was completely wrong. Because when I got to the egg drop contest, just bringing it from the house to the contest, the whole thing fell apart in the car, which meant that by the time I got it there to the building, there was basically nothing left. I had completely screwed up what it meant to actually build something. But the math contest was actually pretty easy. Right about the time I was starting to think, "Maybe I'm not the best at building things. Maybe I really do like the theory of things. But maybe this math thing might be OK." I just really wasn't interested in the contest. I still wanted to know how things worked. I actually spent a lot of time reading in the encyclopedia about electronics. At the time, I was totally obsessed with how a battery works. I definitely understood how to build a battery using a cup, and water, and salt. I knew a lot about these resistance devices, an ohm meter. I knew a lot about how those devices worked.
There was a book that came out when I was in high school called A Brief History of Time, by Stephen Hawking. That book caused me to rethink the way I thought of the universe. That book alone convinced me to be a physics major. I didn't understand much of the math. I'd heard about these things called Lorentz transformations. But I was just in algebra at the time, was definitely not taking calculus. I didn't have the best physics teacher. But I still wanted to read more and more so that I could learn about a lot of these things. I say all this to say that probably by the time I was in the 11th grade or so, when it came to engineering, I realized that I wasn't good at it at all. I learned that through the egg drop contest.
When it came to science, this book by Stephen Hawking just changed the way I thought of everything. I really started to love physics at that point. When it came to math, the only thing I knew about math was contests. I was not competitive enough to be in contests, so I kind of saw maybe I could do contests, but I didn't want to because I just wasn't competitive like that. Definitely by the 11th grade, I was moving a lot more towards physics.
From South LA to Pasadena
ZIERLER: Just to give a sense of your high school, would they place the top students in places like Caltech and Stanford?
GOINS: No, no. I'm proud to say that I went to probably the worst high school in Los Angeles, if not the worst in the state of California. It's unclear. The high school actually had two magnet programs. They had the math and science magnet, and they had performing arts magnet. I went to a really interesting high school. Before I got there, it was known for being one of the worst schools, but they had this teacher that they had brought in named George McKenna. I forget exactly where George McKenna came from, but he made it a point that he wanted to kind of turn around the high school. At the time, people knew about this guy in New York City and the high school that he had turned around. There was a movie called Lean on Me about this guy named Joe Clark, this very rough high school in New York, how this guy kind of came in and had turned it around.
I think that George McKenna thought the same thing of my high school, the George Washington Preparatory High School. In fact, it wasn't even called Preparatory High School when I got there. It was just a high school in Los Angeles. He got there maybe in the early 1980s, I'm not really sure. He decided that he was going to completely turn around the high school. He decided to start a magnet program. He changed the name to Preparatory to kind of tell the students that, "We are preparing you to go off to college, for a life, what have you." He changed the mindset of the school. Long story short, he eventually figured out how to have a movie made after him. This movie was supposed to be kind of like the Los Angeles version of Lean on Me. It starred a young Denzel Washington, and it was called The George McKenna Story. Now, 1987, when I was going to go to high school, I remember in Los Angeles, CBS LA showed this movie on TV called the George McKenna story, and it was all about George Washington Preparatory High School, where I planned to go to high school that fall.
Now, let me first say, I did not want to go to this high school. It was the last high school I wanted to go to. I went to Audubon, which is right there in the Crenshaw District. Most people who graduated from Audubon either went to Dorsey High School or Crenshaw High School. I wanted to go with my friends. At the time, there were a couple of elite private schools that were also doing heavy recruiting out of Audubon. This would be Cate School and Thatcher School. I desperately wanted to go to those schools. My mom did not want me to go to those schools. We argued about them quite a bit.
ZIERLER: What was her reasoning?
GOINS: She was very concerned that I was pretty much going to be the only Black student at those schools, she was worried about the racism that I would experience, I wouldn't be allowed to go into the top classes, that I would be held back. In hindsight, she probably was right. I have a mentee who's here at Pomona, and he actually went to Thatcher as his high school before he got here to Pomona. Ironically, we spent a lot of time talking about his experience there, being a Black student, what he had gone through over the last three years. So I really wonder if I would have gone through the same thing if I were a student there. But I can say that those two were my top schools. I wanted to go number one, to Cate, number two, to Thatcher, number three would've been Dorsey, number four would've been Crenshaw. Everything else was kind of at the bottom of my list. But my mom decided–I think more for parental reasons, because she was working in Englewood, and Washington Prep was not far away from where she worked, maybe two minutes away–that she really wanted me to go to Washington.
I didn't want to go, but that's where I ended up going to school. I was very much aware of George McKenna, I was aware of this movie, I was aware of the problems the school had before and also the changes that the school wanted to go through. From my junior high school, I had graduated number one there at the school. That's technically not true, I graduated number two, but that's a whole story in itself. But I ended up winning various medals and awards for the academic pentathlon, I'd gotten maybe ten different awards over the years from top student in history, top student in math, what have you. I'm already coming to this school being essentially the top student from Audubon. I remember that I was placed in a remedial English class my very first day.
The teacher in this class gave us an assignment, which was something simple like, "Describe your summer vacation." Something simple like that. Now, remember, I had been reading books since I was 5 years old. To me, that wasn't an assignment. That was more like an exercise in short storytelling and how I could possibly be very creative with this. I think I was reading existential plays at the time, kind of doing all these really crazy things. I might've written a one-page haiku. Something really insane that I did. Because I was like, "This is a boring exercise." The next day, this teacher came up to me and said, "You don't belong in this class. You should be in the top English class here in the school. I'm going to make sure that you transfer over to that." That was pretty much my three years of high school. The teachers knew how good I was.
And because of that, they were very, very encouraging. I'm not going to say it was the best school at all. Because I was lucky to have some really good teachers, but for the most part, it really wasn't a great school. I can't say that we had any of the resources we needed. Certainly, we had teachers who were not very knowledgeable at all. But I will definitely say, from the amount of encouragement I got from the teachers, it was more than worth it.
ZIERLER: It sounds like you were able to carve out the best that that school had to offer you.
GOINS: That's exactly right. Let me tell you how I really got interested in math there at the school. 11th grade year, I was taking trigonometry. I was very behind all of my friends. Remember, I wasn't super interested in math. I was much, much more interested in physics. Most of my friends were taking calculus. It was because we had a brand new teacher there at the school, Michael Semenoff, who was teaching AP calculus A/B, and it was pretty much the first time the school had ever done this. You had a lot of students who didn't really know what these AP classes were. They definitely didn't know what this AP exam was. There might've been four AP classes at the whole school, and I think it was AP calculus, English, history, and Spanish. Even then, people really didn't take those classes. It's not really anything anybody was interested in.
For example, in my graduating class, there were 647 students. I think less than 100 went to college. There was really no interest, no reason for people to take these AP classes. But calculus, there were maybe about 20 or so students taking that AP calculus A/B class. I was not one of them. I didn't know what calculus was. I was sitting there learning about sines, cosines, these kinds of things. Doing OK, but I wasn't really all that interested. Where fate shone down on me was the class before my trigonometry class with the same teacher, Michael Semenoff, was calculus. That meant when I came in from my trigonometry class, I would see these funny integral symbols and derivative symbols, and I didn't know what any of the stuff was. Of course, that piqued my interest.
And I would ask Mr. Semenoff, "What are these funny symbols?" And he would say, "Well, that's just from the calculus class." And I wouldn't really think much about it. But of course, this went on for a whole year. Maybe he got tired of me asking questions, maybe I just got really frustrated and wanted to see more of them. But at the end of that class, I was then scheduled to take calculus in my senior year of high school. well, Mr. Semenoff said, "I'll make you a deal." He wanted to teach the next semester of calculus A/B to go to calculus B/C. But he also knew that of the 20 students in that class, only one of them wanted to take the B/C. So he had to figure out something to do. The deal was this. "I will teach you all of calculus A/B over the summer, but you have to take calculus B/C in your senior year, and you have to write up the solutions to all of the free response questions for the AP calculus A/ B exam for the last ten years."
Of course, for me, it was something I couldn't pass up because I really, really wanted to know what these symbols meant. So I said, "Cool, let's do it." That meant that summer, in between my 11th and 12th grade year, we did summer school. Probably for 15 minutes a day for, I don't know, four weeks, six weeks, something like this, he basically taught me calculus. He would kind of teach me little things here and there like, "Here's what a derivative is. Here's what an integral is. Here's the power rule," all these things. But because I'm soaking it up like a sponge, he's teaching me everything. He can spend one day and say, "Here's what a derivative is." And I got it. We move on to integrals. One day. "You have area underneath the graph. Here's how you do it." "OK, cool. I got it." Move on to the next thing.
It really was like I was soaking up everything like a sponge. I got all of calculus within about one summer. Then, came the free response questions. There, you have questions that more or less involve physics. For me, the free response made perfect sense. They would say, "Let's say that you're a person, and you shoot an arrow at this initial velocity at this angle. How far away from you will the arrow fall?" Well, I knew physics because I was kind of obsessed with physics. This, now, was using calculus. Now, I could use this math that I had just learned to explain the physics that I was interested in. I went through all of those free response questions with no problem. The teacher, Michael Semenoff, told me that essentially, I got them 100%. I must've done 20, 30 exams over the course of half a year, just writing up all these responses.
He would grade them, but he would also use them as solutions for the students taking calculus A/B my senior year. Which meant by the time the calculus B/C exam came around, I was ready for two things. Number one, the B/C exam for me was a piece of cake. So I got a five on it. I can't even really brag about it because calculus just made sense. All of it just made perfect sense to me. But also, I understood the mathematics of physics, which meant I took the AP physics exam. What's weird about that was, I had a teacher who was teaching AP physics, but he was a horrible teacher. He basically taught us nothing. But I had learned so much from the calculus that I knew how to do all of the physics problems anyway.
The funny thing was, I took the AP physics exam. I was the only person there at the school to take it. It wasn't really like I took it as part of the class. It was more I just asked this teacher, "Can you just purchase an exam, and I'll just be one to take it?" I ended up taking the AP physics exam and got a five on it. The crazy thing is, I'm pretty sure that the teacher can say, "100% of the students who took the AP exam at the end of this class got a five," which is true, but it's a little bit misleading because I was the only one to take it.
And I did it because of what I was learning from my calculus class. Now, end of my senior year, I have a perfect five on the B/C, a perfect five on the physics, and it's all from this one teacher who just sat down with me one-on-one for weeks to show me all of this. That's when I realized, "I'm really good at math, and maybe I'll consider it for a career." But again, I was hesitant because the only math I knew up to that point was doing contests. I did not like contests. But it was something I was starting to think about.
ZIERLER: Was there a beauty in calculus that made it all click for you?
GOINS: Ironically, it was the physics. It was 100% the physics. Everything that I saw in calculus just made sense when I could see it in the applications to physics and what I was supposed to do. One thing this teacher did was, he knew that I knew physics very well, and he knew that I could say things like, "You take an arrow, and you shoot it at a certain angle. Under the influence of gravity, it's supposed to follow a parabola. You just solve things out. Here's what it is." I knew from just memorizing formulas from physics, "Here's what the formulas are," but I could also derive the formulas because I knew calculus really well. The teacher also knew that I had an interest in programming. Because remember, way back in the 7th grade, I had done all this programming.
It wasn't something I wanted to do as a career, but I was still really, really good at it. One day, he said, "I see you have a graphing calculator." I loved my Casio. I basically did everything I wanted to do on this Casio. "Can you write a computer program that numerically solves the following problem? Say that you have an arrow. You shoot the arrow a certain initial velocity at a certain angle. But what if there's air resistance?" Now, I didn't know this at the time, but he was asking me to numerically solve a differential equation. I more saw that as a challenge. Because I first had to think, "Physically, what should the path look like?" Then, I had to think, "What are the equations that should govern this looked?" Of course, he had to kind of convince me that air resistance is proportional to the velocity.
And once I understood that it was proportional to the velocity, then I could kind of write down these equations. Then, he showed me how to use a computer to kind of numerically solve these equations. Once I had an idea of what the equations were and how things should look, it was just a matter of writing the program, coming up with the graph. I just remember working on this for probably two months. Then, I eventually showed him, "Here's the answer. This is what an arrow under air resistance looked like." I think he was more shocked that I spent as much time as I did actually going through all the steps, writing down the equations, writing a computer program that did this, plotting everything, and then eventually showing him what the solution was there in my calculator. But that's where I loved math, seeing the whole picture altogether. It wasn't just, "Here's calculus. You're going to solve a problem." It was using the calculus, using the physics, using the computer programming, and putting it all together to come up with one solid answer.
ZIERLER: Was this amazing attention you were receiving from this mentor unique? Would he do this for other students?
GOINS: He probably would have. I don't know if he did. I just know that he and I got along really well. We got really very close. Plus, he could see how good I was. I appreciated the fact that he was willing to just talk to me about these things. It's a lot to sit down and tell somebody, "Explain to me calculus." This is what he did. Remember, it wasn't like he spent five minutes one day, gave me a quick explanation, and that was it. We're talking day after day for weeks, and weeks, and weeks, he would say, "OK, let's talk about this part. Let's talk about this new topic today." And he really invested the time and energy to do that. I appreciated and adored the fact that he was willing to do that because no teacher had ever done that before. I don't know if it's because they didn't want to. I think it was probably because they couldn't. I really think most of the teachers I had up to that point didn't know math well enough to be able to explain to me anything that wasn't already in the textbook. But he could, and he did.
ZIERLER: This academic bubble that you carved out for yourself in high school, socially and culturally, did that also help you stay away from all of the other problems that school districts like this would encounter, like violence, drug use, teen pregnancy, and things like this?
GOINS: I think I was very fortunate, and I don't know why even now. Yes, we had a lot of gangbangers at my school. There were definitely shootings just outside of the school all the time. Movies like Boyz N the Hood were basically filmed literally outside of my school. Menace II Society was filmed outside of my school. Those stories that you see in the movies were real life. In fact, a lot of us actually joked that Boyz N the Hood was a little bit too watered down. Actually, Menace II Society, where pretty much everybody gets killed, was real life. Every day at the start of school, we would spend about five, ten minutes talking about who we knew who got shot the night before, or who died the night before, or what drive-bys we saw, what drive-bys we experienced. This was every day. Going there to Washington Prep, even now, when you walk into the school, they have lined on both sides of the corridor all of the people who have died who were students there at the school. George McKenna started this back in the early 80s when he was the principal.
And what's sad is that even during the time I was there as a student, during those three years, there were more and more names that were added to that list. The violence in the area in South LA was very real. It wasn't something that we were shielded from or something that we didn't see. All of us saw it on a daily basis. However, there at the school, there were lots of gang members who would tell me every day if I ever got harassed by anybody, let them know. If I ever got bothered by anybody, to let them know. They would always say they thought I was the best and the brightest that the community had to offer.
And they wanted to see me excel. You might think here I am, this weird, quiet, short, nerdy kid, all I care about is math and science. No, that wasn't the case at all. There was so much of a sense of community that they just said, "We know you're going to excel. We know you're going to do well." There was no question about that with anybody. They always said, "Look, we are proud of you now, so we want you to do as best as you can." People told me this. Almost word for word.
ZIERLER: Math and science kept you safe in a very real way.
GOINS: It did. But I feel very fortunate because I have Black friends at other schools who will tell me that either they felt harassed or made fun of by other Black students, or may they were one Black student at a predominantly white school, where they had a hard time getting into the top classes and the calculus classes, and they felt pushed back or held behind. But this was not the case where I was. I really felt very much supported by the teachers and by the students. Again, it wasn't like it was one of the best schools. For example, I mentioned earlier that only about 100 out of the 650 or so students graduated and went to college. From what I can tell, I was the only student to even apply to Caltech in maybe the 30 years of students before me, let alone get in, let alone go there.
I think there was one guy maybe a couple years before me who got into MIT. But I didn't keep up with him to know where he went or how he did. Going to the top places like Caltechs, MITs, or Ivy Leagues, that didn't happen. There were only three of us who broke 1,000 on the SAT. For a place like Pomona, if you don't get at least 1,500 out of 1,600 on the SAT, there's no way that you're going to get in. So students at my high school didn't even have the SAT scores to get into these places, let alone apply, let alone go. I was in a very, very unique situation. But I felt the support of the community behind me in doing that.
ZIERLER: To go back to this very profound observation that you shared with me in our first conversation, where your Blackness and your mathematical abilities, of course, are inseparable, did this occur to you in high school, where all of these things came together, where you were doing math in this racial, socioeconomic environment?
GOINS: I think it was always there, definitely even in elementary school. I don't think I thought of it very closely until high school. For example, junior high school, there were always a lot of discussions about, "What does it mean to be Black? What do you do to help the community?" Because again, the community was right there. There were all these discussions happening right there in the Crenshaw District, so you really couldn't get away from it. There were more discussions in high school, probably because people realized that they were going to go off to college, and they weren't going to be in this bubble of being in a Black neighborhood, and we wanted to figure out exactly what that meant. I think for me in particular, I was very involved with student leadership, and I don't even know how this happened.
I got involved with something called the California Association of Student Councils, or CASC. The idea of CASC is, you would take representatives from every high school in the state, so there were something on the order of maybe about 100 high schools in Los Angeles Unified. I know that there are more now. But there would be conferences all over the state where people could get together and talk about what it means to be a student leader, what the things are that you need to make your campus better, and so on and so forth. It was maybe in my 11th grade year that I went to a statewide conference in San Francisco.
Now, again, there are supposed to be representatives from all over the state, so there should be representatives from all the different schools in Los Angeles, all the schools in San Francisco, all over. I found myself to be the only Black high school student at the entire conference. That's when I realized that there was a totally different world. Now, remember, up to this point, all my schools are primarily Black, all the teachers I had were primarily Black, the neighborhood that I lived in was primarily Black. I go to this conference, and for the first time in my life, I'm the only Black person there. Something in that experience clicked. I'm not really sure what. But I came back with this renewed sense of, "We do live in a bubble, and we don't even understand the rest of the world that we're not a part of." I think even now, just having that jarring sense of, "There are still communities of people out there that just have no idea what the rest of the world is," is kind of a scary thought for me.
And I realize that it goes both ways. Me kind of growing up in a Black neighborhood, not having any idea what a non-Black neighborhood is like. Similarly, I'm sure there are people who grew up in white neighborhoods who have no idea what it's like to grow up in a non-white neighborhood. But that experience, I think, is what caused me to really think differently about, "What does it mean to help the community?" Just understanding that there are larger issues at play, that there are more resources than what we just see in front of us. It just caused me to think, "We can do things on a much larger scale, but we have to think outside of the bubble that we're in."
ZIERLER: Last question for today. In the way that I asked when your family moved to Los Angeles, if they understood that there would be significant racial problems, even though they were leaving a place like East Texas, when you applied to Caltech, did you understand what you were getting into? Did you understand what a white environment it would be? Or were you naive to that?
GOINS: Totally naive. Something I had not even thought about at all. I think my naïveté runs a little bit deeper than that, in that I think I assumed if you are really good at math and science, this would transcend whatever issues come about due to race or ethnicity. That, I think, was probably the hardest realization I had about Caltech, realizing that there are some people who are really, really good at math and science, but at the same time, they can be really horrible people. Now, don't get me wrong. I love the math and science that I learned at Caltech. I wouldn't trade that for anything. At the end of the day, I really loved learning about math and science. I loved the fact that I could take these crazy math classes, physics classes, chemistry classes, and they would teach things that were completely cutting edge, that nobody else in the world knew because they were being done at Caltech for the first time. But at the same time, I think I learned a hard lesson that the world is not a meritocracy. That's still something I'm trying to deal with even now, still trying to wrap my head around.
ZIERLER: We'll pick up for next time when you arrive at Caltech and what happens next.
[End of Recording]
ZIERLER: OK, this is David Zierler, Director of the Caltech Heritage Project. It's Thursday, November 18, 2021. It's my great pleasure to be back with Professor Edray Goins. Edray, as always, it's wonderful to be with you.
GOINS: It's good to be back.
ZIERLER: Today, we're going to start in the year 1990. We left off last time with you sharing with me your naivete about notions of race at Caltech, notions of integration or lack thereof at Caltech. Let's start, now, on the math and science side when you get to campus, just focused, to the extent you're able to, on the courses and professors. Is the game plan for you right from the beginning to have a dual focus in math and physics?
GOINS: No. I did want to have a dual focus, but ironically, it was going to be art history and physics. I definitely knew I was going to be a physics major when I got to Caltech. There was absolutely no question about that. Started in 1990. I believe Richard Feynman passed away maybe 1988. His ghost was very much in the physics department. People were telling Feynman stories right and left. I was aware of the Challenger disaster. I wasn't aware of all the influence he had with the commission, the discovery with the issues about the O-rings and what have you. But all of that was really being discussed in the time that I was there in the physics department. Let me say that I took kind of the standard classes you would expect a freshman at Caltech to take. It was Chem 1.
I want to say Nate Lewis was one of the professors, Jackie Barton was one, Harry Gray was also a professor. I also took Phys 1, and I don't know if they do physics this way these days, but you had to take a placement exam when you came in for the physics department. The rumor was there were ten problems on the exam, and there were ten sections that you could've possibly placed into. The second you placed into was exactly correlated with the number of problems you got correct on the placement exam. I never found out if that was true. That was the rumor that we all, as students, had. I believe I placed into section three. I think that's right. I'm not completely sure. Of course, a lot of us were feeling a little bit depressed that maybe we didn't get as many problems right on this exam. But I'll come back and say more about that section.
The person who taught Phys 1 was David Goodstein. He taught it that first semester. I had mixed feelings about David Goodstein. He taught out of The Mechanical Universe. I wasn't 100% familiar with The Mechanical Universe. I know that they had episodes that were airing on the local PBS station, so I caught a couple of them when I was in high school, but I never made the connection between The Mechanical Universe and Caltech. It wasn't until I got to Caltech that it all made sense. But he very much taught the class as a combination of, "Here are some really cool things in The Mechanical Universe," and, "Here's the way Richard Feynman would've taught it. That gave a lot of us mixed feelings. On the one hand, I think a lot of us really appreciated The Mechanical Universe because it wasn't your standard physics class. A lot of us were used to memorizing formulas. "Here's F = MA."
You memorize it, here's a problem, plug in the numbers, get everything to work. This class was getting to the heart of what physics was. I can tell you one problem that was in The Mechanical Universe that I still don't know the answer to to this day that kind of blew me away because I didn't actually know that physics problems were this way. You have two jars, and both jars are full of flies. Nothing else in the except for flies. The jars are sealed. They are opaque, so you can't see in them to see exactly what's there. In one jar, the flies are stationary, not moving. In the other jar, the flies are all flying around.
The question is, by weighing the jars, can you tell which one has the moving flies versus which one has the stationary flies? That's not one of these problems where you plug in some formula to get an answer. That's more a very deep understanding of what it means to have things moving in a closed environment where air doesn't come into play, all of these things. I remember that we spent a lot of time really discussing what this problem was and what it was getting at. Again, I have no idea what the answer was. I think I was more shocked that this was an actual homework problem someone could work on because it wasn't anything I was used to. In class, David Goodstein would spend a lot of time discussing things like this.
Yes, we did have the problems where you could talk about, "Here's the straight numerical question. Here's your equation, you plug in the numbers," and all the rest of that. He spent a little bit more time showing us, "Here's how physicists think." That's one of the things I loved about Phys 1. It really gave me an insight as to how physicists do some of these things. I will say, towards the end of class, I didn't really like some of the jokes that he made because he'd say, "Here's something that Richard Feynman would always say when he taught Phys 1." And again, this was about three years or so after Feynman had passed away. We were very much aware every single lecture that Feynman had just passed away a few years ago, but it just felt a little bit…
ZIERLER: Like Caltech was living in the past.
GOINS: Like Caltech was living in the past. That's right. I think we very much appreciated the personality that Goodstein gave towards physics. I will say, his personality was not liked by everyone. But still, the fact that he was willing to show us, "This is how physicists think," what stuck with us. Going back now to the sections we were in–you had the lectures, but you also had these recitation sections, where you were supposed to sit around with the TA and talk about the homework problems. What was beautiful about Phys 1 at Caltech is, the people who taught the classes and did the recitation sections were all well-established professors. They weren't grad students, they weren't younger faculty, they were all very well-established professors. I had Ward Whaling as my recitation leader. I adored Ward Whaling. He probably was in his late 60s, early 70s at that point. It was definitely clear that he had already had a very long, established career.
But what I think I liked about him was, first, he was kind of an older, grumpy guy. It was clear he was very much an engineer type. He could build things, he understood how the world worked. He would kind of come into class a little bit disheveled, and he would say, "We're supposed to do problem number one this week." And he'd pull out the problem, look at it, and it was clear he hadn't looked at the problem before he came there to the section. He started to try to work the problem at the board, typically would kind of get lost in some of the details. For us, as 18-year-olds coming from high school, I know it sounds weird, but this was great. Because we could really see that if a Caltech physicist couldn't figure out the homework, we shouldn't feel bad that we couldn't do it ourselves. It was actually an ego boost going to this every single week, watching Ward Whaling try to figure out what was happening there with the problems. He would kind of curse under his breath a little bit, he'd get a little bit stuck. But I will tell you that the thing that stuck with me the most, whenever he was working on these problems, he would look at it and say, "OK, you're supposed to use the formula. I don't remember the formula. But let's derive it." And he would do this concept of dimensional analysis.
I had never heard of this before, but he would do this almost every lecture. He would say, "All right. I know that the answer is supposed to have the following units." Maybe something like meters per second squared. "If we know that this is the answer, how do we actually get these units?" He would say, "Maybe we might want to have something like meters, so we have to measure length. We might need to have the denominator second, so then we might need to measure time. Maybe the formula we want is something involving length in the numerator and something involving the square of time in the denominator." And he would get this right every single time. As students, we would have the formulas. We would know. But he wouldn't have them walking in. He would do this dimensional analysis at the board, stand there, look at it, and say, "OK, I think the formula is this."
And we would all look at our notes and realize he was 100% right. It's that concept of dimensional analysis, being able to re-derive the formula based on what the units were supposed to be, which showed me the way physicists thought. Another thing I liked that I had never thought about before was this idea of a back-of-the-envelope computation. Ward would say, "We have this question. Before we even try to answer the question, let's get a rough idea of what the numbers should look like. Basically, are the numbers going to be too small or too big?" He would kind of say, "Here's the formula. Before we really worry about trying to come up with the exact answer, let's get a rough idea of order of magnitude." He would say, "What is the difference between saying that something is one meter long versus 100 meters long?" Intuitively, what that would look like.
He would tell us something like, "Maybe one meter long, it's about three feet, so that might be about a yardstick. If we come up with an answer that's 100 meters long, we're talking several orders of magnitude of how a football field is going to look." He would always tell us, "On the back of the envelope, roughly throw in some numbers based on what you know about intuition, what you see in the real world. If the numbers you get are in the ballpark of what you expect, chances are, your answer's right. But if you come up with some numbers that physically make absolutely no sense, then you know you're doing the problem wrong." Again, how physicists think. Even to this day, whenever I do any problem, I do a quick back-of-the-envelope computation, I think intuitively, "Do these numbers make sense?" I learned all of this my freshman year in Phys 1, and I love it.
ZIERLER: What did that teach you more broadly about the interplay between theory and observation in physics?
GOINS: It definitely showed me that they have to go hand-in-hand. I appreciated pretty early on that a physicist doesn't just sit around and just do experiments all day without thinking about the theory behind it. Conversely, a physicist doesn't just do a whole bunch of theory all day without worrying about experiments or the real life applications. They definitely droned into us at Caltech that they are very much hand-in-hand. When we had Phys 1, we also had a physics lab. In this lab, even freshman year, the experiments we were doing weren't crazy difficult. But they always said, "If you're going to do an experiment, you have to make sure that your lab equipment all makes sense, that everything was kind of cleaned, calibrated, ready to go. Make sure you write a lab notebook to keep track of exactly what you're doing.
In this notebook, you should say yes, you calibrated the instruments to make sure everything looked fine, you cleaned the instruments after picking them up from this rack." It wasn't so much just doing the experiment to come up with the numbers, and then you're done. It was also about being a really good experimentalist, making sure that you really are keeping track of everything that you're doing, so that when you have the numbers, you can go back and say, "Do the numbers make sense?" And if they don't make sense, can you figure out where you went wrong? What part of the experiment completely failed? Is it that you didn't calibrate correctly? Is it that some of your instrumentation was dirty?
If you have all of this written up in your lab notebook, you can just go back to see where your mistakes were. That lab course freshman year, I loved it because I didn't realize that it wasn't enough to just sit around, look at the formulas, and plug them in, and say, "You're going to get the answers." There was this other side of it of doing the experiments. Again, the experiments weren't crazy experiments. It was more the philosophy of being an experimentalist, calibrating your instruments, being very careful about writing down really good lab notes. It just kind of completely changed my world of what it meant to be a physicist. I really, really loved freshman year, the way the physics was done at Caltech.
ZIERLER: Where does the art history come in? Did you see that as sort of a separate interest? Or were you coming from a deeper, Leonardo da Vinci, you want to make these intellectual connections even as a freshman?
GOINS: No, nothing so ambitious. When I was in a high school, I did a competition called the academic decathlon. It's just like it sounds. There are ten subjects you have to go through, and sometimes the subjects change a little bit from year to year. You do have your standard subjects, like a mathematics exam, an economics exam. I don't remember all the different subjects, but sometimes, the big subject they would change would be part of what they called the super quiz. This was basically a big almost quiz ball competition, where you have all these students in the room who have not quite buzzers, but this list of questions in front of you, and you only have ten seconds to answer the questions.
You have to quickly write down the answer and move on to the next one. That subject changed every year. One year I did it, it was Native American history, but another year I did it, it was art history. I completely fell in love with it. Very specifically, it was actually the Impressionist movement from about the 1860s up until about the 1920s. But we had to know everything there was to know about the Impressionist movement. Which meant that we learned about different painters, about their works, sometimes some of the influence that they had on musicians, influence upon poets. It was very much learning as much as you could about that one very narrow subject.
Learning about that for academic decathlon inspired me to want to learn more. I didn't just want to learn about the art. I wasn't very interested in the concept of impressionism, how to paint it, the idea of pointillism. It was more learning about the whole culture of all of it, how the painters influenced the musicians and composers at the time, and how they influenced the poets at the time. I was very much interested to know, "How does this work in other time periods?" Hence, the interest in art history. When I got to Caltech, again, it was very clear I was going to major in physics. That was never going to be an issue. I looked through the course catalogue to see if there were classes in art and then classes in history I could possibly take. I want to say there might've been total maybe three classes in art that Caltech had to offer. There was one professor, I don't remember her name, she was a visiting professor, I think she was more like an adjunct, who I believe was maybe a professor over at CalArts, I'm not completely sure.
She taught a handful of those classes at Caltech. One in particular she taught was on the art of Buddhism. I didn't know anything about Buddhism, I didn't know anything about art in Buddhism, but that was a really interesting class. It was one of those classes where you're in a room, she turns off the lights, she's showing photograph after photograph on the big screen of all these different artworks. I think she spent a lot of time traveling in Southeast Asia, so some were pictures she took on her travels. I just remember struggling to stay awake in this darkened room, but it was still really interesting to me, seeing all of that. I got a little bit discouraged when I realized that after I was going to take those three classes, that was it. There really weren't any other art classes at Caltech. But I still had an interest in history.
That's when I really had to make a decision. Do I stay at Caltech knowing that I'm not going to go into art history, like I wanted to? Really, that I'm not even going to be able to take classes in art history? Or do I maybe compromise a little bit and decide I can do history instead? It took a few months to kind of convince me that that was something I was willing to do, but I eventually decided I was going to take more and more classes in history itself. That's where, really, my interest in the history of Caltech came from, in making that decision in freshman year.
ZIERLER: Now, when you talk about the history of Caltech, are you specifically thinking about the history of Black students and professors at Caltech, or more of an institutional overall approach?
GOINS: It was mostly the former but partly the latter. I had some really, really good advisors when I started to take history classes at Caltech. Doug Flamming was certainly the most influential person of all the people I met at Caltech. He had come from Vanderbilt, he was there in Humanities and Social Sciences. He taught a lot of classes in history. He actually was writing a book on the history of Black Los Angeles, but actually, he spent most of his research on labor movements on slavery and just in general, commerce in the South. That was really kind of his thing. I want to say maybe his doctoral thesis was on tobacco in Virginia, South Carolina. I'm vaguely remembering this, so I'm not completely sure if that's right. but when I first really got to know Doug, I was taking a lot of classes in the history of the Southern United States.
This was where he was teaching classes in things like the reconstruction period, what happened after slavery, how the United States really got its start after the Civil War with things like cotton, tobacco, how the South kind of reinvented itself. Really, a lot of the issues that were happening with Black folks in the 1920s and 30s, when Blacks moved out of the south and into states like Illinois and California, specifically to cities like Chicago and Los Angeles as part of the great migrations of the 1940s. Doug was teaching all of these classes. I must've taken four or five different classes.
ZIERLER: He was teaching your family's history, for that matter.
GOINS: He was. He definitely was. I just loved it. I loved everything that he was teaching. I say all of this to say that what I learned from Doug Flamming is, if you want to understand the history, perhaps of something very, very narrow, say, the history of Los Angeles, you need to know the history of a much larger picture. Understanding the history of Black Los Angeles, I needed to know the idea of the Great Migration. People who were moving to Los Angeles from Eastern Texas, Western Louisiana. But in order to understand that migration, I had to understand why they migrated. What happened in the South from, say, 1920s up to the 1940s.
And to understand what happened in the South, I had to understand what happened with reconstruction from the 1880s up to the 1920s. I learned all of this from Doug, but it wasn't just enough to say, "You're going to focus on this narrow period." You really had to have a much grander idea, a much grander scope of what was happening as part of the larger picture. When I approached Doug Flamming roughly the end of my junior year with some very basic questions, "Who was the first Black student to graduate from Caltech?" the very first question I had, Doug made it very clear you had to understand a little bit more about the history of Caltech itself, professors coming in and out, how many women were at Caltech over the years, what was even happening in the city of Pasadena.
I was very interested in learning specifically about the history of the Black students in Caltech. But I did need to spend some time learning about the history of Caltech more generally. I will say that I wasn't perhaps as good at that as I should've been. Even now, I feel that there are a lot of gaps in knowing about the history of Caltech more generally that I still have, but it was something I was aware of, that I did need to know that larger history in order to understand the more narrow history.
ZIERLER: Were you so enthralled that you thought about leaving the math and physics focus and focusing more exclusively on history?
GOINS: That's a good question. I had to do a lot of soul searching about, one, whether I wanted to stay at Caltech, and two, exactly what I wanted to take away from Caltech. Freshman year, yes, I did take classes in the Chemistry Department and the Physics Department. I also took classes in the Math Department. I took Math 1, but they don't have this anymore. They actually had an honors class in math. Tom Apostol would teach this class every year. It was just for a select few students, maybe 20 of us or so, who placed extremely well on the placement exam that we all had to take. That was a very elite class. Tom Apostol was the math consultant for The Mechanical Universe, which meant, in seeing David Goodstein teach Phys 1, that was the physics side of things. I could then compare and contrast with the way Tom Apostol taught the math and Math 1.
They went very much hand-in-hand. There were stories that David Goodstein would tell about physicists, some of the issues they had, and the revolution, this concept of–at one point, people really thought that the sun revolved around the earth, and things changed, and people eventually realized that the earth revolved around the sun, we were heliocentric. That was not taken very politely, let's say, by the church at the time. Apostol, on the other hand, would spend time explaining the mathematics behind it. Essentially, now, looking at motion, but moving over to polar coordinates and trying to understand Kepler's laws of motion or writing down these really elaborate series of differential equations. It was really beautiful to kind of see both sides of it, but from very, very different points of view.
I loved Apostol's classes. Apostol's classes are what convinced me to strongly consider mathematics. However, Apostol's one of the people who caused me to think, "Do I really want to be at Caltech?" In his classes, I can't say that I really–I will say that I gained a lot of confidence in how he did his classes. He said, "Depending on how well you do in the homework, you can place out of taking the final exam." Remember, when I was in high school, I had really just learned a lot of calculus on my own. I hadn't formally taken a Calculus A/B class. I kind of took a Calculus B/C, but that was more working with this high school teacher 101. I didn't really know what a typical calculus class looked like. Coming into Caltech, I'm around a lot of students who score perfect scores on the SAT, perfect scores on their Calculus A, B, and C exams.
A lot of students had taken calculus at local community colleges when they were 16, 17 years old. As you might expect. These really bright students coming in who had taken a lot of calculus. I was a little bit, maybe, shellshocked, a little bit nervous when I was taking this class at first. But I was doing really, really well on the homework. Eventually, I would do so well that I would place out of the final exam, which meant that I was in the upper echelon of this class. I was actually feeling a little bit good about myself, a little bit cocky in taking this class. But I did love the way Apostol was showing the material, and I loved the way things were going. I found a book at the bookstore, I believe it was A Modern Introduction to Classical Number Theory, something like this.
And I spent some time reading through this book because I had never heard of number theory before. I could see that I was doing pretty well in Apostol's class, and I just wanted to learn a little bit more behind this weird phrase I'd never heard of. I knew calculus. I had never heard of number theory. In reading this book, as fate would have it, Apostol one day announced in class that there was a Caltech alum who was going to give some fancy address in the Math Department, and he was recommending that the students in his class maybe go to one of his talks. The person who was giving the talk was the author of this book I was reading, a guy named Harold Stark. I thought, "It must be fate if I'm just reading this book, and this guy's coming to Caltech, and this guy happens to be a Caltech alum. Let me go ahead and go to his talks."
It was actually two weeks' worth of talks. The very first week, I understood maybe the first 30 minutes. Didn't understand the last 30 minutes or so. The second week I went, I understood maybe the first five minutes. Didn't understand the rest of the hour. But still, something about that, it seemed this person in number theory giving his talk, knowing that I could see his face right there, that made number theory a little more real to me, something I could possibly do. The next semester, that spring, I told Apostol I wanted to spend some time going to his office, chatting with him once a week just about some ideas I had in number theory, some things I was reading in this book by Harold Stark. I can't say that they were very coherent sessions I had with Apostol, but I would go in and just tell him, "Here are some things I'm thinking about, here are some things I'm working on."
I actually spent time over in his office at Project Mathematics. It wasn't in the Sloan, it wasn't in the math building. It was a little bit of ways, but it was a nice walk to go down the street there to chat with him a little bit. We chatted for maybe about eight weeks, me kind of showing him some of these ideas. I knew that there was this idea of a SURF, a summer undergraduate research fellowship, and I really wanted to do a SURF, where I could maybe work with Apostol and also kind of expand on some of these ideas I had. So I told Apostol I really wanted to work with him doing the SURF. He said, "Great, sounds like a good idea." I wrote up the proposal. One day, at the end, one of his classes–this was actually the day that proposals were due–I came up to Apostol at the end of class saying, "I've finished writing up the application.
Here's the proposal. It's due at 5 pm." It was maybe 2 pm at the time. I was just going to walk it over to the SURF office, and it was going to be a done deal. Apostol gave me a strange look and said, "I'm sorry, I don't really understand the project that you want to do. I know we've been talking about it for weeks, but I don't understand it. I don't feel I could do a good job being your advisor. I don't feel comfortable signing off on this document, being your SURF advisor." He walked away, and honestly I was a little bit dumbstruck because I was kind of screwed. It was due in three hours. We had been talking about this for weeks. This was the first he ever said that he didn't feel comfortable doing it. I didn't really know what to do at this point. I wasn't really upset with Apostol, it was more this confusion of, "What did I not do right?"
As you might imagine, a lot of the other freshman were interested in doing research, they'd already lined up projects with other professors, so this wasn't something that was out of the ordinary, finding a professor to work with. But I felt confused in that all of my friends had research projects lined up. Some of them were going to travel off to other schools, others were going to do a SURF, and I had no one now. SURF proposal's going to be due in three hours, and I had nobody to work with. This was when I really started to think, "Is Caltech really the right place?" I actually did spend some time the quarter before looking into transferring to UCLA. I had gotten my hands on an application, I filled it out.
I never submitted the application though. But I will tell you that that next quarter, when all this happened with Apostol, was when I really had to think hard about, "Do I really want to stay at Caltech?" I wasn't really sure whether math was something I wanted to major in. But being so inspired by Harold Stark's visit, Apostol's class, and this book in number theory I was reading, I was starting to think maybe this was a direction I wanted to go in. But after that one meeting with Apostol there in…
[End of Recording]
ZIERLER: OK, this is David Zierler, Director of the Caltech Heritage Project. It's Tuesday, November 23, 2021. Once again, it's my great pleasure to be back with Professor Edray Goins. Edray, as always, great to be with you.
GOINS: Yeah, thanks for having me again.
A Meeting that Changed Everything
ZIERLER: Last time, before we were rudely interrupted by a power outage, you were explaining a quite dramatic narrative transition in your educational trajectory, where you were seriously considering leaving Caltech. The very last thing I heard you say was, you were in a meeting with Tom Apostol, and that changed everything. Then, we went silent. First of all, what did Tom say, and why did it change everything for you?
GOINS: Let me maybe try to back up and go to the beginning of all of that, at least so I can get my own mind set in what we were saying. Freshman year, I was taking this Honors Calculus class that Tom Apostol was teaching. The idea was that if you had done really well on the homework assignments, you could place out of the final exam. I had placed out for the first two quarters, and really, during my second quarter, I wanted to work with him doing number theory. We spent a good amount of time in his office at Project Mathematics! chatting about some things that I had been reading about. Remember, I had this book by Harold Stark called An Introduction to Number Theory. But there were a lot of things in the book I didn't really understand. I would go to Apostol's office, try to chat about various things I was seeing.
I even had some ideas of how I could generalize some of the concepts that were there. But by the end of that quarter, I wanted to do research with him and continue some of the projects that we were discussing. One day, a Friday afternoon, we had just finished class. I'd spent part of that week writing up a SURF proposal, and all that I needed him to do was sign it. I was going to walk it over to the SURF office immediately after class and then hopefully work with him that summer. Well, at the end of class, when I handed him the SURF proposal, he looked at it and then said, "I'm sorry, I really don't understand what it is you want to do this coming summer." Of course, I was a little bit shocked because we had spoken about this for weeks, probably five to six weeks at this point.
And I thought it was pretty clear that I wanted to work on properties of what are called binary quadratic forms and some of the multiplicative properties there. But he told me because he didn't really understand what I wanted to work on, he did not want to do research with me, and he was not going to sign this proposal, this application to be sent to the SURF office. Of course, I was devastated because the applications to SURF were going to be due in the next three hours or so, which meant that I was not going to do research that summer. This was halfway through my freshman year. I was seriously considering being a mathematics major. I really thought I was doing well in his class since I had placed out of the exams and was getting 100% on the assignments. I came to each and every lecture.
We had spent weeks and weeks talking about all of this. But if that wasn't good enough to convince him to do research, I didn't really know what was. I really had to think hard whether Caltech was where I wanted to be and whether mathematics was something I wanted to do. Earlier that year, I had seriously thought about transferring to UCLA. I had gotten an application in the mail, was filling it out. I eventually decided not to apply. But the point is that still, I was really wondering whether Caltech was really the place for me. I definitely liked the classes. I didn't really like the lack of social atmosphere that was there. Math and physics were certainly two things I was interested in.
Apostol was only one of two people in the department doing number theory. I knew Apostol was out. We weren't going to work together or do number theory. If I wanted to continue in number theory, I had to think about working with this other guy I hadn't even met yet. It was really kind of a scary thought, halfway through my freshman year, "Should I stay at Caltech? Should I stay in mathematics?" I was very, very much on the edge.
ZIERLER: If I can just note here, the questions that you're dealing with seem to be primarily of an academic nature. On the social side of things, and this, again, goes back to your naïveté, not really thinking about the lack of integration at Caltech, how diverse it was, so my first question there is, today, we have diversity training, and we have officers in diversity, and there's all sorts of messaging that conveys, at the institutional level, that diversity and inclusivity are important across the board. Circa the early 1990s, was there anything like that at Caltech? Aside from the individual level, the professors, your colleagues, your friends, the students who were supportive of you, was there anything at the institutional level where you received the message that people who look like you were valued at Caltech?
GOINS: Absolutely not. This was during the days when there wasn't any kind of diversity office, it was before the days of the Women's Center. Lee Browne was the only person who really had an office, and he had student support programs. That's what it was called, SSP. It wasn't even a diversity office. There were a handful of students on campus, there was one office, which essentially had no funding, which was supposed to help out this handful of students. But there was nothing else on campus that I'm aware of.
ZIERLER: What did that make you feel?
GOINS: On the one hand, Lee Browne did a very good job, when we were all in high school, of letting us know what we were getting ourselves into. He made it very clear that Caltech was going to focus on academics. It wasn't going to focus on whether or not you wanted to have parties, have a girlfriend, hang out and be social. It didn't even care whether or not you were going to get along with your professors. You had to work really hard, get really good grades, and hope and pray that you were going to graduate. That was pretty much the pep talk that he gave us all coming into Caltech. I knew that it was not going to be a friendly place. I knew this walking in. I don't think I was really prepared for how one-dimensional Caltech was.
A lot of it came down to professors and students only focusing on what you could do when it came to academics. I'm not even talking about whether or not you're getting the best grade in the class, whether or not you know how to do the homework assignments. It was more this pecking order of who was considered to be really smart and who wasn't. That was really a depressing thing because I think that some of us had a lot to bring to campus that would've made it a much better place. But really, it never felt that the campus in general appreciated that. One story I'll give you is this. I mentioned that Eddie Grado came to campus, and he took over for Lee Browne. The guy who was in the admissions office was Dan Langdale. Dan Langdale, if I remember right, came in 1989, and he wanted to have a very different admissions freshman class.
That's where the 12 or 14 Black students came in there in 1990 because he was really big on that class. My understanding is that he also fought to bring Eddie Grado from MIT, where Dan Langdale was coming from. Here we were, freshman year. We knew that Eddie Grado had come from MIT, but we didn't really know much about the admissions office. Dan Langdale had dinner for all of the freshman minority students. His wife was there, he also invited Eddie Grado. Remember that most of us on campus didn't really know Eddie at the time. We definitely didn't know Dan Langdale. But there must've been about 20 of us there at the house, of course, all very awkward Caltech freshmen, all standing around not really knowing what to do. The one thing that stood out for me that evening was, Dan turned to us and said, "I want you to all know why I admitted you."
He started by saying, "All of you were Affirmative Action admits." Now, some people took offense to that. But Dan continued by saying, "The way I view Affirmative Action is, by bringing in individuals using criteria that isn't your standard criteria, I didn't just bring you all in because you were really good at academics. I brought you in because I knew that you were going to change the culture of this campus, that you all are coming in from very different beginnings, you have very different perspectives, and these different backgrounds or perspectives are sorely needed here on this campus." He went on to say, "All of you are leaders and movers and shakers. I saw what you did in high school, I saw the organizations you were a part of. Now, I put onto you the charge of doing the same thing here at Caltech." That speech that Langdale told us actually really stuck with me for the next four years.
I saw it as my responsibility not just to be this one-dimensional person who would just focus on being a really good student and scientist, but I really saw it as my responsibility of changing Caltech for the better. It was all because of this one speech that Dan Langdale gave us during freshman year. I'm not going to say that it made my life any easier to decide to take on that charge my freshman year, but it gave me a very different perspective of what it meant to be at Caltech. I think that perspective really helped me survive through the place. After everything that happened with Apostol, I did have to do some serious soul searching of, "Do I really want to be at this place where I understand it's going to be an uphill battle? Not just in terms of academics, but also in terms of the lack of social life that I'm going to have." There was never any question whether I could do it.
I certainly knew that I could make it through Caltech, I could graduate, and I could thrive. I wouldn't just survive. But I was actually doing really well at Caltech. The question really was whether it was going to be worth it for me to sacrifice the four years. But I will tell you that hearing Langdale give us that speech of him saying, "You are movers and shakers. You are here because you are to change this place," definitely is what kept me inspired.
ZIERLER: These communications, of course, are overt. You're hearing these things loud and clear without any nuance whatsoever. What about what we might call today micro-aggressions, either from professors or students? Comments that might seem innocuous but can be deeply hurtful, assumptions that maybe you're not a student, you're a staff member, maybe you're there for athletics, things like that. Did that happen to you also?
GOINS: It did. I'm going to have to go back 20-some-odd years, where I can remember everything that happened. Actually, I guess it's 30 years now. There were various things that happened even as early as Frosh Camp, when we all went to Catalina Island. When we did the equivalent now of FSI, this freshman summer thing that lasted for about six weeks or so before classes started, I would say that we got along pretty well as a group. We were having some very awkward conversations of what it meant to be a minority, but all of the minority students were there together. We bonded pretty well as a group. Our first real test of being Caltech students was going off to this freshman camp.
I remember in particular being a little bit nervous, somewhat anxious by seeing all of these brand new students for the first time. We're talking probably 30 of us were on campus for about six weeks, all kind of working and living together. Then, that 30 then ballooned up to about 200-plus people when we were all supposed to go on the boats to Catalina Island. One thing I remember is wanting at one point to listen to rap music. Now, this is back fall of 1990. Rap was not something that was part of the mainstream. MTV made it a point to refuse to play rap videos. Yo! MTV Raps was relegated to Friday evenings for a half-hour show because they wouldn't play any videos the rest of the time.
Rap was not played on the radio at all. But this is something that, of course, I had grown up with in Los Angeles. When there were maybe one or two parties happening at Frosh Camp, I remember requesting to the DJs that they play something. But the DJ looked at me and said, "I'm not going to play that crap," and just told me to go away. The next day, I don't even remember where I got this from, but I got a boom box and decided that because I had one or two rap tapes, I was going to walk around the island there at Catalina and play this loud music that I was used to. That gave me a lot of nasty looks from people. Me kind of walking around, people wondering, "What is this music? Why is he playing all of this?" But I really did that in defiance.
That was really my first introduction to knowing that the culture that I was used to was not going to be welcome at Caltech. I can't really remember a lot of other micro-aggressions. It's probably just been blocked out of my mind over the years. But certainly, issues such as walking into some of the buildings in the evenings, getting stopped by campus security, being asked to show an ID. Me wondering, "It's the middle of Caltech's campus. Who else is going to be in here dressed like a student, 18 years old, walking into the building?" But it didn't matter. Being harassed, stopped all the time. The rap music thing was a thing that happened for all four years. It essentially never got played at any of the parties. Whenever I would come in with a tape or a song I wanted to play, no one ever wanted to listen to it.
At another point, I lived in Ricketts, and I put up outside of my door the information about the old negro leagues, the baseball league. It was something I just got really interested in when I was a sophomore. So, my junior year, I decided I was going to wear baseball jerseys that had some of the negro league players. Outside of my door, I would have information about who this player was, the history, and what have you. I know that those were not well-liked in the dorms. People wondering why I was being divisive, why I was putting these things outside of my door. There were a lot of minor things like that. Lots and lots of minor things. The only awkward interactions I can think of at the moment that I had with faculty members–and I'm still debating to this day whether it was a good or bad interaction–I was taking ACM 95.
At the time, we called it AMA 95. But this is the class that discusses mathematical methods for scientists. For a lot of students at Caltech, it's probably the scariest math class they will ever take. For me, it was my most favorite math class. I ended up getting an A+ in this class. There were only maybe two Black students in this class altogether. But the professor for this class, he and I hit it off really, really well. I could tell he really liked me. I don't even know how we first hit it off. I think we would chat outside of class a little bit, I would see him on campus, and sometimes we'd just kind of walk places. But I do know that right about the time I was taking AMA 95, it was right about the time the LA riots happened.
Of course, people did not know how to discuss race. It was just something that people didn't do. It wasn't clear how to bring it up or talk about it. I remember, this professor and I did actually have different conversations about race. For example, the movie Malcolm X by Spike Lee had come out right about that time. For me, this was a big, big movie. Actually, I saw it three times in the theaters. This professor and I actually would talk about the movie Malcolm X, about the person and what have you. It did feel a little bit awkward that here I was, this older white professor who was teaching my applied math class. You would think we would have no reason at all to talk about anything other than applied math. But one day, he just brought it up, and we would just talk about it somewhat casually. Again, I'm not really sure if this was a good or bad thing, but I definitely enjoyed the conversations I had with him. So yeah, there were a lot of things. Probably, if I think about it more, I could come up with more stories.
ZIERLER: Do you have a specific memory of the Rodney King beating and where you were at the time?
GOINS: Yes, I do. This was during my sophomore year, if I remember right, and I was not having a great time at Caltech. I definitely was a math and physics major, but I just really wasn't happy in the math building, wasn't happy in the Physics Department. I definitely wasn't happy living there with people on campus. But I was doing what I could to kind of make it through. Eddie Grado's office, the equivalent of Minority Student Affairs, was in the middle of campus at this point. There was a small building, which was located, I believe, between Page House and Lloyd House, right where the mailboxes used to be. I think it might've been [the] director [who] lived there for a while. I'm not sure. Anyhow, it was a very small office, and Eddie had his office there. This office was so small–it was large enough that Eddie had his desk, there was a secretary at the front door, and that was it.
There was really no space even for students to hang out. But I remember hearing about the Rodney King beating, watching the video, knowing that the trial was going on, and just feeling that "All of this kind of craziness is happening, nothing's fair," and what have you. The day the verdict came out, I went over to Eddie Grado's office, and I remember all of us just feeling really depressed, first, about the fact that the verdict was going to come out, knowing that it wasn't going to be positive, and second, actually just watching everything happen. But I remember in general there at Caltech, people really didn't know how to talk about race, so it wasn't like it was being discussed in the dorms. It wasn't. Nobody was talking about it.
I didn't really know Eddie Grado very well, but being able to go over to that office, the fact that he had this on his television at least made me feel comfortable enough to kind of bring it up with him and chat a little bit. I remember being there in his office, watching for a little bit, knowing that the verdict came out, and watching Tom Bradley, who was the mayor at the time, go on this press conference with Rodney King standing right next to him, saying, "We know that you're not going to be happy with how the verdict's going to come out, so please don't riot. Please don't do anything crazy. Let's just try to survive through this." Of course, watching the mayor freak out about that, I knew that something bad was going to happen. I went back to my dorm, turned on the television, and there, I could see some of the newscasters reporting that the verdict came out, people were not happy about it.
LAPD was on alert, but at the time, I was watching television, the local station, I was also listening to the Black radio station out of Los Angeles. This is something I had done every day anyway because I grew up with this radio station. I was kind of watching both at the same time. The TV stations were saying that they were kind of worried about maybe some of the riots that were starting to happen in downtown, but they really phrased it more as, "People are starting to go crazy in Los Angeles." The Black station, on the other hand, was reporting something completely different. They were saying that, for example, a lot of the stores were closing early. They noticed that the police cars were actively leaving South Los Angeles. They were actively telling people on the radio, "Get off the streets. Things are not going to be good tonight. Try your best not to act crazy."
Then, I saw on television, there was a guy in the middle of an intersection being pulled out of his truck, and it looked like he was being beat up by a few different people. Now, the rest of the world knows this as Reginald Denny, who was being pulled out of his truck right there in the middle of the intersection. I recognized that instantly as the intersection that was about two blocks away from my house. I recognized that right away. I called my mom on the phone because it looked like total chaos from what they were showing there on television. She didn't answer, but my brother answered the phone. He says that he can see all of this happening essentially from the back of the house because he can actually see Florence and Normandie just a couple of blocks away.
He can see that there are helicopters flying overhead. They also know that the police had totally pulled out of the city. He also said that a lot of this craziness was localized right there at Florence and Normandy. Even half a block away, it was perfectly fine. There was nothing happening. But he also said that this wasn't what they were showing on television. I knew that there was a lot of craziness happening right there in the neighborhood that I grew up in. I knew that my mother and brother were probably not in the safest of situations. But of course, there was really nothing that I could do. I continued to do all this for the rest of the night, kind of watch the television but really with the sound turned down low, then also listened to the Black radio station to kind of hear what was really happening there in the community. It was a completely different narrative, watching the two of these happening.
What you see on TV is almost hysteria, madness, and mayhem, people breaking windows and looting stores, whereas if you listened to the radio station, they made it very clear that almost all of that was localized to downtown Los Angeles. The rest of South LA, people were staying inside and didn't really want to go out. A lot of people on the radio were talking about the similarities with the Watts riots back in the 1960s. There was also a lot of discussion of why people were really unhappy with the verdict, why they were also unhappy with what was happening in South Los Angeles. I spent pretty much the next several days watching this dichotomy, listening to the radio station but also watching, without sound, everything that was happening on television.
As I went to class, though, during the day, I would hear people talk about what was happening, but there was no sympathy at all towards what was happening in LA. For example, in my humanities classes, I remember students saying things like the people in LA where all this stuff was happening should be shot, that they got what was coming to them, they got what they deserved, they can't believe why people are ripping up their own communities. Now, remember, they're saying this about the people I grew up with, my family and relatives. But since I'm the only Black student at Caltech who's from South LA, no one really has any sympathy behind all of this. Doug Flamming, who was the person teaching some of these humanities classes, was very good about having people kind of back up a little bit when they were saying some of these insensitive comments.
He definitely wanted them to speak up and speak their minds, but he was saying, "You can't really say things like, 'Those people should be shot,' because some of those people are here in the room," these kinds of things. I was very grateful that Doug Flamming understood that this was not a comfortable situation for me. But that whole week, watching the students at Caltech just be so vicious to what was happening in LA, and then being selfish, saying that they were scared to death that all of these rioters were going to come to Pasadena when there was absolutely no way any of this stuff was going to happen, and it showed that they didn't understand why it was happening in LA in the first place.
It caused me to really despise the fellow students at Caltech. It was a really hard year, watching all of those comments go through, watching students say what they were saying. Then, to think that these are the same students I'm supposed to be taking classes with, calling my friends, living in the dorms with. Realizing that there was this disconnect between what they viewed as people in LA and the reality of the people who were there. I can't say that I ever really got over that experience back then.
ZIERLER: Of course, Pasadena's only a few miles from South LA, but you must've felt like you were on a different planet, to some degree.
GOINS: I did. I did. Growing up, we all knew that Pasadena was a very conservative white city. My mom and I would joke about this growing up. You could turn on the Tournament of Roses parade and see things like the Rose Court, and it would be completely white every single year. Growing up in LA, you see the Rose Bowl Parade every New Year's Day, every single year, and you understand that if that's really emblematic of the city, the city must be a totally different world from what's happening in South LA. In moving to Pasadena, I was very much aware that the city itself was not the same city as LA. I think what surprised me was realizing that Caltech itself was a very different world from anything that I had ever seen, but a different world, and not in a good way. Students that really did not have any real connection to the rest of Los Angeles. They really saw it as people who were beneath them. That was something that stuck with me.
ZIERLER: As a coping mechanism to deal with this very difficult situation, when did you find it healthy for yourself to be out in front of the issue, to confront people, to correct them of their misperceptions, to tell them when they're acting in an insensitive way, and when did you just want to close up the shell and not want to deal as much as possible?
GOINS: I never worried about correcting people. As far as I'm concerned, if that's the way you're going to think, I just don't really have any interest in interacting with you. I focused a lot more on what was happening with the Black students at Caltech. This is where I did a lot more work with the equivalent of the Black Student Union with the NSBE chapter, the National Society of Black Engineers. I spent a lot more time trying to make sure that the Black students were graduating, that they were doing well, that they were doing well in their classes. I remember signing up as a dean's tutor so that I could get paid to tutor as many of the Black students there on campus as I could. Ironically, the California Tech, the student newspaper, wanted to run an article on what was happening in Los Angeles with the riots, Rodney King, and what have you. As I've mentioned several race wasn't something that was discussed at Caltech. One of the reporters eventually found out that I was a Black student there who was from South LA. They would to interview me on exactly what we're talking about now, growing up in LA, why the riots were happening, what it was like me being there at Caltech. It was a very awkward interview because I wasn't really interested to talk about it. I almost felt that this was…
GOINS: Exploitative. Exactly. That they wanted to feature me because it was a nice narrative. "Black student from Caltech has riots discharge two blocks away from his house." The article ran, and people read it. But I was never happy with it. Not so much not happy in what the reporter said, more in that it was exploitative. I was much more interested in making sure that the other Black students at Caltech were healthy and surviving than I ever was in helping Caltech come to its racial reckoning. There were some people on campus who wanted to have discussions about the Rodney King beating, about police brutality, the riots there was were taking place. I remember at one point during that entire week all the riots were happening in LA, there were people who put up various posters and flyers around campus saying that they wanted to have a discussion about Rodney King and all of this.
A lot of those flyers were actually torn down, and people were saying in general in the dorms that they didn't want to have discussions around this, that they were very angry that all of these things were happening in Los Angeles. Just seeing that vehement response to wanting to discuss what they were seeing on television also made a big impact on me. I realized that this was the one opportunity, probably the first opportunity for many people who attended Caltech that they really saw race upfront and in their faces. But they did not want to talk about it at all. They really went out of their way to make sure they weren't going to talk about it. I didn't want to be a part of that.
That's when I made the conscious decision, "I am not going to spend time engaging students at Caltech about race. I am only going to engage the students of color to make sure that they survive." It's an ironic thing, but I don't think that most people knew I really had no interest at all talking about being a Black student with other students at Caltech. I had a main interest in making sure that the other minority students were going to graduate.
Interacting with Extremes
ZIERLER: What did you learn about yourself in your natural inclination to worry about other students of color?
GOINS: I think I learned that I was a natural leader. I also learned that I had a lot of patience. I learned that I was a very good listener. The minority students at Caltech were all coming from very different backgrounds. They had very different perspectives. Some were from inner cities, and they really took it personally to see the police brutality that was put out there on television. Others had never been around minorities before. They themselves did not know what it meant to be a minority. Being at Caltech, they were closeted. They were very uncomfortable discussing any issues dealing with race or even what it means to be a minority student.
I had to learn how to interact with those two extremes. Specifically, chatting with Black students who wanted very much to have rap music played at parties, and they very much wanted to talk about their African non-slave names kind of thing. Students who wanted to go off campus to go see Malcolm X, the movie. Also, to deal with those students who had never been around other Black students before who actually were uncomfortable when I would come say hello to them because they had never interacted with anyone Black before, even though their parents were Black. These same students, I had to figure out how to get them into one room so that we could all work together and be a part of this organization. That took a lot of creativity, but it definitely took a lot of patience. But I learned that I was really good at it.
ZIERLER: Because this required coordination, was there anybody on staff or in the faculty at Caltech who were supportive of this effort, who helped you wherever they could?
GOINS: I would say there were a handful of people. Of course, the main person was Eddie Grado. He was very much in front of this first day, freshman year. He was always supportive, always there at the meetings. Always said if you needed money or anything, that he'd be the first person to help out. There also was the secretary in Eddie's office, Michelle McLanahan and she was wonderful. She was amazing. She was definitely always there 100%. In terms of some of the other faculty, there were a good number of faculty in Humanities and Social Sciences who were 100% there. Of course, Doug Flamming, even though he wasn't really there for the meetings, he was definitely my rock.
I would go to him with different ideas, things I was thinking about, and he was certainly 100% supportive. He's the one who would kind of let me know about maybe different activities happening on campus, if there was a speaker coming by, whatever. I do remember in particular when the movie Malcolm X came out, he actually drove myself and another person to South LA to go see the film. It took 45 minutes or whatever to get over to the Crenshaw District to go see the film. But we wanted to go see the film. I was really grateful that Doug was willing to do that. There were a few other people over in humanities that I just remember were always very supportive. Morgan Kousser was one, and I still think it's ironic that I've never taken a class with Morgan Kousser, but he was someone where I could just show up at his office, and he is certainly one of the most liberal and politically active people I know.
Whenever I was feeling frustrated about things, I could go talk to Morgan, and he would get me riled up and motivated to do even more. There was a visitor named Bryant Simon, and I believe he was visiting maybe for a year, maybe two years. But he was basically visiting, working with Doug Flamming. Bryant and I just had wonderful conversations the whole time he was there. I considered him to be my second advisor because he was really the one who was the main contact when I did my SURF project on the history of Black students. Over in the Physics Department, you had Steve Frautschi, who was wonderful. I met him when I was at freshman camp for the first time. He's the one who kind of convinced me to stay in physics, even though I really wasn't happy in the Physics Department. I would see Frautschi all the time. He would come to dress dinner over at Ricketts, and we would hang out, chat about this or that. I really can't say enough great things about Steve.
Steve was the reason I went to Stanford for grad school because I would just ask him, "Where should I go?" and he said he liked his time at Stanford and thought I would, too. That's the reason I went. There were various people like that. I know that there are at least a dozen other people I'm forgetting about right now.
ZIERLER: There was a support network is what you're saying.
GOINS: There was, but it was a rather odd network. I don't know how many of these people knew each other. HSS, they knew each other, but I don't know if Doug Flamming knew Steve Frautschi, I don't know if Steve Frautschi knew Eddie Grado. There was even another woman over in geology, Jean Grinols and my understanding is, she was one of the Black women on staff who had been at Caltech the longest, something like maybe 25 years by the time I got to Caltech. But I don't think that Jean knew Eddie, or Doug, or any of the rest of these folks. Me kind of becoming that leader, I just got to know a lot of people from all over campus. You name the department, I pretty much got to know someone there.
I got to know the people who were allies, and I also got to know the people who tried their best to kind of put a halt on everything. But the funny thing is, in learning these different pockets of campus, I also learned that they didn't know each other, that there really wasn't any one concerted effort to have all of us work together. I kind of got the feeling that a lot of those people I interacted with saw me as the glue because they knew if something was happening, I would let them know about it. They all knew about the NSBE chapter. If things were happening in the Minority Student Affairs office, I would happen to be in their office or seek them out and tell them, "This here's happening. This is what's going on."
I don't really know if that ever kept up after I graduated. But that's probably the one regret that I have, that even though I was really happy that I was interacting with all these faculty and staff, and we had this nice, coherent network, I could never find a good way to make that permanent. That all of these people working would permanently be working together.
ZIERLER: Of course, now, after the year 2020, and the decision on renaming with Millikan and others in the eugenics movement, was that on your radar at all as an undergraduate? Were you aware of this connection that Millikan and others had to the eugenics movement? Was anybody talking about that then?
GOINS: No, absolutely no one was talking about that. You have to understand, Caltech was just a very, very different place. Caltech had its gods, and you didn't talk bad about its gods. We're talking people like Millikan, Feynman, and what have you. You just didn't say anything negative about them. Ironically, the fight that we had in our day was making Martin Luther King's Day an institute holiday. That was our serious fight. I would say that probably grad students like Sarah Sam, what was happening with the Black students at Caltech in the last couple of years, we had a similar fight with NSBE '91, '92.
We spent many, many days in Thomas Everhart's office trying to plead with him that Martin Luther King's birthday was a federal holiday, but it was not a holiday observed at Caltech. Everhart had made it very clear that as far as he was concerned, Caltech was a very unique place. That it only took certain days as holidays, but it did not observe all of the federal holidays as institute holidays. I know we had argued maybe to move one of the other institute holidays to Martin Luther King's Day, but Everhart said no. He was not going to do it. He was steadfast in this and would not budge. His philosophy was, if individual professors wanted to make their own decisions to cancel classes in observation of this day, he would have no issue with it. But he wasn't going to declare universally that that day was a holiday.
Now, this was the catch-22 that we were going with. Yes, we met with Thomas Everhart, we wrote many, many letters to him. He met with us, but he would just smile and say, "Thank you for coming. It's not going to happen." We did spend some time in a campaign to try to convince the undergrads and the faculty members, "Cancel class, or don't go to class." Humanities and Social Sciences backed us up 100%. They canceled classes. They decided as a department they were not going to have classes at all. In fact, they went one step further. Every year, they would bring in an outside speaker to celebrate Martin Luther King's birthday. We loved the support we got from HNSS. Of course, we tried to convince the undergrads on campus, "HNSS has this Martin Luther King speaker. We're going to support it as the Black Student Union. We're asking you to go as well."
The universal response we got was, "I can't go to it because I have classes." And that was our catch-22. We tried to convince students to go to this thing because it's a good thing to do. We think that the students thought it was a good thing, but they couldn't go because their professors weren't going to cancel classes. We were stuck. Every year, we would have this celebration, we would have this outside speaker, we'd have 100% support from HSS, we would advertise it on campus. Every year, we could barely get any students to go because the students who were taking classes in physics, math, biology, you name it, they had to go to classes those days, and they wouldn't go to the events. We would get maybe ten students to attend these, whereas we probably would get another 15 people from the local Pasadena community that would come to it. I assume that it's the same activity happening now.
I think it's a much bigger event on campus. I just remember being frustrated at this event every single year because we could never get Everhart to pay attention to us. I remember talking to Doug Flamming every single year about this, wondering why it was that Everhart was not willing to listen to us about this. We could never come up with a good answer.
ZIERLER: Did the social and political context affect your academics in terms of the kinds of courses that you poured your effort into, where your interests were? Or did you try to keep those worlds separate?
GOINS: I think everyone knew that I had at least a dual life. The life of a scientist, and the life of–I don't want to use these words, but I'll say a student activist. Those are words I definitely would not have used when I was an undergraduate. But I was a math/physics double major. As math/physics double majors go, you have to take a lot of really difficult classes. I was taking five, six classes every quarter, constantly in the Math Department, taking grad-level courses, and I had friends who were grad students in the same classes I was taking. They could see I was still the top student in the class. Again, I mentioned this AMA 95 class. That essentially is a grad-level course.
There were a good number of graduate students taking that course. I then took the corresponding classes after that. I don't remember the numbers, maybe AMA 101, 105, something like this. Those were almost entirely grad-level courses. But I was still getting the top grades in those grad-level courses. Same thing when it came to the mathematics courses, taking group theory and classes that were meant for first- and second-year grad students, but still getting the top grades in those classes. The students knew, the other undergrads on campus, that I was doing really, really well. But they also knew that I was very much involved with the NSBE chapter, essentially the Black Student Union chapter, and I was making a big stink about things like having information about the old negro leagues on my door and trying to really push hard that Martin Luther King's Day should be an institute holiday, and really putting out there what was happening with the Black students on campus, how people were getting harassed by campus security.
These were things I was actively talking about whenever students would meet with me. I think on the one hand, I was respected because of the academics, because of how well I was doing, but on the other hand, I was somewhat despised because I was bringing up all these issues that people just didn't want to talk about or hear about. We're not just saying from the white students, but from the minority students as well. There were a good number of minority students who did not want to hear about Martin Luther King's Day being an institute holiday or what was happening with the other Black students on campus, why students were failing out. It was a very difficult time because I decided to wear both hats. I was a mathematician and physicist, but I was also someone running the NSBE chapter. It was hard finding ways to balance the two because one was respected by the students, but the other one was not.
ZIERLER: What classes or professors offered you options in mathematical to the physics to the extent that it bridged the divide?
GOINS: There really wasn't any bridge to that divide. The divide was there, and it never got any easier. I've read all these things that Richard Feynman notoriously did not like the Mathematics Department. Unfortunately, you could tell the Math Department didn't like the Physics Department in return. Math and physics, even though they were in buildings right next to each there, they never spoke with each other. There was never any interaction. The closest it got, of course, is this guy named Barry Simon, who was there in the Math Department. But no one else in the Math Department interacted with anyone in physics. It was very clear, separate worlds, separate departments, and they were never going to interact with each other. The Physics Department was very much an old school, classical department that said, "You learn theoretical physics in the classroom, but then you learn experimentation in the lab, and you must do both." There wasn't any of this, "You can sit in a classroom, do a whole bunch of math problems, and that's how you understand physics."
You had to do both. I believe that as physics majors, we had to take labs freshman year, junior year, and senior year, all three years. Now, I loved the labs. I'm glad that I did the labs. But I ultimately decided not to do physics because Caltech droned in me this idea that you have to be able to do both. You have to be able to be in the lab and also do the theoretical part. I never saw physics at Caltech as something where you could just do math and be a good physicist. It was more the philosophy of, "If you just do math, you're a mathematician." Which, of course, is ultimately why I decided to do math. But I will definitely say there wasn't mathematical physics at Caltech. There were physicists who could do math, but at the end of the day, they were physicists.
ZIERLER: And for you, do you have a clear memory of when it was going to be math that you wanted to focus on for graduate school?
GOINS: I have a clear memory at Caltech of what pretty much pushed me over the edge. It wasn't until my second year of grad school that I really made the firm commitment that I was going to go into math. But there was an incident that happened my senior year that pretty much told me, "Yeah, you're going into math." Senior year, we had our physics courses, but we also had our lab courses. I really struggled with senior lab. Part of this was, I was very involved with the NSBE chapter. Eddie Grado had been fired. There was this new guy, Frank Vargas, who had come from the admissions office, and he was running the Minority Student Affairs office, but the reality was, he wasn't running it. I was still running it full-time. He wasn't there for any of the events on the weekends or on the evenings because he kept saying he had a new baby, and he wanted to be involved with that. But the point is, he wasn't involved. The students knew it.
The students despised him for it. I pretty much ran that office my entire senior year. But I was also trying to graduate with degrees in math and physics, which meant I was still taking these grad-level courses in math, and I still had to worry about finishing off this senior lab in physics. I was paired with an unfortunate person who was really good at the labs, and she decided she was going to do all the labs by herself. Which meant after about maybe the third or fourth week of the quarter, I did not have a lab partner. I had to figure out how to do the rest of the semester by myself. The guy who ran the labs really felt sorry for me, one of those grad students in physics. Because he could see me there in the lab every week, struggling by myself to get all of this together because my lab partner came in at these ungodly hours to get the labs done, and she never told me. If I had known, I would've found a new partner, but I didn't know. I spent, really, the rest of the semester trying to struggle with these labs, get everything done. Whenever there was a mistake, I had to redo the experiments.
And of course, it was just crazy trying to find time to be in the lab for all of these extra hours, and then run this office, worry about NSBE, worry about math classes, and so on. But I put in my hours there at the lab, and I eventually got it done. There was one day one of the older white physics professors came in, and there weren't many people in the lab at this point because it was getting close to the end of the day. But the grad student TA was there, I was there, maybe one or two undergrads. He looks at me working by myself, and he's seeing that I'm kind of struggling just to get certain things together to get this experiment done. He looks at me and says, "You are a very poor physicist. Based on how badly you're doing here in this lab, I should fail you on this lab to make sure you don't get a physics degree," and walks out of the lab. The grad student TA hears this, comes over, and says, "I am so sorry. I can't believe that he just said that." But I just decided to brush it off.
Of course, I wasn't happy with it. But I had to finish the lab. I must've worked for maybe another hour, another half an hour, then I had to pack up, and I went to Minority Student Affairs so I could do my next thing, send off emails to the students, and the rest of that. But it was that one interaction, last quarter at Caltech, senior year, that this guy's going to tell me that he thinks I'm a poor physicist. That's what pushed me over the edge. That's what made me decide, "I'm not going to do physics." And now that I think about it, after that semester ended, I don't think I've really set foot in the physics building since then. Once or twice to see Steve Frautschi, but yeah, not really since.
ZIERLER: This is a few years before the dot-com boom really gets started. But was there a startup culture among undergraduates at Caltech? Specifically, the mathematics and physics majors, were they going to Silicon Valley? Were they talking about being quants on Wall Street? Did you think about not going that route of graduate school and pursuing something in technology or finance?
GOINS: This is way, way before the dot-com days. This was, let's say, '93 because I graduated in '94. I went to grad school in the Bay Area, and that's when the dot-com started, so I saw Apple blowing up. I remember the day that Red Hat Linux went public. I remember all of it happening quite vividly when I lived in Palo Alto. But in '93, '94, all of that was too far off in the future. I remember, in particular, one guy who was one of the two Black students majoring in physics. Stanley Grant. He decided when he graduated, he was not going to go to grad school. Remember, at Caltech, everybody decided they were going to go to grad school. The people who decided not to go to grad school because they want were going to work full-time were looked down on. We thought, "What's the point? You're at this big research institution. The point is to go off, do research, become a great scientist, win a Nobel Prize, and so on."
This guy said he wasn't going to grad school, he'd kind of had enough. He was going to go work full-time. So we asked him where he was going to work. He said, "This small company in Seattle called Microsoft." We thought, "OK, fine, if you want to work at this place to work on some word-processing software, knock yourself out." We kind of felt sorry for him because we thought he was going to be a loser and do all of this. As the story goes, when he got there, they convinced him, "Take so much a percentage of your salary and put it in stocks. Don't just take the money upfront." He did this when he graduated in '94. I believe they said that he was a millionaire first time over maybe five years after that. But I just remember around the year 2000 or so, asking people how Stanley was doing, and they all said that he had this big, beautiful house in Seattle, he was doing incredibly well.
But I just remember it shocked a lot of us because we thought he was going to work for this company that wasn't going to be much. But we had no idea the dot-coms were going to blow up like that just a few years after graduation. But yeah, nobody did that. Nobody went off to Silicon Valley because it really didn't exist. No one went off to hedge funds because again, that was looked down upon. What everybody aspired to do was go off, get a PhD, and worry about winning the Nobel Prize. I don't remember anyone that I talked to who even wanted to go work for, say, Boeing, Lockheed. No one wanted to do that. It was all about going off to grad school and getting your PhD. Of course, it's different now. It's a very different world nowadays. But in '93, that was not the case. Absolutely no one talked about that.
A Breakthrough at Stanford
ZIERLER: Besides Steve Frautschi's formative advice, what other programs did you consider?
GOINS: Well, my story about grad school is this. Senior year, I knew I wanted to either go to grad school in math or physics. I was leaning a lot more towards math, but very specifically, I wanted to work in number theory. I had gotten really obsessed with this idea of group theory and the other ideas in number theory. I went online to try to see who some of the more interesting number theorists in the country were. I don't really know why, but I got obsessed with this guy Richard Taylor. I can't even say that I met him. I have no idea how I learned about him. But I may have just gone online, saw his name at Harvard University, got really interested in some of the stuff that was done on his website. I had a plan that went as follows. My number-one choice of grad school was to go to Harvard so that I could do a mathematics PhD with Richard Taylor.
If that didn't work, my number-two plan would be to go to MIT because it was right down the street from Harvard, where I could still work with Richard Taylor to get my PhD. If that didn't work, I could stay in California, go to Stanford, possibly transfer to Berkeley if I needed to. But Steve said he really liked Stanford, so Stanford was going to be my number-three. Because those were the three top schools in the country in math, maybe that was a little bit arrogant for me to apply to. So I was going to apply to UC Santa Cruz as my backup. If things didn't work at Santa Cruz, at least I would be at California, and I could just decide to apply to grad school all over again next year. I had seen Allen Knutson do something similar to this the year before. He had just graduated as a senior in math in '93.
He's someone who would come to my dorm room once a week to check up on me and encourage me to go on to math. But the rumor was he had applied to grad school, asked for a letter of recommendation from some of the faculty, they didn't write him a good letter, and he didn't get in anywhere for grad school. So he went to UC Santa Cruz for a year, found a new set of letter-writers, eventually got into MIT for grad school, which is where he went, and now he's had a stellar career. He's a professor at Cornell University these days. I thought kind of the same thing. If everything went to hell and didn't work, at least I could go to Santa Cruz for a year, I could reapply, and then I'd be just fine. For grad school, I only applied to four places: Harvard, MIT, Stanford, and Santa Cruz.
And I know that's completely insane, but I was pretty cocky as an undergrad. I was convinced I was going to get into at least one of those, so I wasn't worried at all. When I applied, somewhere halfway through the application season, it just turned out that there was a math professor from Santa Cruz who was maybe giving a talk in the Math Department. He reached out to me and said that he was going to be kind of recruiting students on campus, and he wanted to sit down and meet with me. I met with him, and came in the room, and I was a little bit surprised because I didn't realize that he had read my application and knew it well. He said right away, "You are a really good student. We know that you've applied to Santa Cruz. You're probably going to get in, but we also know that you're going to go to other places, so good luck to you in your career because we know that you're not going to go to Santa Cruz."
It was kind of his funny way of saying, "You're really good. You're too good to come to Santa Cruz, so see you later." That was somewhat of a validating conversation. Remember, I didn't really get a lot of support–I really got no support from the math department. Seeing this professor from this totally different campus who just read my application and thought I was good really did mean a lot. But the three schools I really wanted to go to, Harvard, MIT, and Stanford–I had gotten into Stanford, and I felt somewhat bad that it was my third choice of all these places. Again, I was kind of a cocky undergrad. I remember going to this admissions weekend, where they really had invited all of the minority students from all of the departments at Stanford to come at once.
This is kind of the way Stanford did things back in the day. They coordinated over all the different departments that all the minority students would come in and all get to know each other. So yes, I got to interact with some of the newly admitted students in the Math Department, but I also met minority students in engineering, humanities, and all these other areas. When I was there at Stanford, I ran into this guy who was in his first year, but he was a Caltech alum. He had just graduated maybe the year before. I didn't remember him. But he said he remembered me. I met with him, and he tells me he's leaving Stanford because he's going to transfer to some other school. I ask him why, and he says, "Coming from Caltech, Stanford is too easy." Here I am at this visitation weekend, already a little bit depressed that Stanford is my third choice, seeing this guy leaving Stanford after his first year, telling me Stanford's kind of a joke.
And I'm kind of wondering now, "Am I going to be OK for grad school?" That was kind of where things left off at the end of my senior year. I will say, though, it all has a happy ending. Stanford, for me, was the best decision I could've ever made. I was certainly happier there five years at Stanford than I ever was at Caltech. But certainly, I did have these weird interactions when it came to applying to grad schools.
ZIERLER: Obviously, as a graduate student, you can claim the kind of naïveté you had as a high school senior thinking about Caltech's diversity or lack thereof. How much homework did you do in thinking about graduate programs where you might've said to yourself, "I want an easier experience on that level for graduate school than I had at Caltech"?
GOINS: I probably thought more about what I wanted my graduate experience to be than I think any grad student I've met to this day. One of the nice things about Caltech is, you are taking classes with other grad students as early as your sophomore year. Being a part of NSBE meant that literally half the people I knew were grad students. Starting sophomore year, I understood what it meant to take qualifying exams, worry about language exams, and this whole thing of [planning for the] dissertation and finding an advisor. I had heard about this for three solid years before I went to grad school. I had seen some students come in and struggle with things like trying to get TA-ships and apply for these outside fellowships.
I knew about the NSF fellowships that were out there. I also saw some people getting kicked out of grad school because they did not do well on their exams. I saw some people have really good relationships with their PhD advisors and others have really bad relationships with their PhD advisors. I saw all of this firsthand. Some of these were friends I had because I was taking classes with them. Others were students I could see through the NSBE chapter, us having conversations, saying, "So-And-So just failed on their qualifying exam. They're probably going to get kicked out of school, and we need to figure out what to do." I saw all of this, sophomore, junior, senior years, which meant I thought really hard about the kind of graduate experience I wanted to construct. But I do use that word very precisely.
I wanted to construct the experience. I thought about going to a department that wasn't too large. If you take a look at Stanford and Harvard, they're about similar-sized departments, roughly 20 or so faculty, another 100 or so graduate students. I wanted a department that was only going to bring in about 15 grad students a year because I wanted a department small enough where I would really not feel like I'm just part of this machine. That was the reason why I did not apply to Berkeley. I did not want to go to a larger department. I also was very sure in the area that I wanted to work in so much as the advisor I wanted to work with. I knew the number theory faculty at Harvard. I knew the number theory faculty at MIT. I also knew the number theory faculty at Stanford. Which meant, when I got to Stanford, day one, I was going to work with one of two people. I knew that right away.
I met one of the two people I was going to work with, realized pretty quickly we were not going to get along, so then I went to the second person. Now, the second person, I probably scared him a little bit because I told him the very first day that I met him I wanted him to be my advisor, and I specifically wanted to work on how elliptic curves form ternary group algebras. You typically don't do that. When you find a new advisor, you kind of come in and say, "I'm interested in working with you. Let's maybe chat a little bit, do a reading course, work on things." I told this guy right away first day, "Here's what I'm going to do for my dissertation."
Because again, I had really thought about this very carefully. I also knew I did not want to have a social life in the Math Department. I did not like the social atmosphere at Caltech, and I did not want the same for grad school. within the first month or so when I got to Stanford, I asked the question to as many people as I could, "Who are the movers and shakers in the Black community?" And within a month, I found out who they were.
ZIERLER: And by Black community, do you mean campus or Palo Alto more generally?
GOINS: In the Black community on campus. I learned about this thing called the Black Graduate Students Association, I learned who the officers were, I learned about the activities they had, and I latched onto that organization right away. I pretty much became an officer by my second year at Stanford. Like all of these things, I knew exactly the kind of experience that I wanted to have. I knew the kind of advisor I wanted, I knew that I wanted to have an advisor that was more hands-off, that I wanted to work at my own pace, and I would come in once a week and tell him what I was working on. I knew I wanted to be a place where there already was a strong, vibrant Black community, where I could come in and just kind of be a part of it and not have to worry so much about building it myself from scratch.
I wanted to be in a dorm that was going to focus on multiculturalism. I was very careful to look online to see which schools had these things. When I came to Stanford, day one, I knew exactly what I wanted my life to be. Which is why it's ironic because you might think that the Math Department at Stanford was a hostile place. In some ways, it was. When I got there, there had only been two Black students before me who had successfully graduated with their PhD in the whole history of Stanford. I was going to be number three. There were no other Black students in the department, no other Black faculty. In fact, in all of STEM, I believe there were only two Black faculty. One guy in physics, and one guy in geosciences.
No Black faculty even in biology or chemistry. It wasn't, I'll say, a more diverse place than Caltech. It was probably about the same. But I wanted to leave all of that that I saw at Caltech behind me. I really embedded myself in the Black community at Stanford. But that's because that was part of my conscious decision of what my grad school would be like.
ZIERLER: And it was more organized. There was something for you to join rather than something that you needed to create.
GOINS: That is correct. That is definitely right.
ZIERLER: Did you ever look into the origins or history of that community, how it got started, how far back it went at Stanford?
GOINS: I never did, but I know that it had a very long history. It must've started back in the 1940s, 1950s or so. I think the thing is, Stanford really has had such a great long history that I never worried about it much in the same way that I did at Caltech. It was more that you could really just focus on being a Black student at Stanford and not worry about anything else, and you had such a history, a community, a culture there that it didn't really matter. I was in the graduate residences, where I was an RA for the multiculturally themed house. This is one of the houses that apparently was started by some of the Black graduate students maybe ten years before I got there. There were various demands that they had on campus about just having a place for the Black students to live and celebrate their own cultures.
I had tried to do the same thing at Caltech some years before, and the whole thing failed spectacularly. But Stanford had this, and it had existed, and it had a budget, and it had complete buy-in from the campus. I was amazed that I could come in, and now I was the RA for this thing. I had my own staff, my own budget, and there were activities we could put on. One of the people who worked in the housing office was a Black alum, this guy who had graduated back in the 1970s or so. The fact that he was there as part of my housing staff, I could constantly go to him and ask about the way things were 20, 30 years before. He could definitely tell us stories about when he was an undergraduate. What's actually even crazier is, his son was an undergraduate there at Stanford at the time, and his son actually was a pretty well-known rapper with this group that was my favorite group at the time.
I had no idea that his son was a student there. I had no idea that his son was actually the lead rapper as part of this group. It was almost the opposite of Caltech, me wanting to play my rap music, and nobody wanted to listen to it. Now, here at Stanford, the guy who's the lead of this group is a student there at the school. It was like heaven for me. But again, there was this whole Black excellence culture that was there that had been there for decades. It was just a very, very different place.
ZIERLER: To go back to the specificity on day one with your research agenda, to what extent was that about the fact that you had taken courses at the graduate level at Caltech, and you had excelled in those courses?
GOINS: It was very much about that. It wasn't just the courses that I was taking. I just read a lot of books on my own. I was constantly at the library, I was constantly reading more and more. I had a pretty good idea of what I was interested in. I did want to go to grad school because I wanted to prove some big, big theorem. I wasn't there just to say, "I just want to get another degree so I can keep moving." But I saw it as one step towards a larger plan that I had in mind. This project that I worked on, pretty much, I started working on my sophomore year at Caltech. Yes, I learned some of these concepts in grad-level courses, but as I started to read more and more on my own, I wanted to really turn this into a full-fledged project, and eventually, a full-fledged career. This is why I completely knew the scope of the project and what I wanted to do. That's why I could walk in to Dan Bump's office day one saying, "I want to combine all of these together," because I wanted to continue doing what I had been doing for the last three years or so. I just didn't quite realize that you don't really do that. But that was still what happened.
ZIERLER: I wonder, again, for our non-mathematician audience, if you could translate that initial interest and then explain why it was this topic that you wanted to pursue in graduate school.
GOINS: As an undergraduate, at first, I was exposed to the concept of calculus. Of course, I saw calculus in high school, but you see it in a very different way when you're at Caltech. You see calculus in the sense of differential equations, how things come about in physics, and chemistry, and all these other areas. Everything all kind of blends in together. You see calculus in trying to explain how the world works around you, how things move. You also use calculus when it comes to things like quantum mechanics, the Schrödinger equation, and even the periodic table. But that's stuff I saw my freshman year. I could completely understand calculus, differential equations, it was all very powerful in bringing all of these subjects together. What I didn't understand is where calculus had its play in mathematics. Math took a very different direction for me starting freshman year.
I saw this book in number theory, so I realized that there was something that wasn't calculus, but I didn't really know what it was. By sophomore year, I was taking a class in abstract algebra, which is almost like the way it sounds. You take algebra, but now you're kind of abstracting different concepts. I didn't realize that this was something you could do. I just thought if you were told, "Solve for X," you just do all this arithmetic, divide, multiply, what have you. I didn't understand that you could actually question the concept of addition, the concept of multiplication. What does it mean to solve for X if X isn't a number? What if X is a matrix or a function? These are things that just completely blew my mind and caused me to think about mathematics in a totally different way. As I took abstract algebra, I became obsessed. I took three, four different courses in this idea of group theory when I was there at Caltech. One of the things that happens in these classes is, you're taught to think in a very abstract way, but you're really taught to question a lot of the assumptions that you originally had.
Like, if you solve for X, asking the question, "Does X really need to be a number?" When you try to do things like multiply things together, asking the question, "What's multiplication exactly?" That's where I became really obsessed, even questioning what abstract algebra was showing me. Wanting to abstract what I was learning in abstract algebra. That was the whole idea for grad school, taking a lot of those questions I had and going one step further. It really became an obsession because I had never thought about this before. I never thought in high school that you could question these concepts of what it means to solve for X.
I just got used to almost the cookbook approach from calculus of, "Here's a problem in physics or chemistry you want to solve. All you have to do is write it as a calculus problem, you run through the recipes, solve the calculus problem, then that gives you back an explanation of what you see in physics or chemistry." I just thought that was the way the world worked. I did not know that you could abstract all of these concepts. That became my graduate school experience, abstracting all of algebra.
ZIERLER: If you can explain the coursework component to graduate school, the individual study in graduate school, and the one-on-one time with your graduate advisor in mathematics.
GOINS: I was in grad school for five years. The very first year, you take general classes with most of your first-year classmates. There were around 15 of us, I believe, that came in my first year. This is in 1994. We all took, I would say, three classes together. Real Analysis, Complex Analysis, and Algebra. I was considered to become the resident algebraist because I just knew algebra so well coming from Caltech. I also knew complex analysis really well because of AMA 95. I can't say that I knew real analysis really well. But we all took these classes together, going to the same lecture together, working on the same homework assignments together. But that was the very first year. You're all taking the same three classes or so for the first year.
The summer between the first and second year, you take a series of qualifying exams. For us at the time, these were written exams. Each one was, I believe, maybe three hours or so, and you have to take them. At Stanford, they were actually very harsh. You have only two tries at the exam, but you must pass all three before you start your second year. Most of us passed all three of them. The ones who don't are allowed to stay for one more semester, at the time, one more quarter, and then you have to go elsewhere. I want to say of the 15 of us, all but maybe four of us made it through to the second year. The second year is very different. Because you aren't really taking classes together. The idea of the first year is, you're all in a class together, so you can all take exams in these three areas, real analysis, complex analysis, and algebra, but then at the end of that summer, you're kind of own your own to do whatever you want.
I tried to take a couple of classes with some of my other friends, but of course, they're starting to move in different directions research-wise. I remember taking this one class in an area called algebraic topology, realizing that when we got our very first homework assignment, I didn't want to do homework anymore. I dropped the class. That's the last homework assignment I've ever been assigned. I just decided I did not want to do any more homework at all. I had friends who were taking this class, but I wasn't taking any classes with them. Instead, I decided to work with this guy in a one-on-one reading course just so that I could get to know him a little bit better. This is when, start of my second year, I introduced myself to Dan Bump, who would eventually be my advisor.
This is where I walked in pretty much the first day of the quarter saying, "I want to work with you eventually. I'm thinking about doing this as my dissertation." But he said, "Well, why don't we think about doing a reading course first to get to know each other?" What that meant for him was, there was a book he wanted me to read, and then he would just say, "Just read a chapter or so, and then come back once a week. We'll sit here at the chalkboard, and we'll talk about it." What I didn't know at the time was, he had done this with all of his students. He would give this book, which is notoriously a very difficult-to-read book. I didn't know this because his other students were pretty far advanced. They were already in their fourth and fifth years. I was only in my second year. In a sense, I was kind of working by myself.
After about maybe two months of me kind of reading through this, I just had to be honest with him and say I didn't really like the book, I was kind of struggling to understand it, but I wanted to work with another book. What I learned is, all of his other students balked within the first week, told him that they hated the book, they didn't want to read it anymore, and he assigned them a different book. I was the only one that actually stuck with it for almost two months. I think that meant something to him, that he did give me this test, and I somewhat passed it. He then gave me a second book to read through, which he saw as kind of an introduction to what he wanted to do for my thesis. It was more like an algorithms book. It had a list of these different commands you could write in for a computer that would explain how to compute certain things with elliptic curves, modular forms, some of these other funny things.
I really liked this book because I was really good at using Mathematica, something I'd learned at Caltech, and I just figured everybody knew Mathematica. I didn't know that, but I just was really good at it. He just said, "Here, read this book." I would go back home, I would code up various parts of this book just for the fun of it. Eventually, he made it clear he wanted me to really write a serious series of computer programs that implemented what was in the book. I worked on that for maybe another three months, and I told him–at this point, we had worked together for almost half a year–I wasn't interested. I didn't really want to do it. That turned out to be fortuitous because about three months after that conversation, Dan happened to be invited to go to Berkeley to give a talk, and I met this guy who was a grad student who said he had been working on implementing that same book for the last two years, and he was nearly done with all of the implementation.
If I had started working on this book the way Dan had wanted, it would've been a complete waste because this other guy had been working on it much longer and had gotten a lot farther. Actually, this guy and I became fast friends because I completely understood what he was trying to implement because I had tried to do the same thing. This meant that Dan had to find a second project to work on. Now, we're still kind of meeting once a week, just chatting about things here and there. He's still saying, "Read this book, learn this concept." I'm still learning from him. It's not a formal class, but we are sitting in there one-on-one in our chairs, chatting about what's in these books.
Somewhere at the start of my third year, Dan says, "I have this one student who's now finishing. She did the following in her thesis, but she didn't really finish it. I would love for you to finish this and make it much stronger." I read her thesis, didn't really understand what he wanted me to do, and we spent probably the next three months with me constantly asking him the question, "What do you want me to do? Why do you think this is possible?" What inspired me was when he finally said, "I have no idea if this is possible, but I want you to try it anyway." When he said he didn't know, that lit a green light. I was completely inspired to keep working. My third year, I decided to go off on my own.
I kind of told Dan what I wanted out of our relationship was for me to come in once a week, and I would just give him a report. I would go to the chalkboard explaining what I was working on, but I wanted to spend the rest of the time on my own working on things. Dan said, "In return, what I want to do is spend time at the chalkboard giving you mini lectures on these other areas that may you should know." Dan was trained in representation theory. I wanted to work on elliptic curves. Our compromise was, this was what we were going to do every week. For about two years, this was what we did. We would come in Wednesday afternoons. I would go to the chalkboard for half an hour, say, "Here's what I learned from reading this thesis. Here are some papers I read on the field. Here's how I think I can generalize this. Here's the direction I'm going to go in. Here's my outline."
Then, for the next hour, hour and a half, Dan would pull out his yellow notepad with his black felt pen, and he would say, "Here are things you should know about representation theory." And we had this one-on-one back-and-forth for two years, and it worked beautifully. Whenever I could explain things to him, he could explain things to me. Where everything culminated was, in the start of my fourth year, when I walked into Dan's office–remember, after being at Caltech, I knew I wanted to finish in four years. That was the plan. Not five years. Finish in four years. I kept telling Dan, "I want to finish in four years." I don't think Dan believed me when I told him this, but I kept telling him this. Starting my fourth year, I walk in, and I tell Dan, "I've solved the dissertation problem." Dan's like, "I don't believe you." Because at that point, I just kind of told him, "Here are all the outlines." I said, "OK."
Came in the next week, plopped onto his desk an 80-page dissertation. Remember, with my days as an undergraduate, I saw grad students struggling to try to solve the dissertation, struggling to write the dissertation. They would spend the last two months trying to write all of this. I told myself, "No, I'm going to write it every week over the four years. I am not going to write it at the very end." I saw too many people stress out. I spent about two and a half years writing the thesis. I did not wait until the end. But I didn't tell Dan I was spending two and a half years. So he questioned whether I was done. I plopped this 80-page thesis on his desk. His eyes went wide. He's like, "I didn't even know that you were working on this."
ZIERLER: Why did you keep that from him?
GOINS: I didn't really see any reason to tell him. I just assumed if I'm working on the thesis, I'm working on the thesis. I didn't know until I talked to other students in the department that that wasn't the way they did it. They all waited until the last minute. But I worked on it each and every week. So all the conversations he and I had been having this whole time, I was writing up each and every one of those. I had this beautiful manuscript that had everything written up in detail. This other thesis that he had me reading through, I reworked all the formulas. I understood every last detail of what she did. That was a chapter in the thesis, [in] rewriting the thesis. I had worked out all of this stuff, but I never bothered to tell Dan, probably because I was too focused on saying, "This is what I want to do. This is how I want to finish things."
When Dan saw the thesis, that's when he realized that I really had solved the problem he'd given me. I didn't really put everything in one place, but when he saw it all there, he realized that, yeah, it was done. It was completely solved. This is when Dan kind of turned a little bit and said, "This is great. I'm kind of in shock that the thesis is written and everything is done. However, what if you can prove this slightly stronger result?" Just like the two years before, I asked him, "Why do you think this is true?" He said, "I have no idea if this is true, but it'd be really great if you could prove this." I was inspired, and I went back and worked for the next year and a half on trying to prove this larger result.
ZIERLER: Obviously, you felt it was in your interest to spend this extra time.
GOINS: It was. I wasn't happy with the idea of spending a fifth year, but I spent all of that fourth year working on the new result, and then at the start of the fifth year, I got it.
ZIERLER: What do you think Dan's motivation was? Did he see that you could achieve something that wasn't just good and early, but great?
GOINS: I think so. I do think so. The other students that he had up to that point were good students, but it was definitely clear that they were only going to go so far. They had figured out their thesis, and they were ready to move on, have a full-time job, this kind of thing. I think with Dan, he could really see this hunger. He had given me this problem, the very first one, the easy one, and I solved it. Then, he said, "I'm going to go for broke. Let me give him this big, big one." When he told me the big problem, the one he really wanted to do, I could actually see that was a significant problem. But I could also see how to solve it.
ZIERLER: Can you explain this significant problem?
GOINS: I can. When Dan himself was in grad school, he had this really good friend who was a grad student at Harvard. He knew about this guy's thesis from Harvard for years and years. What the guy at Harvard had done, there was an outstanding conjecture in the field that's known as Artin's conjecture of icosahedral Galois representations. No one knew if that conjecture was true back in the 70s. But this guy wrote a computer program in the 1970s that figured out how to come up with one example to show that the conjecture was true in this one specific case. In the decade or so after that, other people figured out how to make the computers run a little bit faster so that instead of having the one example that Joe Buhler had, they had maybe another eight examples.
But this was going from maybe 1975 through about 1995, there were max ten examples in the literature of this conjecture. Dan had this idea that instead of going through this computer program, writing this nasty algorithm that Joe Buhler and others had done, can you explain his example using a completely different method? Because the idea is that if you can write a completely different method, you could potentially come up with infinitely many examples to show that the conjecture was true. What Dan didn't tell me was he first needed to know from Anette Klute's thesis how to even generate one example using this weird stuff that this German mathematician wrote back in the 1880s or so.
Once I figured out the German from the 1880s, what Anette had done, and how to come up with the one example, that was what I had showed Dan at the start of my fourth year. I could explain this one example, and the formulas were beautiful enough that I could wrote down as many examples as I wanted to, and I could do it very easily. This is when Dan said, "If you can do it with this one example, can you actually go one step further and figure out how to redo Joe Buhler's thesis?" Starting my fourth year is when I even heard any of this. I had no idea that this was the plan all along. Simply put, in my fourth year, I figured out how to come up with an elliptic curve that should be associated with Joe's thesis. What I had to do was prove that this elliptic curve was modular. That's the parlance.
That's what Dan did not know how to do. I had to rack my brain for a year to learn a completely different field, totally different direction to figure out how to do this. It turned out, it was actually a good thing because right about that time, if you remember back, the guy I wanted to work with originally for my thesis, Richard Taylor, actually was working on exactly the same problem. It was kind of this weird twist of fate that in my last year, I started to look through the literature to see some ways to do this, and Richard Taylor's name came up. I realized he was working on exactly the same problem. Given the elliptic curve, how do you prove the dissociative one modular form? And an even more bizarre twist of fate, in my last year, Richard actually comes to Stanford so that he can give a talk on the research that he's been doing. Because he's kind of blown up the math world at this point by proving some really great results, coming up with some really clever ideas.
I'm basically in the library every week, reading the papers of what he's doing and all the rest of this. It goes back to my undergraduate days. I'm always at the library, reading things. Richard Taylor comes to Stanford, and remember, there's only one number theorist at Stanford, namely, Dan Bump. The three of us are now in his office, myself, Richard Taylor, and Dan—Dan because I'm his grad student. I'm really the only one at the time. The other ones had graduated. He introduces me to Richard, and I turn to Richard and say, "I've been reading this paper of yours that just came out, how to prove modularity of these elliptic curves to weight one modular forms." Dan is completely shocked because he doesn't know about this paper. He's trying to figure out how I know about this paper. I know the paper well enough that Richard and I can go to the chalkboard and actually talk about the details of what's happening here. I'm telling Richard about what I've been trying to do for my thesis and how I'm very interested in what he's been trying to do the last couple of years.
Richard and I totally hit it off. Richard invites me to basically visit and come work with him at Harvard for the next year. It just completely worked out in this incredibly fortuitous way. I think Dan was completely shocked that I had really taken the initiative with all of this. Again, he didn't work in this area, he had no intuition on how to solve this problem. I had done all the work on my own to go to the library, look up all these papers, read up all these things, learn everything on my own. It was a good time. It was kind of a strange time that this all worked out the way that it did. But Dan and I had some really, really good, fun conversations like that. I definitely shocked him more than once. He definitely told me that I was the most enterprising grad student that he ever had. But it was a fun time back then.
ZIERLER: Of course, being at Stanford with the tech boom in full swing, did you ever think about jumping in, not continuing on the academic route?
GOINS: No, never did. I had a lot of friends who did. A lot of friends in other departments. They were really wondering why they were struggling as a grad student, making no money, when quite literally ten minutes down the street, you had undergrads finishing from Stanford who had their own startups, who were making millions and millions of dollars. There were a lot of grad students I had as friends who seriously thought about dropping out of grad school so they could go work for one of these startups. It was a really bizarre set of days my last few years at Stanford.
I can't even explain what it's like to live in the middle of something where the undergrads you were TA-ing for are graduating, working for a startup, and you know for a fact that they made their first million within six months of graduation. This was happening all the time, right and left. It was just a very, very strange set of days there at Stanford. I always wanted to be a college professor. Very specifically, I wanted to be a professor that was going to make my mark on the field of research. I just never felt making money like that, working for a tech firm was something that was going to make me happy.
ZIERLER: The timing after you defended, was the first stop Harvard? Where is the Institute for Advanced Study in this?
GOINS: This is where it's a little bit complicated, so I'll try to simplify things. My last year was kind of a crazy year. What I did for my thesis caused a lot of excitement. Joe Buhler, the same guy whose dissertation I was working on, actually came to visit Stanford. We talked quite a bit about what I did in my thesis and what he did in his thesis. He actually was the deputy director for a math research institute over at Berkeley. He offered for me to come to Berkeley for the whole year. However, Dan, because I was his last grad student for a while, was going to go on sabbatical at the Institute for Advanced Study. It's right there at Princeton, it's basically administered by Princeton University. He was going to go there for the fall semester. He recommended that I come with him because it was a special sabbatical year for all of the famous people who were working in number theory.
Everyone I had possibly even thought about, every name I had heard for the last five years was going to be there at Princeton that year. Dan told me, "Just go ahead and come to Princeton." But remember, Joe Buhler also wanted me to stay at Berkeley. I decided to apply to both. I got a position at Berkeley, at MSRI, that I stayed at for maybe a month. I don't remember exactly. But then, I went to Princeton for the whole year. While I was at Princeton, Richard Taylor and I chatted a bit more, and he wanted me to come visit him at Harvard. I went to Harvard for a few weeks, but someone else convinced me to go to Germany for six months. The plan was kind of threefold. Joe Buhler really wanted me to come back to Berkeley for six months, so I agreed to that.
Someone else I'd met, Don Zagier, wanted me to go to Germany for six months, so after Berkeley, I went to Germany for six months. Richard wanted me to come visit him at Harvard for six months. After Germany, I came back to California, but I decided, "Let me try to get things to work out at Caltech." At this point, it's 2001. I worked out a three-year position at Caltech even though Richard wanted me to come visit him at Harvard for six months. So I kind of had a dual position at Caltech and Harvard. It got awkward because Barry Simon kind of pulled the plug on a lot of things and told me I wasn't allowed to be at both. I kind of ignored him anyway and ended up being at Harvard for about two months. The five years between when I graduated in '99 and when I got my first tenure-track position in 2004 are kind of confusing.
I was at MSRI for about a month in California, went to Princeton at the Institute for Advanced Study for almost a year. I, then, came back to Berkeley for MSRI for another six months, then went to Germany, where I was at Max Planck Institute for Math in Bonne for another six months, went to Caltech for three years, but I actually had an apartment in Cambridge and was at Harvard for two months. It was very, very confusing. But I was having the time of my life going back and forth to all these different places.
A Grand Tour of Mathematical Institutions
ZIERLER: It's a flurry. I'm curious in what ways being at all of these top-flight programs was great for the research, interacting with all of these people, and in what ways it was difficult because you weren't just staying put in one place for too long.
GOINS: It was great to see the world, it was great to interact with a lot of different people. I liked how many contacts I made with people. I think even now, for my career, it's worked out really well. There are a lot of friends I have who are famous, well-known professors at different places, and a lot of these folks are people that I met when I was a post-doc, traveling to these different places. Even the position I got at Purdue University, I got it because I was a post-doc at the Institute for Advanced Study. Remember, all the famous people were there. Two of the people who were faculty at Purdue were there also visiting. They were on sabbatical that year. I got to know them for a whole year, in '99 to 2000, even though I wouldn't even work at Purdue until 2004.
There were just a lot of great contacts I made during that time. The downside was, I'd gotten my first real taste of racism in mathematics. I think being in grad school, I did spend a lot of time talking with the other Black graduate students. I didn't spend a lot of time in the Math Department. There were still incidents that happened with the faculty in the Math Department, don't get me wrong. But I ignored a lot of it because I spent so much time with the other Black grad students at Stanford. When I left Stanford, though, I didn't really interact with many other Black mathematicians. I'm off doing number theory, traveling around to all these different places. I could see people being a lot more condescending, people questioning more whether I knew what I was talking about, and it just becoming more and more difficult finding people to talk to and to interact with.
I can't tell you how many times I was in a room with individuals, other post-docs, where people would just naturally go around the room to say, "Where did you get your PhD?" And the conversation would always go, "I got mine from Berkeley," "Mine from Yale," "Mine from Princeton." And when it came to me, I would say, "From Stanford," and the conversation would just die. People just wouldn't want to talk anymore. Other conferences where people would talk about the projects they were working on, I would say I was working on something similar and ask if they'd want to collaborate, and the conversation would turn to, "Not really, I'm kind of busy doing other stuff." These awkward things, but it was consistent. It got more and more consistent as the years went on.
Even when I came back to Caltech as a post-doc from 2001 to 2004, it was bad and blatant. Some of the same faculty that I had known not even a decade before, taken these same grad-level courses, been the top person in the class, the same faculty were being condescending, saying, "I don't really know if you're going to get a job somewhere." I'm not going to name this person, but I will say that when I was an undergraduate, I took his group theory class, did really well in his class, was one of the top students. I even did research with him while I was an undergraduate, working in group theory. Came back as a post-doc, and I remember in my last year as a post-doc, feeling really bad because here it was, February, getting kind of close to the end of the job market season, and I didn't have any job offers yet. This same professor, who I had known for almost a decade, just kind of joking, said, "Well, I guess you don't have a job. Too bad for you." I thought, "That's kind of a messed up statement, and it would be nice if you were a little bit more encouraging."
But he just kind of laughed it off as, "Maybe you won't get a job. Oh, well." I won't even talk about a lot of the other really negative things that happened in my last year there at Caltech. But it just amazed me how everything turned in those three years that I was at Caltech. People being very supportive when I was a grad student, being maybe a little bit awkward in the first couple of years that I was a post-doc, but by the time I got to Caltech, everything had totally changed. People were being very condescending, very nasty, not being supportive at all. Actually, kind of the opposite. People telling me to my face, "You're not going to make it. You're not going to amount to anything." Just story after story. I just got very shocked that all of this was as blatant as it was.
ZIERLER: If you can explain the obvious disjoint in the narrative here is that obviously, there are gatekeepers who are welcoming you into these very elite places, Harvard, Princeton, Berkeley. Yet, you're telling me the things that you're telling me among the people you're interacting with on a daily basis. How do those things work together?
GOINS: All I can guess, and this is a guess because I don't know this for sure, is, I didn't fit the mold of what they were expecting one of their peers to look like. I do have friends that we were undergrads together at Caltech. We all graduated with math degrees at the same time. A couple of them are now professors at Caltech. I could see how they fit more the mold of what a typical Caltech professor is, whereas I do not. You can define the mold however you want. I like to think it's not so much the pedigree because some of these folks graduated from MIT, Harvard. I graduated from Stanford. I think it's more kind of the culture, how you interact with people. I don't interact with other Caltech professors the way that Caltech professors do.
When I made it very, very clear early on, "I am a post-doc at Caltech because it is my ultimate goal to be a professor at Caltech," I told this to everyone who was willing to listen, more and more people told me, "Oh, I had no idea you had an interest in being a professor at Caltech." I must've heard that 20 or 30 times while I was a post-doc. I couldn't really figure out why they kept saying this. Because to me, if you take a look at my résumé, undergrad at Caltech, grad at Stanford, post-docs at Berkeley, Princeton, Harvard, why would I not be on the track to be a professor at Caltech? Even me being a post-doc at Caltech, people would say, "I didn't know you had an interest in being a professor at Caltech," which always surprised me. But again, I can only chalk that up to maybe I just didn't fit the mold.
I can only guess that as the years went on, more and more people just didn't see me as part of that culture, being a Caltech professor. So they were more ready to be dismissive of this concept of me being a Caltech professor. Again, I've never really understood why things happened the way that they did in those three years. But the two years I was a post-doc before I got to Caltech, things were reasonable. But in the three years being at Caltech, I just felt that people, especially Caltech professors, were being quite unreasonable.
ZIERLER: Coming back, obviously, you're at a different station in life. What had changed and what had not culturally at Caltech?
GOINS: Not much. I really have to say, it was pretty much the same place. I graduated in '94 with my undergraduate degree, and I came back in 2001 as a post-doc. This meant that almost all of the same faculty I had as an undergraduate were still there when I came back as a post-doc. I think Tom Apostol had retired, Wilhelm Luxemburg had retired. They maybe brought on one or two more new faculty members in the department. But all the same people were there. Dinakar Ramakrishnan, Gary Lorden, David Wales, Alex Kechris, Michael Aschbacher, all of the same faculty were there.
Barry Simon was department chair when I came back as a post-doc. He was also department chair when I was there as an undergraduate for some time. It was the same. I can say the faculty never saw me as a post-doc, they only saw me as this former undergraduate that came back. They certainly continued to treat me as a former undergraduate. One quick story, there was one student I had in one of my classes, she actually was a Caltech undergraduate. She wasn't doing well in my class. She basically had barely came to class. She came at the end of class one day at the end of the quarter to say she wasn't doing well, can she get some extra points back? And I basically told her no, because she wasn't ever coming to class, she wasn't turning in assignments.
She was just a poor student all around. I did have some sympathy for her because she was an undergraduate majoring in math, but still, she didn't ask for any help at all the whole semester, and I wasn't going to budge on this. So she went to one of the more senior faculty members in the department and gave him the same sob story, that there's this post-doc that isn't supportive of her, that she had a very difficult time in this class, and she's wondering if there's a way she can get an extension so that she could do better in the class. This professor came to me saying, "You are being unreasonable with this undergraduate, and you should change your policies, and you should make sure that she gets a better grade." Of course, I'm thinking, "Here's a senior faculty member telling me what to do," so I backed down a little bit and tried my best to help the student. I kind of regraded a couple of assignments to bump her grade from something like a C to a B.
Instead of this undergrad being grateful, she went back to this other professor to say, "This post-doc is still being unreasonable and not being kind to me in this class." The professor comes back to me a second time to harass me a little bit more and say, "Well, you should do more for the student." That's when I tell the student, "I am not bumping your grade from a B to an A. I don't care what you say, I don't care how many people you talk to." And I was very upset that she was willing to go to the senior professor, but I was even more upset that this professor had so little regard for me as a colleague that he would essentially tell me what to do in running this class. But that was just one story of many things that I experienced there in the department. I never was really seen as their peer. It was always this guy that had taken classes with them years before.
ZIERLER: Given that you were an undergraduate so recently, and it's always hard to shake people's association when they know you as an undergraduate. That, plus this line not being a tenure-track line, to what extent, in retrospect, were the odds just stacked against you?
GOINS: Here's the question that I always had coming back to the department. Several people in this department would tell me how much they cared about diversity issues. They knew that I was very critical in saying this department had never had a Black faculty member, they really had graduated no Black students out of their undergraduate program, and that they needed to do something different. They knew I was critical about this when I was an undergraduate. Now, the only question I had for the department was, if I wasn't good enough to be the first faculty member, then who would be? Now, you could make the argument that maybe I didn't have enough papers, hadn't done enough work. But the question I always had was, if Caltech, specifically the Math Department, is willing to say, "Here's a guy with a degree from Stanford, with positions at Berkeley, Princeton, and Harvard," if he's not good enough to be in this department, and he's someone we know because we've known him for years, then who will be good enough to be at Caltech?
I understand that sometimes you set the bar at some point, and then the bar's going to move. I get that, I understand it. It was more of a frustration of some of these individuals, who told me to my face, they care about diversity, they're fierce advocates, but they're the same ones that when I told them I had an interest in staying as a faculty member, I got zero support from. When I say zero support, I mean one person in particular, someone I had known from my undergraduate days who told me he cared about diversity was department chair and knew that I had an interest in staying. Specifically, the president's office, David Baltimore, was very clear that he wanted to diversify the faculty. I know that there was a representative from his office that talked to different people in the Math Department to say, "We want to work with you to make sure that Goins is going to be hired in a tenure-track position."
She warned me that this would happen. I went to go talk to this guy who was department chair to make sure that it was true. He said that they were not going to read my application for the tenure-track position, and that when I get to be a better mathematician, they will consider me in the future. The same individual who just told me years before he cared about diversity and so on. So yes, I do agree with you. I think that it was stacked against me. I just don't really know if anyone will be hired in the department if I feel that I did everything that I could, support from the president's office, doing post-docs at all these places, coming back as a post-doc for three years, trying to work in a department where people already know me. If that wasn't enough, I don't know if there's anything that will ever happen to change that Math Department.
ZIERLER: Last question for today. Perhaps we can end on a more positive note. If we can just strip away all of the problems in the social context and just focus on the math, it's such a unique opportunity to ask you, given that you had done this whirlwind tour at all of these really impressive institutes, what were some of the big ideas in math at the time, at the turn of the century? And just in terms of your research, in terms of being a mathematician, where did you connect your research to those bigger questions in math at the time?
GOINS: You may have heard of something called Fermat's Last Theorem. There's this cute theorem that had been around since about the 1670s or so. There was a French lawyer named Pierre de Fermat. I'm not going to worry about going into what the theorem was, but I'll just say that the rumor was he was this lawyer by day, mathematician by night. He kind of read this book to understand a little bit more about the things called Diophantine equations, and he came up with an idea of a result, but he didn't have enough room in the margin of his textbook to write down the proof of said result. People called it his last theorem, although people didn't have any proof of this theorem. Lots and lots of people had worked on this for about 250 years or so, and then finally, there was this professor at Princeton named Andrew Wiles who announced in 1993 that he had a proof of this result.
Turned out that there was a small flaw in the proof. He had to work with this other guy named Richard Taylor who helped him fixed the flaw in the proof by 1994 so that by the end of the century, early 2000s, number theory was a really exciting field. People had a proof for Fermat's Last Theorem, and it wasn't so much the proof of the theorem, it was the techniques that Wiles had introduced. People could see that those techniques could be used to prove a lot of things. That's where I come into the picture. When I saw that you could use these techniques even for this specific conjecture that I was working on, that's when I wanted to work with Richard Taylor. Then, lots of people wanted to work in this area to learn a lot more about what these techniques were. I'd say early 2000s for number theory was a really exciting time. There were these techniques that were just coming out, people just wanted to learn about them. Lots of these crazy conjectures in number theory were falling right and left.
You have the Taniyama-Shimura conjecture that was solved in the year 2001, you had the Sato-Tate conjecture that was solved in 2011. They were all coming from exactly the same techniques that Wiles had put out back in 1993. The number theory world was really exciting the first ten years of the 2000s. That's the one thing I'm going to remember the most, going to conferences and seeing people talk about these crazy new papers that were coming out, proofs that people were having of these conjectures. There must've been maybe five major conjectures that had been standing around for about 100 years that all fell between 1993 and 2010 all because of those techniques that Wiles had put out. It was a really fun time in math back then.
ZIERLER: Next time, we'll pick up on your decision to join the faculty at Purdue and hopefully where some of this excitement in number theory takes you in the next chapter.
[End of Recording]
ZIERLER: OK, this is David Zierler, Director of the Caltech Heritage Project. It's Thursday, December 2, 2021. Once again, I'm so happy to be back with Professor Edray Goins. Edray, as always, great to be with you.
GOINS: Great to be here.
ZIERLER: Today, we're going to pick up on the next stage in your career, when you joined the faculty at Purdue. Just to set the stage, we were talking last time about your interest in joining the faculty on a tenure-line position at Caltech. Were you broadly looking on the job market at that point? Or before Purdue, you were exclusively focused on a possible faculty position at Caltech?
GOINS: Yes, and yes. I'll say it was more the latter, but certainly the former. I was a post-doc at Caltech from 2001 to 2004, so that meant that about 2003, 2004, I had been out of grad school at that point for four years, coming up on five years, and just very naturally in the world of mathematics and academia, that's right about the time you should consider a tenure-track position. I had a couple of schools that had approached me about 2003 or so about applying to them. Purdue University was one of them, also the University of Iowa. But I really made it clear to a lot of people I wanted to stay at Caltech. Of course, there are a lot of reasons. One, my family was right there. Two, I had grown up in Los Angeles. Three, I really had a lot of respect for Caltech, and it was just a place that I felt would be a good fit research-wise, and also a good fit just in terms of the things I wanted to do in the world. But 2003 or so was definitely the time that I went onto the job market.
ZIERLER: Did you specifically think about HBCUs? Was that on your radar at all?
GOINS: It wasn't. What I'll say is, I really had only focused on a handful of places where I wanted to work. Mainly, I wanted to stay in California. Just for all the reasons I mentioned earlier. California was my main place. When I say a handful of schools, I had seriously thought about Caltech, number one, Stanford, number two, but outside of those two, really, I didn't want to move anywhere else. Purdue had really convinced me to consider going there for years. I believe I first visited the campus maybe 2001, 2002. They invited me to come out there for a week or so, just to kind of get a feeling of what Indiana was like. It was a place I was going to apply to. I also knew several people in the Math Department at the University of Iowa. I just really didn't have any interest to move to Iowa and be in Iowa City, but that was at least a place I also had considered. But I would really say outside of those four schools, I didn't really consider anything seriously. Also, I wasn't interested in going to anything that wasn't a so-called Research I university, so no liberal arts colleges, no historically black colleges, HBCUs. Really, just the R1s were the only places I seriously considered at the time.
ZIERLER: Intellectually, is that simply because that's the environment you wanted to be in, and those were the kinds of colleagues you wanted to have?
GOINS: That is right. I really saw myself as someone who was just going to do research full-time. Teaching perhaps was something I could do in my spare time. Mentoring students was something also that I could do in my spare time. But I really viewed myself as just a full-time researcher, spending, I'll say, ten hours a day kind of focusing on research, writing papers, writing grants, giving talks and presentations at conferences. But I really didn't view myself as someone who was going to spend a lot of time, say, writing up lecture notes, preparing for class, or really focusing on that larger educational component.
Galois representations at Purdue
ZIERLER: On the research side circa 2003, 2004, what were you working on?
GOINS: Really, three different projects I'll say that I was working on. Of course, I wanted to generalize some ideas I had from my doctoral thesis, and at the time, I was very close to proving this big conjecture that I mentioned last time, which is called Artin's conjecture of icosahedral Galois representations. Without worrying about what all those fancy words mean, I was trying to come up with a way to prove that there were infinitely many cases in which the conjecture was true. Maybe not to prove that the conjecture was always true, but at least to show that infinitely often, the conjecture was true.
Up to that point, there were only maybe ten or so examples in literature where people knew the conjecture was true, but there weren't infinitely many. I was very close to coming up with a proof of that, and that really was the big, big project I was working on. The second project I was interested in really had to do with a generalization of that. Simply put, in Artin's conjecture of icosahedral Galois representations, I want to focus on that word icosahedral because it relates to one of the platonic solids. Plato had this idea that there were only five perfect types of solids in the world. You have the tetrahedron, the octahedron, the cube, the dodecahedron, and the icosahedron. Well, for each one of those, you can write down what's called the Galois representation, and with those, you can kind of associate those things to elliptic curves. There are all these fancy things you can do. I specifically worked in my thesis on how to relate all this to an icosahedron, rigid rotations of the icosahedron.
I wanted to be able to do this with all of the platonic solids, and this was kind of the other part of my work, figuring out all of the details and putting it all together. The third one I was interested in was really this more specific idea of properties of elliptic curves. Elliptic curves are kind of this funny thing you have in number theory, but there's a lot of computational aspects to them. I was trying to come up with a series of algorithms on how to compute what's called the rank of an elliptic curve. I won't even try to explain what any of this stuff means. I'll just say that even as of today, there's no algorithm known to end after a finite amount of time that says, "Here's the answer on what the rank of an elliptic curve is." Let's say that I want to take all the numbers up to 100, and I want to ask the question, "Which of those numbers is a prime number?" This is something you can do in a finite amount of time.
There's something called the Sieve of Eratosthenes, which basically says, you first take the number two, which you know is prime, and now cross out in that list up to 100 all of your even numbers. Then, you go to the first number that's not crossed out, the number three. That is prime. Now, cross out all the ones that are multiples of three. The next one that's not crossed out is five, and you continue in this fashion, and that way, you have all of the 25 primes that are up to 100. This takes a finite amount of time to do. But what if I tried to ask the following question? Find me a prime greater than 1,000. This is a slightly different question. Now, you have to ask, "What's a good algorithm of finding a prime greater than 1,000?" This is one of these subtle questions that happen in number theory, especially in the theory of elliptic curves. You want to not only ask the question, but you want to come up with a really good algorithm that numerically can answer this question. This is kind of what I was doing with elliptic curves, trying to come up with really good algorithms of computing the ranks of curves. It's basically those three I was focused on in 2003.
ZIERLER: Did Purdue recruit you? Was there an open position you applied to? How did that play out?
GOINS: They definitely recruited me. I guess we would call it a target of opportunity hire. Although, the funny thing is, it was spread out over several years. Typically, a target of opportunity hire means something like this. Most of the time, when someone gets hired in an academic position, there is an opening. This could be either someone retires, or the dean decides that there's enough money they can hire in a specific area. Then, a department writes up a job announcement, they put it in the newspaper, magazines, hundreds of people apply, and you picture the best person to come in for that position. A target of opportunity hire is a little bit different. There, people in the department say there's one person that they really, really want, and they go to the dean, and they say, "Perhaps we don't have a position open, perhaps no one's retiring this year."
But they ask the dean, "Can you just find the money from somewhere so that we can go after this person and try to hire them?" I'm pretty sure that was the case at Purdue when they came after hiring me. As I mentioned earlier, I graduated in 1999. I was at Princeton University at the Institute for Advanced Study for a whole year, and that year, everyone who was anyone famous in number theory was there visiting the Institute. There were probably 100 or so people in my area who were there. Well, there were a couple of people from Purdue, and they understood what I had worked on for my thesis, so even in 1999, they approached me just to say, "We're very interested in what you're working on. Would you consider working at a place like Purdue?" And I'll say at the time, the answer was no. I was very focused on trying to stay in California. At the time, I wanted to move back to California.
But the plan then was to either get a position at Caltech or a position at Stanford. Well, the folks at Purdue still kept after me. They knew I was at Caltech in 2001. Again, they invited me to come out to visit Purdue, so I could get an idea of what the campus was like, what Lafayette, Indiana was like. Still, I wasn't extremely interested. I really liked the people in the department I met. I had a wonderful visit when I was there for a week, but still, wasn't extremely interested. I would say what kind of sealed the deal was, one of the professors, a pretty famous number theorist at Purdue, was visiting Caltech for a month in 2003. I got to know him pretty well for that month. I could actually see myself working with him and being colleagues with him at Purdue. I'd say that just as fate would have it, because he happened to be visiting Caltech the year that I was on the market, it worked out very, very well. But it took a few years, almost four years or so for them to really convince me that I should be working at Purdue.
ZIERLER: Once you got that offer, did you try to leverage that at Caltech to see if you could gain any more traction there? Or the message was pretty clear from Caltech?
GOINS: Yes, and yes. I certainly did leverage it. At least, I tried to mention that I did have this offer from Purdue. But it didn't matter. I think that the folks at Caltech had a very clear image that I was not what they were looking for. Which is understandable. It's fine. I do understand that the Math Department there is very narrow and exactly what they have in mind for a faculty member, whereas for really, the appreciation Purdue had for what I could offer, it was night and day. I think I pushed for a while for Caltech to at least consider my application, considering that I did have this offer on the table from Purdue. But remember, I also had a lot of leverage coming from the President's Office. The President's Office was pushing very hard in general at Caltech to diversify the ranks with the faculty.
They were very big on trying to get a more diverse set of post-docs to come there at the time, they had funding from the Irvine Foundation specifically to bring in a diverse set of post-docs. They hoped that once they had the post-docs with one foot in the door in these departments, that the departments would consider keeping the post-docs for tenure-track positions. Some departments, I think, were pretty good about that, but especially in Physics, Math, Astronomy, PMA, I don't think they were serious about that at all. Again, for the Math Department at Caltech, I know it was not considered seriously. Even with those two pushes from the President's Office at Caltech and also from Purdue, as far as I could tell, the Math Department wasn't swayed by either.
ZIERLER: Once you arrived in Purdue, it must've felt nice to be someplace where you felt wanted, where you were so strongly recruited.
GOINS: It was, very much. Indiana is certainly very, very different from California in pretty much every way that you can imagine. But it was a really nice department. I felt that I came in with several people in number theory who I had known for years, four, five years or so, seeing them at conferences and also seeing them at Caltech and some of these other fancy places. I came in already knowing several people in the department very, very well. It was a very nice experience the first couple of years I was there. I think I still had to kind of learn the ropes of what it meant to be a tenure-track faculty member, which meant you kind of go from being a post-doc, where really, your life is filled with just the goal of writing papers.
That's it. Even at Caltech, they are pretty good at sheltering the post-docs in that you don't have a very heavy teaching load. Mainly, your responsibility is just to write papers and get them out there. But then, moving to Purdue, I had to learn how to balance continuing to write papers, but also having a teaching load, teaching essentially three, four courses a year, and then on top of that, writing grants. I had no experience in writing grants at that point. I had to learn how to do all three of those at the same time the first several years I was at Purdue. That was perhaps the hardest transition I had to go through.
ZIERLER: What were your impressions of the student body at Purdue? How diverse was it? What kinds of opportunities did you have to interact with students for whom it was important to see professors who looked like you?
GOINS: I have mixed feelings about that at a place like Purdue. Understand that Caltech has on the order of about 1,000 freshman undergraduates, maybe another 2,000 or so grad students. Purdue, on the other hand, has about 40,000 students, so it is a massive, massive place. The Math Department itself had about 100, 120 faculty if you count the tenure stream faculty as well as some of the visitors and the post-docs. It has another 200, 250 graduate students. This is just the Math Department. We're not even counting the Statistics Department or people in Computer Science or some of these other mathematical science-related fields. Even in the College of Science alone, I think there's on the order of, like, 800 faculty. It's a very, very different place. When I was at Caltech teaching classes, I think the largest class I had maybe had 30 students in it.
The smallest class I had at Purdue had about 45 students in it. I easily had classes that went up to 100, 200 students at a place like Purdue. Just the scope was very, very different. Caltech is homogeneous in a lot of ways. Mainly, it's homogeneous in that it really is an institute of technology. You have a lot of students very, very focused on the hardcore STEM fields. I don't even consider engineering. I'm thinking more like theoretical math, physics, working in a biology lab, a chemistry lab. The students there are very, very focused on the science they do. Purdue, on the other hand, is primarily an engineering school. Yes, there are English departments and physics departments, But really, most of what you see at Purdue is pretty hardcore in engineering. This means that you're always seeing students building things. One of the things I used to see at Purdue is, the students were very proud of this couch that they would ride around campus.
They figured out how to take this couch, basically put it on the chassis of what would've been a motorcycle, and they could literally ride the couch all around campus. I think this made it on Good Morning, America a couple of times. This is kind of the thing you would see at Purdue, these weird engineering feats that students would have. I had to kind of get used to this idea that I wasn't really around scientists anymore. I was around engineers. Perhaps the hardest change was seeing that mainly, we had students from rural Indiana, who had grown up on farms, who would spend summers working on their parents' farms. They had never left the state before. They didn't even know what California was or where it was. The city of Chicago, which was two hours north, was the big, scary city that nobody ever wanted to go to. For me to come from California, I might as well have come from a different planet.
Because it was so far away from anything that they had even comprehension about, it was just night and day, talking with them about things. A lot of the students I met the first few years that I was there had never met anyone Black before. They had seen some Black people, maybe, on television. But for them to actually be in a room with me was just a novelty that they hadn't even comprehended in their lives. Sometimes, we'd have sort of awkward conversations about what all of this meant. But it was just a very, very different world in a lot of ways. I definitely appreciate the conversations I had with students the first few years I was there, but it was like being on a different planet, talking with some of the students.
ZIERLER: That same year that you joined Purdue in 2004, Black Issues in Higher Education named you an Emerging Scholar of the Year. Tell me about that.
GOINS: That was a nice experience, but it was very unexpected. This is what I think happened, although I'm not completely sure. When I was at Caltech, especially in the year 2003, there was a Black physicist who happened to be visiting there named Sylvester Jim Gates. Jim was, at the time, a physicist at the University of Maryland at College Park. Now, he's at Brown University. But he's someone I had known for a very, very long time. I first learned about him when I was an undergraduate at Caltech, and I kept asking around, "Why are there no Black physics professors in the department? Has Caltech ever tried to hire someone Black to be a physics professor?"
Steve Frautschi told me, "Yes, there was one. This guy who used to be a post-doc at Caltech named Jim Gates." Apparently, there was an issue. Caltech didn't quite make him an offer. He left Caltech as a post-doc, eventually went to MIT as a professor, moved around, and eventually became a pretty famous, distinguished theoretical physicist at College Park. Well, Jim was visiting Caltech the same year that I was a post-doc. In some sense, the roles were kind of reversed. Now, here I was, the post-doc at Caltech, hoping that Caltech would make me an offer to stay there as a professor, and I had Jim, who now was my mentor and happened to be visiting.
We spent a lot of time having lunch, walking around campus, chatting about different things. I would make it very clear to him that I wanted to figure out how I could stay as a faculty member, but I was very worried that pretty much the same thing that happened to him when he was a post-doc was going to happen to me. Well, Jim and I got to know each other pretty well, and he certainly was a very big champion of mine. He told me years later that he learned about this Diverse: Issues in Higher Education, which at the time was Black Issues in Higher Education, and how they had a call for people they wanted to feature in their magazine.
Apparently, he nominated me as one of these emerging scholars. I had absolutely no idea that he did this. Now, fast-forward a few months. Jim had gone back to College Park, and I get an email from Black Issues saying they were going to feature me in this magazine. For me, it was great because it was 2003, I was going on the job market, and I could use anything I could get to hype up myself and my application. This guy, I believe Ronald Roach, I think is the one who wrote up the article. We talked on the phone a little bit, and he got some more information. Black Issues actually called Caltech and said that they wanted to do a photo shoot, but they knew that Caltech had media services, so they got the folks at Caltech to come to my office and do this great photo shoot. I had never done a photo shoot before.
But we had to do funny things. They said, "Write some math at the chalkboard so we can take a photo of math. It doesn't matter, we're not going to understand what you put up there. Write some math, and we'll take a photo of it." Some of the pictures you see of me there in that Black Issues article are me standing at the chalkboard, writing some stuff that I was thinking about at the moment, and the two people in the room taking the photo making silly jokes because they just want photos for the magazine. All in all, it was a really fun experience, and I'm really glad that I did it. After it came out, I then told several people that, "I'm on the job market, I'm featured here in this magazine. Is there any way I can leverage this?"
Of course, Purdue thought it was great, but I believe right before the article came out is when Purdue had made me an offer, so it didn't really help with the Purdue offer, but again, I knew I was going to Purdue because they had tried to recruit me for years and years. I wanted to use this, though, to leverage a Caltech offer. I went to Caltech–remember, I had the offer from Purdue. Now, I had this feature article in Black Issues in Higher Education, and I tried to tell several people in the department, "Look, I have this offer from Purdue, I have kind of some help from the President's Office, now I have this article in Black Issues. Is this going to help at all?"
The response I got from the Math Department at Caltech was, "I've never heard of this magazine." And it was just left at that. The response from the Math Department at Caltech was frustrating. But on the other hand, the people at Purdue thought it was wonderful because they saw it as, "Look, we really wanted this guy to come to Purdue, and our efforts of trying to recruit him for five years haven't paid off. We made him an offer, now he's featured in this great magazine." For Purdue, it was the complete opposite kind of experience. They were very proud of the fact that this here came out. When I eventually went to Purdue in fall of 2004, they certainly heralded the article as a really great thing. For me, that only just kind of emphasized that Purdue was a good choice, that it was a good thing that I decided to go there.
ZIERLER: Tell me about the summer research culture in mathematics. You spent so many summers designing research programs for undergraduate students, both at Caltech and Purdue. Generally, tell me about the research culture in mathematics of these summer program and some of your most meaningful work doing this.
GOINS: The summer research experiences are something that probably has now been around for close to 20 years. It wasn't really the case in math when I was an undergraduate. I want to say when I was an undergraduate, '90 to '94, there might've been about 10, 15 math majors at Caltech, if we're going to be generous. This is counting all of us, seniors, sophomores, so on and so forth. There might've been about 10 to 15. I don't think more than half of us actually did a summer experience in math. Other fields, physics, biology, chemistry, that was standard. If you were an undergraduate in those fields, you would do research. But there weren't a lot of math undergrads I knew of who did a summer research project.
When I got to be a post-doc at Caltech, I was very well aware of the SURF, the Summer Undergraduate Research Fellowship office, and I was also aware that there were a lot of undergrads who wanted to do research but didn't know what it meant or how to do it. I certainly tried to encourage several of the undergraduate majors to consider doing research in math, if not with me, then with one of the other faculty members. More generally, though, now, this idea of doing research in mathematics in the summer has gotten to be an extremely popular thing nationwide. It all started with the National Science Foundation, and this must've been around 20 years ago or so. They created something they called RE, Research Experiences, for undergraduates.
Basically, it's a program where faculty members can apply for funding through the NSF specifically so that they can host a site, a region there on their campus, where they can bring in students from all over the country to come to their campus to do research from anywhere between 6 weeks and 12 weeks. The typical RE is about eight weeks or so. These programs vary from school to school. some, when the students get there, they might work with one faculty member for the entire eight weeks, or they might be broken up into three or four smaller groups with maybe three or four students each. Some have students work on one of, say, ten different projects, and the students can kind of jump back and forth between which of the projects they want to work on.
But in all of this, really, the goal of this is twofold. Number one, it's to get the students to be exposed to the culture of doing research in mathematics. This might be in terms of doing research, reading a paper to get an idea of what research is like, learning about these typesetting programs like LaTeX, giving a talk at a conference. The second aspect, simply put, is just furthering research. Some REs are really big about getting as many publications out during the summer as they can. Some REs might only publish one paper at the end of the REU, others I know get out five or six papers at the end of the eight weeks. It really varies a lot. But I'd say that those two goals are kind of the twofold goals. I think nowadays, in mathematics, there might be around 30 or so REUs around the country. It's really gotten to be a big thing. This is all within the last 20 years. I'll say that when I really got into the nationwide REU game, there might've been ten REUs around the country. But now, as I said, there are probably around 30 to 40, and it's really an amazing thing.
ZIERLER: You said it took a little time to understand what it meant to be on the tenure track. Once you got comfortable in the department and had hit your stride, what were some of the things you were learning about, the most important aspects of strengthening your case for tenure?
GOINS: I think what I learned was, there are two aspects to getting tenure that I had never thought of before. One is the spoken part of what it takes to get tenure. This is what you read in the faculty handbook. Everybody says that there are three areas to getting tenure. There's research, teaching, and service. Research is exactly what you'd expect. It's how many publications you can get out. No one will ever tell you the exact number. It's always kind of a moving target. You might say, "Well, what if you published ten papers? Is that enough to get tenure?" A department will always tell you, "Well, ten papers is great, but if you can continue to publish more, it'll be even better." There are very few places that will say, "If you get eight publications, that's enough. That's the cutoff." "If you have ten publications, after that, then you're fine." They'll always simply say, if you have publications, "It would be great if you can do more."
You're always a little bit nervous about the research aspect, just because you never know if it's enough. But what I've learned is that that's part of the mind game of doing academia, that they always want you to publish more because publishing more will always just be a better thing for the department. The second part is teaching. Teaching is kind of a tricky thing. At most Research Is, Teaching really isn't considered to be a great factor when it comes to getting tenure. It's important, yes. But I would say it's more like a threshold. The threshold is set pretty low. As long as you're not getting horrible evaluations, and the students don't hate you, then that's enough. Of course, it's the opposite if you're at liberal arts colleges, where teaching is paramount.
You could have a professor who has 20 publications, but unless they're really considered to be a great teacher, this could hurt you in your tenure application. Teaching is kind of a weird thing depending on where you were, but I certainly understood that my teaching was decent, so I wasn't worried about that at all. The service is kind of the double-edged sword you have to be careful about. On the one hand, it's easy to say you're going to ignore service because you don't really have time or energy for it. Service could mean as simple as serving on a couple of committees in the department. It could be a larger thing about serving on university-wide committees. I personally wanted to stay away from as many committees as I could, and even Purdue would say, "If you don't have tenure, you can always say no to being on a committee."
There were a couple of times where people came to my office when I was tenure track to ask, "Could you maybe serve on this committee?" And I had no issues at all saying no. They'd say, "Perfectly fine, understandable." And they would leave my office with no issues, no hard feelings. I think where I felt a little bit guilty was, there were things I wanted to do in terms of service, being involved with the undergraduate math club, trying to mentor some students of color there on campus, and this is why I say it's a double-edged sword. Because on one hand, yes, you do want to do service because sometimes, you do really care about these things. But on the other hand, you don't want to do service so much that it takes away from the time of doing research and doing a good job teaching.
But I'll say that in terms of the spoken rules, those are the three important areas, research, teaching, service. What I was not aware of were the unspoken rules. Simply put, the unspoken rule is, if the department likes you, they will find a way to keep you. I know that that may seem a little bit weird, but this is what I've learned about the whole tenure process. I was a pretty good citizen in the department. I always tried to go to all of the department meetings, always tried to go to the weekly colloquia, I attended the number theory, representation theory seminar without fail each and every week. Whenever we would have dinner after the speaker would be there, then kind of continue to visit with the department for the next day. I'd make it a point to go to lunch with the speaker, to go to dinner with the speaker.
I tried to be a very good citizen in the department and be active with all those things. I realized that departments like that. They actually do like it when the faculty members are very actively involved in the life of the department. It took me a while to realize how important that was when it came to getting tenure. I think, like a lot of tenure-track faculty, I got very paranoid thinking, "I don't have enough publications. My teaching is not as stellar as it should be. I'm not doing enough with service." But when I realized that the department genuinely liked me and wanted to keep me, it hit me that I was going to get tenure. The department was going to find a way to make sure that I got tenure.
The year that I went up for tenure, at first, I was very nervous thinking, "I don't have enough in those three areas. I'm never going to get it." But as the vote went through the department and then eventually made its way up through the system and chain, more and more people in the department would come up to me saying, "We're really happy that you're here. We're happy you're our colleague here in the department." The start of that year I got tenure was kind of a very scary year for me. But by the end of that year, it was kind of an ego boost. Because I realized that people in the department really liked me and really wanted to have me around. That, I didn't expect when I first got there with the tenure-track position. I didn't understand those unspoken rules and how that worked.
ZIERLER: Because Purdue was a center for number theory, was that specifically important for you academically, even socially?
GOINS: It was. I made the conscious decision that when I went to Purdue, I not only wanted to be a part of that hub of number theory, I wanted to help grow it. I did make it a point to say, "I wanted to go to lunch with the speakers to help interact, I wanted to go to dinner with the speakers to also help interact. I wanted to bring in my own post-docs and encourage them to also join in with these seminars and speakers. I made it a point to teach as many classes as I could, not just undergraduate courses, but also graduate-level courses in number theory to help build up that." A couple of the things I did while I was a faculty member, one, I tried to make it a point once a year to say, "Let's all of us in number theory link together, have lunch, and then map out the classes we want to teach for the next couple of years."
We would have an idea of maybe who was thinking about what. We could all kind of coordinate with each other, talk about whether the classes made sense in terms of what we had in mind. We actually came up with a rotation. There was a series of four classes we were all going to teach, and with that rotation of classes, the grad students would know, "These four will be taught every couple of years." The grad students could then plan out how they were going to take the classes and which faculty members they were going to work with. I also eventually took over the representation theory, number theory seminar, which meant I was responsible for making sure that we had a seminar that ran each and every week. I think I probably did a little bit of an overkill with the seminar because there are 52 weeks in the year, seminar's supposed to meet once a week, and I think at one point, we had maybe 45 seminars in one year.
We were supposed to take the summers off. I think I was just very ambitious and still wanted to have people come by in the summers anyway. But the point is that we had a very consistent regular seminar that met each and every week. I know that the number theorists liked that, that they knew every Thursday, 1:30 pm, without fail, we were going to have a speaker and a seminar. I told everyone, "If you have people you want to bring in, let me know so that we have a calendar and know what's happening. Also, make sure we have money in the departments so that we can pay for these." I was very active in saying, "This is the life of the number theory culture that we have."
I know that the other disciplines were a little bit jealous in how coherent of a group we were because we were meeting once a year to talk about planning the seminar, planning the classes, and we had this very healthy seminar that met every week without fail. We had lots of post-docs, lots of grad students. I want to say we maybe had five, six faculty in the number theory group. We always had, I'll say, three to four post-docs in the group. We had probably 15 graduate students in that group, and I would say that between us, we would teach probably five classes a year. That was a lot. I was really very proud that we had a really good, strong group there at Purdue.
ZIERLER: What would you say the impact was in gaining tenure in your sense of latitude for new projects to take on, both in mathematics and more on the political and sociological side, where you're developing this additional interest in understanding and appreciating the history of Black achievement in mathematics?
GOINS: That's a good question. I'll say that when you are a faculty member, it's said that you have academic freedom to study and pursue whatever you like. That's true to an extent. Yes, the letter of the law says that you do have all of this freedom, however your colleagues do worry a lot about the reputation the department has based on the quality of research that you do. It was very clear that when I first got to Purdue, several people in the department were very excited about the projects I was working on while a grad student, while a post-doc, this Artin's icosahedral Galois representations conjecture. Right about the time I got tenure, I decided for many reasons to slightly shift directions.
I could tell that there were people in the department who did not like that, who were really not happy that I was no longer working on this big, fancy conjecture, that I was working in a slightly different area that maybe wasn't as interesting to the mainstream [research in] number theory, but it was something that was of interest to me. These were little things like them pushing back a little bit maybe when I wanted to teach a class on something that wasn't Galois representations but now was on elliptic curves or might've been on how to compute things with elliptic curves. They wanted to know, "Why aren't you teaching the Galois representations class?" And I had no interest in doing that.
Or, when I would, say, give a seminar talk for my other colleagues there in the department, them not being as interested in the topics I'm covering in the seminar, and the grad students in the room seeing that the faculty members, my colleagues, were not as interested, and then the grad students grumbling to themselves, "Why is it that they aren't respecting Goins's research? Maybe we should think twice about working with them." So there were consequences with all of that. I made the decision to switch areas because I just wasn't happy with the politics of it all. I was realizing I was more caught up with the politics of working in this area, realizing that there were a lot of really fancy, really good people working in this area. I didn't want to compete with all of that. I just wanted to do math because this was the area I really, really enjoyed doing.
And when I realized that I wasn't enjoying it, I was getting more and more stressed out because of the competition, that's when I decided to drop it. I found an area that I really enjoy. I'm still working in this area today, and I definitely love working in it. But I definitely had to experience my colleagues not being as happy with me moving to this different area. Again, it wasn't so much it was a bad thing in terms of me getting tenure and getting promoted, but it certainly was hurtful to see that my colleagues were not as excited with this new area I wanted to move into.
ZIERLER: Why do you think that was the case? Why were they not as excited?
GOINS: They definitely were more concerned with how it looked if they could say that Purdue had faculty members working in these really, really fancy areas. There was certainly a lot of concern with how to move up the number theory group in the rankings. You could say US News and World Report, you could say in terms of the reputation we give to each other in the field. But I think there was a lot of concern about whether we were going to move down in the reputation we had in the field if those of us at Purdue were not working in those fancy areas. I think there was too much emphasis on that, what other people were going to think about us as a department if we weren't working in these fancy areas. For good or for bad, I realized that that's what a lot of departments worry about, especially research departments, "What are others going to think about this department?" I, myself, just couldn't focus on that because I had to worry about my own sanity and whether or not I was going to be happy with the research I was doing.
ZIERLER: How did you respond to those criticisms? Or did you feel compelled to at all?
GOINS: I don't know if I actively responded to them. I think it was more that it felt there was a growing rift in the family. Up to that point, we worked together very well as a team. Things like maybe there was someone I wanted to bring out to Purdue because they were working in this specific area, so I wanted to bring them out for the seminar, and because my college really respected the research I was doing, they respected my recommendations of people to bring out. Then, if the person would come out to Purdue, the other colleagues would be really happy that this person was there, so they'd make it a point to all come to lunch, come to dinner, maybe meet with this person on the side. We might even have conversations of the department wanting to hire this person as a tenure-track faculty member. There was very much this feeling that we all trusted and respected each other.
I think that started to dwindle down to they were doing their own thing, I was doing my own thing. There really wasn't this real sense of trust and respect. It was almost like we all became siloed, even in this general area of number theory. Some people were working in this specific area, they wanted to bring out their own colleagues to come out, give talks, give presentations because they were working in this very, very narrow area. I got to the point that I just didn't want to really interact with those speakers, so I, myself, started to pull away a little bit from going to dinners, going to lunches, meeting with some of these individuals. I just wasn't as interested in attending some of these talks. I would, but my heart wasn't there. I'll say that in very subtle ways, it felt that we were drifting apart and that it wasn't as strong of a community as it was when I first started at Purdue.
Diversifying the Field
ZIERLER: As you started developing more interests in the sociopolitical side, I'll just pick one talk of many in where you were at, for example, in 2011. One talk you gave, Transforming Undergraduates into Researchers: Best Practices from an Afrocentric Perspective, was at a conference in Lexington, Kentucky. How intellectually did you start developing a systematic idea for thinking about these upstreaming issues in diversifying the field? Was that a gradual process? Had you been thinking about it for a long time, but you needed tenure behind you to start leaning into this? How did these things play out?
GOINS: Well, something I started to think about very carefully, very closely when I was a graduate student, when I was at Stanford, I got involved with a tutoring program at a local high school right there in Menlo Park, where I was supposed to help some of the students in really just being graduating seniors, doing basic algebra skills. What I started to notice was, right around the Stanford area, you have a growing schism of the students who were doing extremely well, had parents that worked in Silicon Valley, they themselves are going to go off to Stanford and other Ivy Leagues in the country, and then you have other students who don't have parents from those socioeconomic backgrounds who can't even graduate high school with basic algebra skills. It shouldn't come as a surprise that those who were doing really, really well were white and Asian, and those who could not even graduate with basic algebra skills were Black and Latinx.
And I saw this when I was there in grad school. I ran this tutoring program for maybe three years or so. I had several undergraduates at Stanford who would come out with me once a week to work with the students and interact with them, and you could actually see these Black and Latinx students who were graduating seniors who understood how screwed they were in life that they literally could not do fractions, and they're 17, 18 years old. They would look around the room at some of their colleagues, the other students at their high school, and they knew those students in the same classroom were going to literally go down the street to Stanford and probably work for some tech firm when they graduated four years later. It really stuck with me when I did this for several years as a grad student.
I was really thinking for years and years, "What do you do about something like that?" This is when I started to get involved with these summer undergraduate experiences. The first one I did was summer of 2004 at Miami University in Oxford, Ohio. It was about a four-hour drive away from Purdue, so it was a very natural thing that I get this program there at Miami University. I did that for probably five summers or so. But being there at Miami University, this was an REU, so that meant that they brought in students from all over the country, but the Miami University REU was very good about bringing women and minorities primarily as the focus for the students there in the program. That meant that I had an opportunity to do high-level research with Black, Latinx, and women students in mathematics.
I started to think there were two different ways in which you could really approach math for women and minorities. One is what's nowadays called a deficit mindset, and this is kind of the way we were approaching things when I was working as a grad student with the tutoring program. You could say, "Here are women and minorities who are not doing well in mathematics," and then ask, "What can you do to kind of encourage them to continue maybe to build up the lack of background that they have, but really worry about kind of these remedial programs, kind of get them caught up to speed. The second way to think of all of this is almost like a growth mindset, but it's more really the high-achievement mindset. You could say, "Let's take women and minorities who you are going to assume are really good at math and science. Let's meet them where they are and push them to be even better."
I decided to take on the latter philosophy. That meant that I wanted to work more and more with college students from some of these underserved and underrepresented backgrounds, women and minorities, and tell them, "I know that you have an interest in majoring in mathematics. I'm going to assume that you already have a solid background in math courses, abstract algebra, proof-based course, what have you, and I'm going to push you even harder, have you do some really crazy stuff in algebraic geometry and some of these fancy things in math that you've never seen before." That's the mindset that I've had with students ever since summer 2004, that I'm going to push students past their comfort zones to say, "I know you can do extremely high-level math, so let's just go ahead and do that." I've tried my best to not have a deficit mindset when it comes to working with minority students. Already, my philosophy is, they are really good. I'm going to push them to be even better.
And I'm saying all this because typically when you work with minority undergraduates, the typical mindset is, "These are students coming from very poor backgrounds. They probably are going to be one of the only students who look like them in the classes. Let's try to have some kind of remedial or bridge program to build up their confidence and try to convince them to major in mathematics." I do not have that philosophy at all. It's all been about, "I know that they are really good, I know that they are basically at the top of their class. Let me work with that and push them to be even better." But it's taken a while for me to figure out how to do that effectively. That's really been the hardest part of anything.
ZIERLER: How important has it been to secure external grants from agencies like NSA, NSF in having programs, conferences that really support these efforts?
GOINS: It's crucial. I don't see how anyone can do it without getting this outside funding. When I first got to Purdue, I started to think really seriously about, "What can I do with bringing in more women and minorities to Purdue?" This is either for speakers in the seminar I was running, maybe to have them visit campus so they can consider applying for tenure-track positions. I was even thinking about some of the undergraduates I wanted to work with, how to have them work with me in the summers, how to have them be more involved in the life of the department. I was working at Miami University in Oxford, Ohio, pretty much every summer for the first five summers I was at Purdue, but I still wanted to do something at Purdue. I started to think, "How much money would it cost for me to do some of these things?"
Let's say you want to bring out someone to come to campus, almost like the way Purdue had done with me, but you want them to consider applying to Purdue for one of these tenure-track positions. That might mean that you want to fly them out to campus, which might mean a $500 plane ticket, another $400 for them to stay in a hotel room, you might want to pay them a couple hundred dollars honorarium, take them out to dinner, that might be another couple hundred. Let's say flying out one person to campus might be on the order of $1,000 to $1,500. What if you wanted to do that times eight people, so that you'd have a pretty decent pool of people to come out just to get an idea of what the campus looks like? Now, we're talking $10,000 to $15,000. That's just bringing out faculty members.
What if you wanted to have students come to campus, like Miami University, and do research with you the whole summer? Now, you have to worry about maybe housing them on campus for the summer. That might be $1,500 right there. Let's say you wanted to fly them out to the state of Indiana. That might be another $500. You have to pay them a stipend because otherwise students are going to work for a company and not do research, so they definitely don't want to do research for free. That might be another $3,000, $4,000. Now, we're talking about $6,000 per student. What if you want to have five students? We're talking on the order of $30,000. If you wanted to bring out faculty members, potentially have them apply for a position at Purdue, bring out students so that they're doing research with you, maybe you're trying to diversify the field more generally, we're talking anywhere between $40,000 and $50,000 per year to do all this.
At one point, before I got into the mindset of applying for some of these external grants, I decided to approach Purdue itself about doing some of this. I started to write a series of proposals just internally for Purdue to say, "I want to have a speaker series where I can have faculty members come from all over the country to do this." And I remember writing up a proposal that was going to be $10,000, $15,000 for me to do this. Shopped it around to a couple of different departments and pretty much got laughed at. No department chair is going to look at this and say, "I'm going to write you a check for $15,000 for you to do this." It just doesn't work that way. I eventually found a couple of people on campus who had their own NSF grants, and they could do what's called a sub-award and give me a certain amount of money from their grant to do what I wanted to do.
I did run my speaker series for a few years based on money as a sub-award from some of these NSF grants. Even when it came for me to do research with students, I do remember going to one office, asking for $30,000 for one summer to work with students. Again, got laughed at. They're not going to give me $30,000 for this. I eventually convinced the Math Department to give me a little bit of money, maybe about $8,000, so I could work with some students. But this was happening for the first several summers. Going to the department, going to other departments on campus, trying to ask for a few thousand dollars here and there, and realizing that I really wasn't doing much of anything. I was just asking for handouts from department to department. One day, I just got the idea, "Let me just write my own grant." I will tell you, though, I wrote the grant, but then I kind of convinced myself, "I'm never going to get the money, so don't even send it off."
And I do realize now in hindsight how silly that was because I remember spending about a month or so writing a 15-page proposal that outlined exactly what I was going to do to work with students and faculty, and it was doing exactly what I'm talking about now, asking for money to bring in faculty members from the outside to visit campus for a few days, and to have money to bring in students from the outside. I had been doing this every summer anyway for years, bringing in faculty members and students. All I had to do was just take the proposal I had and send it off to one of these external funding agencies. Well, there was a colleague at Purdue who convinced me to do that, and the first time I submitted that proposal, it got funded.
That meant I went from begging offices for $10,000 here and there to maybe do a little bit with students to now having $125,000 per year to do whatever I wanted to do. It was night and day. This is why I'm saying, I can't even imagine trying to do any of these programs if you don't have external funding. After I got $125,000 to do whatever I wanted and no longer had to go to any department or office to ask for money, I realized that the sky is the limit. I could really do whatever I wanted and how I wanted to do it. I haven't even looked back. To me, now, external funding is the way to go if you want to make any changes here.
ZIERLER: What were the best uses of those funds once you secured them?
GOINS: I really would say it's exactly this idea of bringing in students from the outside to come to campus, actually doing research with them. It's hard to structure a really good program where the students are getting a lot out of the experience. Remember, I mentioned earlier that these REUs seem to have two goals to them. One is the whole publication thing. I think a lot of people who run REUs are solely focused on what the National Science Foundation likes to call deliverables. This idea of having a paper, or saying that a student presented a poster at a conference, or even saying that a student presented a talk at a meeting. These are tangible things you can write down on paper, "Student did this." I'm more concerned with exposing students to the culture of mathematics.
For example, what does it mean to write a math paper? What does that actually entail? Understanding what a theorem is, what a proof is, how to use LaTeX, how to typeset all these things, that whole culture of writing a paper. Also, exposing students to other people who do mathematics, bringing in an outside speaker and having this person talk about their journey from being a student to then eventually being a math professor. Also, this person talking about the research they do, which hopefully is completely different from the research the students are doing that summer because they need to be exposed to something a little bit different. But it's really structuring that whole experience for the student so they really understand all the different aspects, for the good and the bad, of what it means to be in mathematics. But the second part, for me, is the professional development of bringing in a faculty member from the outside.
When I say professional development, I'm thinking a younger faculty member who doesn't have tenure yet, bringing them in to whatever school I'm working at, so that we can chat a little bit about what it means to run an REU. What are all the aspects of putting all this together? I like to kind of show up by saying, "Here's what it's like to work with the students, here's what it's like to actually show off mathematics culture, here's what the students are doing on a daily basis." I really view that opportunity of bringing in an outside speaker as an opportunity that I can then talk with this person about the professional side of being a mathematician. One of the people I've been working with the last several years, as someone who's been assisting me in running these REUs, is a former PhD student of mine.
He and I have been working together, running these REUs. He's been able to see the whole aspect of what it means to run these things. It's not just like the doing research side of it, writing papers and what have you, but it's been reading applications for an REU, deciding who gets into an REU and who doesn't, reading letters of recommendation and learning how to read between the lines to understand what student will be a good fit and which won't. How many younger faculty members who don't even have tenure yet have read applications for REUs? A lot of younger faculty members have no idea what a letter of recommendation looks like, either because they've never read one or because they've never been a part of the whole application process. But this guy who was my former grad student, now that he's a younger faculty member, has been reading applications so he has an idea.
We also wrote a grant together so that now he knows what it's like to write an external funding agency grant to run one of these summer programs. It's all part of this whole larger issue of professional development. Because I have the funding to either hire someone to do this or bring in someone from the outside to pay them an honorarium, pay for a plane ticket, and all the rest of that. It's been really great that I can use this funding to do these kinds of things. I'm just really grateful that I have the funding to do all of this.
ZIERLER: As you became so fully engaged in these programs during your last four or five years at Purdue, looking at the research that you had done during those years, in all of these interactions with the students, did that affect the kinds of research questions you were posing for yourself? Did you take on new areas of inquiry as a result of all of these conferences and workshops?
GOINS: I did. I certainly did. Also, one of the projects I did with some students that got me to think very much out of my comfort zone was a project that I did that involved supercomputers. I mentioned earlier that when I was a post-doc, one of the three projects I was interested in was this idea of computing the ranks of elliptic curves. Really, I was trying to work out an algorithm of what might be an easier or quicker way of computing the ranks of these elliptic curves. That was purely a theoretical exercise. I never actually worried about trying to implement any of this. It was just saying, "Let me work out some formulas to see if one could maybe write this algorithm down in the computer. Maybe this should be an easier thing to do."
One of the summers I worked with students, I decided, "Let's go ahead and implement all this." We did write up a computer program, but we realized that running this program on one computer was not going to work. It was going to be a little bit too slow and inefficient. We just tried this with one example, one computer, and realized it was just painfully slow. Instead, we decided Miami University at Oxford, Ohio had a supercomputer. I have no idea why this small liberal arts college in the middle of Ohio had a supercomputer, but they did. Most people had no idea that they had a supercomputer on campus. When I found out, I reached out to them. I wasn't even a faculty member in Miami, but I was the only person who knew about this. They loved it. They said, "Great, we will work with you, we will help you write the code." This doesn't happen in most places.
At Purdue, for example, they were involved with something called the TeraGrid. It's essentially maybe seven campuses that had literally thousands and thousands of nodes for these supercomputers, but to get access to any of these, you had to write a proposal, wait several months, pay so much money per the number of minutes you were going to use the computer. It was just kind of a nightmare to use. But at Miami, because I was one of the only people, they said, "Great. We will literally come out to your office, we'll work with you, we'll sit down with the code, we'll do what we can to help you." That summer, working with undergrads, I learned how to program on a supercomputer.
I learned with the students. But it gets better. We decided to write this code, and then we decided to test the code with over three million examples. I had never in my mind thought about running code that would run three million examples of elliptic curves. I thought maybe one or two. But we thought, "Whatever. We have all of these nodes, all this time. Let's run it and see what happens." We ran all of this, and we had this massive amount of data sitting in front of us. We had to figure out what to do with this data. I thought, "What if we run a statistical analysis?" I know nothing about statistics, but luckily another one of the research groups there at the REU was a group in statistics, which meant I had the students in my group who were supposed to be doing pure math, working on all the stuff of algebraic geometry and elliptic curves.
They had written all of this code on supercomputers, they had all this data, three million data points. They handed everything off to the statistics undergrads. They looked at it. Now, these two groups were talking back and forth to figure out the statistical analysis of all of this data. That meant that summer, I was learning how to program on a supercomputer, and I was learning how to do what's nowadays called algebraic statistics. It's actually doing a statistical analysis of the data you'll get coming from pure mathematics. My whole world of the way I thought about research completely changed that summer in working with undergraduates. I was writing computer programs, and I was doing statistical analysis on things. But it all came from working with students. So yes, to answer your question, a lot of the ways I think about research nowadays change depending on the projects I'm working on with students over the summer.
ZIERLER: I'll just observe that in explaining the kinds of schools that you were focusing on back in 2003, for you, the name of the game was R1 research universities because the emphasis for you was on the research, on the papers, and that maybe you'd carve out a little bit of time for teaching and writing lectures. It's clear that there's an evolution in your priorities, where you're becoming so much more engaged with the students. Perhaps this is a segue for our next talk, where we'll pick up your decision to leave Purdue. What do you think that says more broadly about the things that were most important to you when you became an associate professor?
GOINS: By the time I was getting tenure, I started to view math research as a selfish endeavor. I like doing math research. I like sitting at the chalkboard, working out formulas and equations. I can spend hours and hours in my office working out the stuff and have a great time doing it. But I started to ask the question, "To what end?" I definitely looked around in the classrooms I had at Purdue just to ask the question, "How many women and minorities do I have in these classes?" I certainly realized by the time I'd made full professor that that number, even though I had taught on the order of 1,000 undergrads in the 14 years I was at Purdue, was less than ten. I really had taught almost no minorities in the 14 years I was at Purdue. I definitely spent more time during the 14 years asking around, "How many Black undergrads are there majoring in mathematics? How many Latinx undergrads are there majoring in math?"
And I realized that even in finding those students, still, we're talking literally a handful. There might've been one or two per year. That's because a lot of the really good minority students at Purdue decide to go into engineering, that they're not going to major in a field such as mathematics. Even when it came to the PhD program, I was on the graduate admissions committee in the Math Department for about four years, and we spent some time trying to travel and recruit to get students to apply to our PhD program. Same thing, the number of students we were getting to apply was very, very small. They might've been on the order of 300 or so domestic students who are applying to the PhD program in math.
We were lucky if we had five Black students, max, to apply to our PhD programs in a given year. The numbers were depressingly low every single year. I just started to think, "Why is this? What can I do to change it?" Of course, I wanted to say, "Maybe I can encourage undergraduates at Purdue to go into mathematics, maybe I could do more recruiting for the PhD program." But the more I worked on that, the more I thought of that, the more I came to the conclusion that Purdue was not the right place for me to do that. It wasn't the right place for me to find the students to encourage them to go into math, to go off to the PhD program.
Maybe I needed to rethink this from the ground up. Just as a teaser, what I'll say is, it was Pomona, right about the time I was thinking about all this, that approached me to say, "We have the math major as the most popular major at this liberal arts college. We have on the order of 20, 30 Black students who have an interest in going into math, and statistics, and other STEM fields." I started to think, "Why is it Pomona is doing all this right? And what can I learn from Pomona?" So yes, it was a very different mindset as I started to think about this more and more.
ZIERLER: Besides the institution, thinking about where you were teaching, how would you compare the difficulties in recruitment for minority students, specifically in math, from this double-edged perspective of on the one hand, math as a research field might feel particularly inaccessible for minority students, and on the other hand, how it might be difficult for prospective students to look at the applicability of a math degree? In other words, "Even if I'm good at this, what am I going to do with it?" I wonder if you could compare and contrast overcoming both of those humps in your efforts to recruit minority students to the field.
GOINS: There are maybe two groups of students to look at, and the answer's going to be different depending upon those two. There are recruiting undergraduates to major in mathematics, and then there's recruiting recently graduated undergraduates into a PhD program. Let me maybe talk about the latter first because that's perhaps a little bit easier to talk about. Those who are recently graduated and are considering going off to a PhD program, in some sense, they're already sold on the idea. They like math, they want to do math as a career. Maybe they're debating the specific area they want to go into, whether it's going to be something more theoretical or something more applied so they know what they're going to do with their degree afterwards.
There, the question comes down to, "Where is a department where I'm going to feel welcome and appreciated?" That's basically what it comes down to. Very few minority students, I've learned, will go to a PhD program if there are not currently a lot of minority students, or if there isn't currently something in place to say, "There are mentoring programs, there are diversity efforts, so on and so forth." Some of the departments that I've seen have done an incredibly great job in attracting women and minorities have these things in place. For example, the University of Nebraska at Lincoln, UNL, have had one of the highest percentages of women in mathematics in PhD programs for close to two decades now. Part of this is because every year, they run a conference called the Nebraska Women in Mathematics Conference, where they really hype up women in mathematics nationwide, and then, of course, this translates into things their department in particular is doing. I want to say their numbers have been sitting at maybe 50, 60% women for the last decade and a half. Most departments are sitting at 20%. The fact that you actually have this department for almost the last two decades at 60% women, they are definitely doing something right.
You have other departments, like the University of Texas at Arlington in Dallas, that have something like 60 to 100 of their graduate students are Black. This is because they actively do recruiting in the South area, somewhere around the Pacific Gulf area. They do a lot of recruiting at the local HBCUs that were there. They even applied for an NSF grant to specifically give money to students coming from HBCUs to be in a PhD program. They've done a remarkable job of getting their Black graduate students to get things like NSF post-docs, other NSF grants. These students are being placed in really, really good jobs. They have this pipeline now. They have students coming from HBCUs into their program, where they're coming in with money, and then they're getting really good jobs. But then, those same students who are now in grad schools can go back to their undergrad institutions to tell the students there, "This program is really great. You should come here."
These two schools, UT Arlington and Lincoln, Nebraska have just done a remarkable job of having that culture of, "The department's a really great place to be." That's something that has stuck with me, this idea of the department having a culture and students knowing about this, but then really the department making sure that it continues this really great culture. Now, for the undergraduate majors, this is the trickier question. What I'm starting to see is women and minorities are a lot more concerned with applicability of the major, but really more having a vision of why they should be in mathematics. I can tell you that in particular, a lot of Black students I've talked with here at Pomona College are very much worried about things like building generational wealth, being able to go back and help out the communities they're from.
They're going to be first-generation low-income, and simply put, they see they could get a degree in maybe computer science and work for a Google, Yahoo!, Facebook, or get a degree in economics and work for a Jane Street or some other hedge fund company, and they can make a lot of money doing that. When they think of mathematics, they see, "I can become a professor, and I could make literally a fraction of what I could make if I'm in these other areas." We in mathematics have to do a much better job of saying, "Being a professor is one of many options of things you can do." We have to do a much better job of convincing the undergraduates that being a math major isn't just about teaching. There are all of these things you can do. It's a very different aspect than, say, going to try to convince a student to go off to a specific grad school. We really have to increase their mindset, change their knowledge of what it means to be in mathematics. That, I think, is the hard part for convincing women and minorities to go into math.
Back to California
ZIERLER: Last question for today, and this will serve as a segue for our next talk, by late August 2017, when you're named full professor, you have an established record of success. At this point, are you starting to put out the idea that you're thinking about leaving? Are you indicating that you'll stay if certain changes are made? Or at this point, have you made up your mind that you can't accomplish what you want to structurally at Purdue, and you need to go somewhere else?
GOINS: August 2017, I had already made the announcement I was leaving. If you go backwards about two, three months before then, I had already signed a contract with Pomona College. I told Pomona, "I have a couple of grad students who are finishing, so I want to defer starting at Pomona until June 2018. I want to spend the next year or so finishing up things at Purdue." Right around May 2017, I make a double announcement. First, I announce I've made full professor at Purdue University. That means everything was fine. I was going to be full professor. Starting August, September 2017, I could spend that year with the title Professor of Mathematics. I also announced I was leaving Purdue, but not just leaving Purdue, I'm leaving a Research I for a liberal arts college. That double announcement shocked a lot of people. I still made it a point to talk to my grad students on the side to let them know before I made either of those announcements.
I talked to the number theory faculty at Purdue to let them know, "I'm leaving, here are my reasons for that." But that double announcement, I think, shocked a lot of people. I had a lot of conversations with faculty members in the Math Department at Purdue who wanted to know about both of those because they thought, "If you've made the title of professor, you must be happy at Purdue. You must be happy being in a Research I university. Why is it that you're leaving Purdue? But more specifically, why are you leaving an R1 altogether to go to this completely different place?" I think also there were a lot of people who really respected that decision in that they could tell I was trying to come up with a plan of how to bring in more women and minorities to the field.
And they certainly knew that in me leaving, going to a liberal arts college, I could finally enact that plan. They could tell that I was really hitting a wall in enacting that plan at Purdue. But that entire year from about June 2017 through May 2018, I had a lot of really interesting and really hard conversations with people behind what were all of the reasons I was leaving.
ZIERLER: Well, on that note, we'll pick up for next time when you return to California.
[End of Recording]
ZIERLER: OK, this is David Zierler, Director of the Caltech Heritage Project. It's Thursday, December 9, 2021. Once again, I'm so happy to be back with Professor Edray Goins. Edray, great to see you, as always.
GOINS: It's great to be back.
ZIERLER: Last time, when we left, you were talking about some of your social and cultural motivations for leaving Purdue, leaving even an R1 institution. On the research and technical side, I wonder what that might tell us about where you were at this stage in your career in terms of not needing to be at an R1 school anymore. To go back even further, when you were explaining your reasons for coming to Purdue, wanting to be in the center of number theory, I wonder what we might divine from, at that later stage in your career, thinking about leaving a place like Purdue. What might that tell us about where you were in the research, both for yourself and in terms of the community of mathematicians you were engaged with at that point?
GOINS: The year we're talking about would be roughly 2017, 2018. I received tenure in 2010. We should probably go back to explain what my mindset was. When I started at Purdue in 2004, I worked in an area, as I mentioned before, that was looking at this conjecture by Artin, looking at Galois representations and how they're all related to elliptic curves. By about 2008, 2009, I was realizing that I really wasn't happy working in this field. It wasn't so much the research, it was more dealing with the personalities. It was a very competitive area, there were a lot of really big names, folks in their 60s, 70s, and 80s who were still publishing in this area, and I just felt it was too competitive, and the people who were doing well were just people I didn't like, to be honest.
This meant I wasn't happy going to conferences, I wasn't comfortable emailing people to ask for advice, and I was feeling more and more disconnected from this research area. By 2009, 2010, I made a very risky move and decided pretty much, because I was going for tenure, I was going to switch fields. For most people, that's like the kiss of death. The year you go up for tenure, people are going to write letters for you based on the research that you've done in that specific area, the work you've done over the last six years or so. I decided I wanted to go into a different area because I didn't like the personalities, I wasn't happy working in that area, wasn't happy going to conferences, and so I just decided I was going to work on a completely different project, something I had not really thought of before, but it was something I found to be intriguing.
That summer, roughly June 2010, I led a research group of faculty at a research facility in Providence, Rhode Island, where we worked on this project that I had never thought of before. I spent maybe three weeks reading the literature as much as I could, but then I said, to the people I met for the first time for those five days, "I don't know much about this area, but we're all going to work in this area together and try our best to learn it together." That reenergized my love of mathematics. These were faculty members who were all minorities. They, themselves, had not worked in this area. They worked in completely different areas. They were no longer in the number theory, representation theory realm that I worked in. They were all over the place. We're talking topology, analysis, group theory, one person was in number theory, applied math.
These are typically areas in the field that have nothing to do with each other. Typically, folks who work in these different areas don't interact, don't attend conferences. In a lot of departments, some of these are actually separate departments, the pure math versus applied math paradigm. But all of us working together, all from different backgrounds, wanting to learn this new material, I started to realize two things about myself. One, I can work around people I really enjoy working with, and two, I was actually smart enough that I could learn a different area. I didn't just have to pigeonhole myself into this one area if I didn't like it. The year I went up for tenure, I got a very different mindset to doing mathematics. What I'll say is that over the next six, seven years, from about 2010 to about 2017, I definitely learned a lot more about this area. But because it was such a new area that most people had not worked in before, this meant that I didn't really have other people I could talk to.
When people came to Purdue to give talks in the seminar I was running, they weren't visiting me to give a talk in this specific area, this idea of Belyi maps and Dessin d'Enfants. I was working in the area where I was really working primarily by myself. I still wanted to learn more about number theory in general, which is why I didn't mind people coming to Purdue to give talks in all these different areas. But really, me working in this one area by myself gave me a newfound sense of independence. When the opportunity came up for me to go to Pomona in 2017, there wasn't really this fear of going to a place where I was no longer going to be in a research environment because over the last six, seven years before that, I had learned to work more or less independently. If I see a definition I don't understand, being able to flip through different books and papers to try to piece it together, or almost like going down a rabbit hole.
If there was something I really wanted to understand, I might look up this one word on Wikipedia, do a couple of links that would eventually lead to this other word, which would lead to a series of papers, which would tell me about this conference of people working in this totally different set of ideas. I kind of learned to piece together all of these things completely on my own. It's been a very different way of doing mathematics from the way I was trained as a grad student and as a post-doc. During my post-doc years, the idea was, I was working on this conjecture, and a lot of people had an interest in understanding this conjecture. That meant I could attend conferences and give talks, and whenever I'd go to these places, there might be 10, 20 people who were really deeply interested in my thoughts on this conjecture.
Nowadays, I work on a problem where there might be five people on the planet total who are really interested in what I'm working in. It's very different. In fact, nowadays, when I go to conferences, I'm talking about a topic that no one in the room has even heard of before. It's a very, very different way of doing math. But I will say I'm happier doing this math now than I ever was doing any math before then.
ZIERLER: To what extent is that a function of you being established in the field, which might accord you a level of adventurousness in your intellectual curiosity that might not be available for a post-doc or an assistant professor?
GOINS: That's a good question. I'm not really sure what the answer is. It is true that when I was a post-doc, because I was working on a problem that was very popular, something people really wanted to know about, it did give me the opportunity to know people in my field. I probably averaged around 20 academic talks a year when I was a post-doc. That meant I probably gave on the order of 60 or 70 talks within about five years or so. I traveled anywhere and everywhere. When I was at Caltech from 2001 to 2004 as a post-doc, I probably gave a talk at every math department at a research university in Southern California. I just got to know everyone. Those contacts I made then certainly help now when I'm asked to sit on committees, serve on panels with the National Science Foundation.
These are people I've just known because of the talks I gave when I was a post-doc. On the other hand, I did take a huge risk in 2010 when I decided to switch fields. Because a lot of people really wondered, "What is this going to mean for the number theory group at Purdue?" I was no longer working in this really hot area of Galois representations and Artin's conjecture. I'm working on this field that no one had ever heard of before, Belyi maps and how these things are all related to branch covers of Riemann surfaces. Certainly, it was very risky when I decided to switch fields because yes, it is true I had some level of seniority because I had done a post-doc, already had a tenure-track position, but I didn't have tenure yet. I still think in a lot of ways, this delayed me getting promoted to full professor because I did switch fields.
I certainly saw some individuals who were younger than me, some individuals who started after I started at Purdue who made it up the ranks much faster in the 14 years I was there. I was told by a couple colleagues that they were going to delay my making full professor because of the lack of publications, the lack of grants, and yes, probably the lack of publications and lack of grants came from me switching fields. But it doesn't really feel good to know that regardless of the math that you've done in the past, they're looking at the math you're currently doing, and they're going to slow your promotion based on these factors of them thinking you're not being as productive as they would like you to be. I certainly had to suffer through the consequences of switching fields almost mid-career, going from being an assistant professor, to an associate professor, to a full professor right when I was going to make that transition from assistant to associate. I think that's what slowed down the next transition from associate to full, because of this change of fields.
ZIERLER: Again, these conversations are such a wonderful opportunity to convey to a non-technical audience how mathematicians go about their work. When you're working in a field where, as you say, literally, there might only be five people in the whole world who are interested in it and understand what it is you're working on, take me through the intellectual process. How do you get there? What's the wormhole? What does that look like to get to that level of rarified scholarship?
GOINS: Most of us, when we take classes, let's say, in college, we see things like calculus, and sometimes we're told, "Calculus has been around for almost 400 years. Isaac Newton did certain things, Gottfried Leibniz did other things. There are some other people over the years who maybe worked out some results." But most of us think of math as being static, something that was created 400 years ago, and that's it. No new math has ever been created since then. When you take higher-level math courses, these are courses in topics such as number theory, discrete mathematics, abstract algebra, differential geometry, all these fancy phrases, you start to realize that math isn't so static, that even new math is being created literally every single day. One of the issues we have as mathematicians is trying to keep track of all of the new mathematics that's being created. When I say keep track, most of the time when students learn math, they sit there in a class.
And in this class, they have a professor at the chalkboard writing things down, and this is how students learn. But if you're a professor, where do you learn this? How do you figure out what's the new stuff maybe somebody just invented yesterday or the day before? This is the concept of having a seminar on your campus or having a conference that takes place semi-periodically, once every so many years. When you are a professor, you want to have faculty members at other schools that will come to your campus and almost give a class. This is the idea of a seminar. You have some professors sit in a room with your pen and paper, you're ready to take notes, and this colleague of yours, a professor at another campus, goes to the chalkboard, and they give a class or talk on the new math they just invented a few weeks before. It's a great experience because it's almost like you never left school.
You're learning this brand new stuff that this person just created, and you're one of the only people in the world who actually knows that this is brand new math that's just been created. Similar things happened at these conferences, but it's on a larger scale. Instead of maybe having 20 professors in one room on your campus, you might have an order of 100 or maybe even 1,000 people in a room watching this person give a talk that's about the brand new mathematics they just created. Now, if someone who's just created this new math gives enough talks, then there are a good number of people around the country or the world who start to learn what this person is doing. Then, they become very interested in learning more about what this person's doing, so they start a series of emails, conversations, collaborations, they may work on papers together, they may talk with the person more and more to ask this person to run a summer school or a weeklong workshop.
But this is really how mathematics is being built up as a community. The more people learn about a certain area, the more they become interested in the new math a certain group of people are working on, the larger that group grows. There's a plus side and a downside to this, though. The plus side is, mathematics is really done almost like a community sport. When one person starts to explain what they do, more people become interested in it, and then this means that you have now a cohort of people that really interested in a specific area. Math kind of grows organically in this way. You have conferences, you have seminars, you have workshops. All of this is totally outside of the classroom, but this is how the community engages itself and gets to kind of promote new mathematics. The downside is, who's encouraged to be in the room when this new math is being discussed?
As humans are known to do, you have cliques that form, sometimes people's personalities kind of govern who really is allowed to be in the room and who isn't. This means you may have areas that aren't as diverse as they could be. Some areas are known to not have any women involved, some areas are known to have more women than men, some areas have no minorities, some areas have a predominantly strong group of minorities. But you do have these issues now of certain areas of math that now are really determined based on the culture of the people doing the math. That kind of creates siloes in the field. A lot of what I'm saying here isn't just unique to mathematics. It does happen more generally in STEM fields and other academic disciplines. But since I'm a mathematician, these are things that I've seen for years and years. Some of it, I do like about math. But others give me pause. They really make me wonder, is math really all that it could be?
ZIERLER: How unique is Pomona as a place where you could achieve the things you want to achieve? In other words, from the outside looking in, were there any number of top-tier small four-year liberal arts kinds of colleges that could've served as an idea place for you to do this? Or was there something really special and unique about what Pomona was doing then and at that time?
GOINS: There was something unique and special about Pomona. 2016, 2017, when I was at Purdue, I knew I wasn't happy, and I knew I had to leave. It was really weighing on my health, my spirit, and I just knew something had to change. But I needed to weigh all the factors that were very important to me to convince me to leave. Being at a place like Purdue, you could argue I was making a good salary, things were OK living in Indiana, I had a house, I had a research program. But you could also argue that I wasn't really feeling respected in the number theory group that was there at Purdue, I certainly didn't feel that I could have any real social life living in West Lafayette, Indiana, a very small city in the middle of nowhere. But I started to wonder if I were to move to a different city, a different school altogether, how many of those factors would remain?
What if I went to a department where, again, I didn't really get along with the number theory folks in the department because of personality conflicts and what have you? What if I moved to a really small city again and felt that I wouldn't really have a good social life? I had to figure out the very important factors for me. I started to think I wanted to be in a department where I could interact very specifically with Black undergraduates. A department where I could really encourage Black students to major in mathematics, possibly even to get PhDs in mathematics. I wanted to be in a department where I could run an REU, but a very powerful REU where I would not only have outside funding to do this, but I would have a lot of institutional support. If I needed money to have a slush fund so I could hire grad students as TAs or have money to print posters, hire on another undergraduate at the last minute if I needed to, would that department, or the campus more generally, give me that institutional support I needed?
Would I have colleagues that would also feel very strongly about the importance of diversity and the importance of having a welcoming department that would have women and minorities alike to feel yes, they really wanted to major in mathematics because of the culture that was there? But I also had to think of more shallow things, like could I live in a city where I wouldn't have a social life? What about living in a city where maybe I could go see movies? Because movies for me are a really, really important thing. Could I live in a city where the weather would be great, and I wouldn't have to worry about driving in the snow? There was a list of all these factors that were very important to me. Thinking of all of these factors, I could come up with maybe two schools in the country where I would feel comfortable.
And remember, I had traveled around a lot to give talks, to interact with people, to attend conferences, to run conferences. I had a pretty good idea of the different types of schools that were in the country. I really thought very seriously about going to another Research I university like Purdue or the different types of liberal arts colleges that were around, or even going to a historically Black college or university, an HBCU. But I thought very carefully about all of these different departments and what parts of the country I could go to. I can tell you that it came down to two campuses. I would consider either Pomona College or Howard University. Now, Pomona College is about as different from Purdue as you can get. Purdue has around 40,000 students. Pomona has 1,600 students.
The endowment at Pomona is actually larger than the endowment at Purdue. The city that Pomona is located in is actually in Los Angeles County, and there are more people in LA County than there are in the entire state of Indiana. You can't get any more different between Pomona and Purdue. But then, I also thought about Howard University. It's a historically Black college, it's in the middle of Washington DC, it's a beautiful, large city. I would be able to live in a nice metropolitan area where I would have a social life. It's a Research I university. I think technically it's a Research II university now. But the point is, it's still technically research-intensive. I know a lot of the faculty there. It would be a great place to work with Black undergraduates, convincing them to go into mathematics and eventually get their PhDs in mathematics.
There was this serious draw of me wondering which of the two I should consider going to because of this long list of factors. Pomona eventually won out because I really liked the idea of being at a smaller school where I would get to know everyone. I really loved that about Caltech. That feeling of being at a smaller school where you would get to know all of the students, all of the faculty, and all of the staff never went away for me. Being at Pomona now reminds me a lot of my undergraduate days. I love the fact that the classes are as small as they are. You get to know each and every student. I have on the order of 15, 20 students every semester. When I have office hours, students can come in, and we can just chat about random things.
When I walk across campus, I get to wave hello to students I know, I get to wave to my colleagues and faculty members from all these different departments. Just knowing that it's a small enough campus that we do have a strong community was a huge, huge draw. I don't know if I would've found this same tight-knit community if I had gone to a larger school like a Howard University. But I will say that for me, knowing that I have everything that I would've wanted in a school and more is what made Pomona win out.
ZIERLER: Was there anybody on the faculty at Pomona, either on the research side or on the more activist side, that you saw as a partner or the administration of Pomona, where you thought the kinds of things you wanted to accomplish, Pomona is providing an infrastructure to accomplish them?
GOINS: I'll say yes, yes, and yes. One of the faculty members I was leading some of these research groups with–I mentioned that in summer 2010, I led a research group in Providence, Rhode Island, where we were researching these Belyi maps for the first time. There was another individual leading one of those groups named Stephan Garcia. He's a faculty member here at Pomona. He doesn't do number theory, he more does what's called C*-algebras, but he's been known to publish papers in number theory. Stephan approached me a few times after summer 2010 just to ask might I be interested in coming to Pomona. Every time he asked, I said no. He would eventually convince me that because I would come to the Los Angeles area to visit family for Christmas or Thanksgiving, maybe I could just come by to visit the department.
I didn't realize that this was kind of a thinly veiled attempt at an interview, but still just me kind of visiting and meeting people in the department, I realized these were people I really liked and could possibly see myself working with. Still, I decided I did not want to move to a liberal arts. I still wanted to try to make things work at a Research I university. Even after I visited people in the department, I just decided it probably was not going to be a good fit. Another person I got to know very well is Ami Radunskaya. We got to know each other in a very different way because I was president of the National Association of Mathematicians starting in 2015. This is the nationwide group of Black mathematicians.
She became president of the Association for Women in Mathematics, I believe, in maybe 2016, 2017. Somewhere around there. This meant that we were on various committees together and got to know each other very, very well. But now, this is more on the activist side of things. We worked together in trying to find ways specifically to promote Black women in mathematics. This meant that Pomona now had two individuals I had gotten to know outside of Pomona. Stephan Garcia more in the realm of research, but specifically working with faculty members of color to get them to get back into doing research and math. Then, there was Ami, who I was getting involved with more in these activist mathematics ideas by saying, "Let's get more involved with Blacks and women in mathematics."
When I realized they were both in the same department, and that there would be this wonderful synergy if I could work with either of them separately, let alone both of them together, that was a big factor for me to consider Pomona. Of course, there are other people in the department I've known in different ways, but I'm going to say that those two individuals, Stephan and Ami, were a huge factor for me with Pomona.
ZIERLER: Because so much of your work during your last years at Purdue was supported through grants, what considerations or concerns might there have been about the transferability of those grants since you were no longer going to be at an R1 school?
GOINS: That is an excellent question. That was a big, big factor I was very concerned with. I received this grant from the National Science Foundation so I could run this research experience for undergraduates there at Purdue. I had the grant for one year, and we ran one wonderful program. But then, I had to ask the question if I could transfer the grant over to Pomona. The main issue was this. The way we had written the grant was to say students were going to come from all over the country to come to a Research I university to spend eight weeks to do research. We had carefully crafted the grant to say things like some of the research assists would be the graduate students there in the department. A lot of the other facilities we had there, we had classrooms for the students to work in, dorms on campus for the students to live in.
We had to convince the National Science Foundation that if we switched over the grant to Pomona college, it would still have the same resources, the same facilities. There were some serious issues. For example, in order to have a research assistant at Purdue, we would have graduate students. Actually, NSF told us that when we first originally wrote the grant, the amount of money it would take to pay for grad students was so much, where they're worried about paying tuition and healthcare through the grant, NSF actually told us they weren't going to pay for grad students. They actually made us take out of the grant paying for grad students. It actually turned out it wasn't a problem because the Math Department was paying for grad students' tuition and healthcare, so I simply had to negotiate with the Math Department, "Give me two grad students you're paying for anyway, and I'll just have them do research with my students."
And the Math Department said that was perfectly fine. But I had to write to NSF to explain that Pomona didn't have grad students because as a liberal arts college, at best, it had undergraduates. Didn't even have master's students. I had to tell NSF I needed to have extra money to pay for whatever students I was going to hire to act as research assists. I had to be very creative in coming up with a good way to do this. The other side was the facilities. Purdue had these great classrooms for students to sit around and do research, other rooms for students to have offices. I had to prove that Pomona had the same facilities. Ironically, maybe five, six years before I got to Pomona, it had completely renovated the math building so that they had specific rooms designed for students to do research. In an ironic twist of fate, Pomona actually had better facilities to do research than Purdue ever did.
There specifically is a room here at Pomona that will hold, I'll say, about 40 undergraduates. There are chalkboards all around, there are lockers for students to put in their book bags, they have extra movable chalkboards, they have movable desks. It is the perfect room for students to do research. They had never actually used the room because Pomona didn't have an REU. It was just very ironic that when they renovated the building, they had all of these rooms specifically set up for undergraduate research, but they really weren't using the rooms. In that sense, it was a really easy sell to tell NSF, "We're moving from a place that had limited resources"–I had to say on the NSF grant that technically, I didn't have enough space for offices for my undergraduates at Purdue. Because as you might imagine, all the offices at Purdue were for the grad students and the visiting faculty members. They had no extra offices for the undergraduate students. Now, at Pomona, there were more than enough resources.
Most of the faculty at a liberal arts college don't really stay around for the summer. They really want to take the summers off. Which meant we had literally the entire building, something like eight classrooms, this one classroom for students to do research in, that were not being used at all. I could put this in the renewal, the grant we were going to use to transfer over, the paperwork to explain why we were going to transfer it over, that we actually had better facilities. The only part I really had to sell was the hiring of the research assists. But there, I just moved around the numbers a little bit to say I could either hire some graduate students from the Claremont Graduate University, which is literally right next door to Pomona, or I could hire one or two grad students from the local area because here in Southern California, in the immediate area within a 30-mile radius, you have Cal State San Bernardino, University of California at Riverside, Cal State Fullerton, the University of La Verne.
You have all of these schools right here, so I could actually make the argument that having a grad student would be no more difficult than hiring one at Purdue. We did actually have to write a report to kind of explain that we wanted to transfer over the grant, "And here are factors that you might think would be issues but would actually be better at Pomona to have it at Pomona than Purdue." It actually wasn't a problem. Transferring over the grant was pretty easy after that.
ZIERLER: Just on the personal side, was it simply nice to get back to Southern California for you?
GOINS: It was. It was very nice. I still have relatives, friends who live here in the area. A lot of my relatives don't really understand this whole thing of being at a Research I, being at a liberal arts, running REUs, and doing research. As far as they're concerned, I'm moving back to Southern California. A lot of my family was very, very happy that I was able to come back. It really has been great that I'm coming back more at a senior level. Being at Pomona, I am one of the more senior faculty members here. I'm coming back with a different level of respect than I think I had when I left back in 2004, and that's very nice. It really has been great on so many levels, coming back.
ZIERLER: Given the considerations you were talking about, Howard, Pomona, thinking about your options, when you were ready to launch the National Association of Mathematicians Network of opportunities targeting students and faculty at HBCUs, what were some of the challenges not being at an HBCU yourself, and what were some of the opportunities maybe as an outsider not directly in the mix of what HBCUs were going through?
GOINS: Let me start by saying HBCUs historically have not really gotten the respect they deserve. There are roughly 100 HBCUs in the country, either 101 or 103, depending on how you count. A lot of them do have financial issues. Most of your HBCUs are run based on government subsidies, and the government really hasn't been great about giving HBCUs the money that they need to do what they want to do. HBCUs really do over-perform based on the resources that they have. If I remember the numbers right, roughly about 10 percent of all Black students who go to college go to HBCUs. This means that the majority of Black students who attend college are not at HBCUs. Of course, I was one of those students who did not attend an HBCU. However, if you take a look at the Black students who get their PhDs in STEM, science, technology, education, and math, I believe it's maybe thirty percent of those PhDs come from students who have an undergraduate degree from an HBCU.
HBCUs are over-performing when it comes to producing students who eventually get their PhDs in the STEM fields. I was always fascinated by that number. Even just to make it very, very concrete, a lot of people ask me about Blacks who are going to get their PhDs in mathematics at some of your top fancier schools. You could say getting a PhD at your Stanfords, Princetons, Harvards, Berkeley, what have you. A lot of people would tell me in order to get to those fancy PhD programs, you have to have a degree from one of those fancy schools, Caltech, Stanford, what have you. The problem is, that's not true you could take a look and ask a really simple question. How many Black students who have gotten math degrees from Caltech have gone onto these fancy schools?
The problem is, Caltech doesn't graduate Blacks in mathematics. I believe in the history of the institute, there are maybe five Blacks who have gotten their undergraduate degrees in math. Five. PhDs, I believe there's only ever been one. But if we just focus on undergraduates who have gone on to get their PhDs, there have been max five in the history of the institute. Now, I know places like Morehouse College, which is an all-men's HBCU in Atlanta, Spelman College, all-women's HBCU in Atlanta, they have done an incredible job of getting Black students to get degrees at places like Berkeley, the University of Chicago, I can go down the list of all these schools where you have students who have gotten their degrees at these small liberal arts colleges, and they're now doing great work all around the country. Something is to be said for being a Black student at Morehouse versus being a Black student at Caltech.
Why is it that Morehouse has produced more PhDs in math than Caltech ever has? No one ever wants to look at that. This is something that has struck me for years and years. That, for me, is a fascinating concept. I've wanted to be more involved with HBCUs just to learn what they're doing right and what Caltech is doing wrong. On the one hand, I had to spend a lot of time at HBCUs getting to know the culture, about what the faculty go through, what the students go through, a lot about the history, all these things. The more I learned about it, the more I wanted to be involved in running conferences at HBCUs so that you would have faculty members from all over the country, some faculty members who are also at other HBCUs, some that are at predominantly white institutions, PWIs, so they could also learn what HBCUs have to offer. Now, I will say that there are pros and cons to doing this.
On the one hand, I think it's great for everyone to attend HBCUs just to learn about the culture, about the campus, so on and so forth. When I was in high school, people knew about The Cosby Show. But what they didn't know is, there was a spinoff of The Cosby Show called A Different World. Now, A Different World basically took place at an HBCU. It kind of took place at a fictional HBCU named Hillman College. All of us know they were a thinly veiled attempt at discussing Morehouse and Spelman right there in Atlanta. I was in high school, I saw the show. All of my friends in high school saw it. We really had this idealized version of what it meant to be a student at an HBCU. But still, we had this really nice idea that HBCUs were the places to be. I still think to this day that people should go to HBCUs, at least for conferences, to get to know what these schools are like and have to offer.
On the other hand, because I, myself, am not a product of HBCUs, there were a lot of people I met who were very wary of me wanting to learn more or run conferences at them. I think a lot of that stemmed from this worry that HBCUs get a bad rap, that there are these ideas that maybe the students aren't as good, that the classes don't cover as much material, that the money isn't there, that the resources aren't there. A lot of people really have these ideas that HBCUs are less-than colleges, that they just aren't up to snuff compared to places like Caltech. Yet, as I mentioned before, that doesn't make any sense because why is it that places like Morehouse and Spelman have produced far more PhDs in mathematics than Caltech ever has when it comes to African-Americans? There definitely was, maybe in a lot of ways, still is, concern that I am not a product, and therefore, I don't really understand the culture.
And I get it, I understand why the concern is there. But on the other hand, I feel that I, myself, have learned a lot from HBCUs. I have a lot of respect for faculty members that are there, I still say one day I may end up being a faculty member at an HBCU. But it definitely has been a really eye-opening experience to learn a lot more behind just what HBCUs have done for the math culture.
Current Opportunities in the Culture of Math
ZIERLER: Moving closer to the present, I asked you about your experiences during the Rodney King beating and the subsequent riots in Los Angeles. Last year, with the murder of George Floyd, and all of the feelings and sentiments that that tragic event and so many others brought to the fore, for you, for what you are trying to do, what opportunities did you see in that moment as people were thinking about these things and as they were grasping for ways to make that situation better? In what ways did you see opportunity for all of the things that you had been working on up to that point?
GOINS: There were a lot of opportunities I saw. Let's say maybe the year before everything kind of went down, I spent a lot of time trying to get the word out about the National Association of Mathematicians. NAM was formed in January of 1969, where there were 13 individuals who were fed up with not being listened to, not being respected, not being allowed to attend conferences, even staying in some of the hotels that were segregated at the time. There was just this real feeling of something had to change, something had to be different. In 2019, NAM celebrated its 50th anniversary, and I wanted to really get out the history of the organization. Not just to say, "Here are some of the reasons why NAM had formed," but really to delve deeply to say, "Here are many, many racist incidents that have happened in our math community. We all need to know the history of all of these."
Now, I don't know how much of that was really listened to in 2019. Some people paid attention to this. But there were a lot of individuals who just thought, "Well, that happened 50 years ago. It's not the same way now. Things are much better now." And it was really frustrating to try to get out the current numbers to explain things like the number of Black students getting PhDs has been steadily stagnant over the last 50 years. In fact, over the last three or four years, the number of Black undergraduates getting their math degrees has been decreasing. You can actually argue that things have been getting worse over the last several years. Again, this was 2019, me giving talks for the 50th anniversary of NAM on what had happened with Blacks over the last 50 years in mathematics, roughly 1969 to 2019.
I probably gave about ten talks that year. Again, it wasn't clear to me how many people had really listened to this. Now, fast-forward to summer 2020 with George Floyd. It was like night and day. All of a sudden, you had individuals who wanted to talk about race and racism in this country, and what had been happening with police brutality, and why things are so horrible for Black Americans. It was almost like living in the Twilight Zone. The year before, I had been preaching for months and months. A lot of it fell on deaf ears. Now, here it is a year later, and I have people emailing me to say they wanted to hear what was happening with Blacks in mathematics, what's happening with police brutality, and I just couldn't figure out where all of these people were 6, 12 months before. It gave me a unique opportunity as president of NAM to say there were a couple of things I could do, but I really had to do some soul-searching and figure out if these were opportunities I was willing to take.
On the one hand, there was this teachable moment, to be able to say, "Yes, what happened to George Floyd was horrible, but let's look very close to home at what's happening in the mathematics community." And there are a lot of us who really tried to kind of tie in some of the current events with more of the historical events to say, "If you're Black in this country, it's not as simple to say that you're Black and you are a mathematician." Those, you cannot separate. You just can't say you're a mathematician, you have to worry about writing papers, getting grants, or what have you, and then you kind of switch and maybe have to worry about police brutality, and racism, and what have you. There were stories that several of us gave of people who, say, were attending math conferences, but still were harassed by security because of the police brutality surrounding the city or what was happening there at the conference site. We did use this as a teachable moment to say, "You can't separate the two. If you are Black, and you are a mathematician, you have to figure out how to negotiate these two worlds at the same time."
In a more exploitative way, for lack of a better word, I also realized that people wanted to do something with their dollars, so I used this as an opportunity to fundraise for NAM. Up to that point, we had been struggling somewhat financially in trying to raise money, having people to pay their dues, and this was more like an infrastructure type of thing. For example, it's easy to send an email to an individual saying, "Please pay your dues for the year so that way, we'll have so much money coming in for our membership." The problem was, we didn't have a great email list, we didn't have a great database of our members, and we didn't have an online system for people to actually pay their membership fees. This is one of the big things I had to do as president, spend a couple of years setting up all of this from scratch. Going in, writing Excel scripts, trying to actually come up with ways we would know what our database of members was.
Literally, creating from scratch a website so people could actually pay their dues. But once we had all of that in place, I decided to use this opportunity of people really wanting to do something to call out a lot of people, to say, "Yes, you can sit around and say that you really want to do something with everything that's happening around George Floyd. What you as a mathematician can do," and I said this to all of my white colleagues over Facebook and other social media, "just become a member of NAM. At the bare minimum, you can become a member."
Saying that then gave us an influx in memberships and an influx in donations. I don't know the exact numbers, but the organization probably raised on the order of $40,000 to $50,000 in a couple of weeks. Which is insane because I think we had raised maybe $40,000 or $50,000 in the three years I had been president up to that point. We raised a lot of money doing that. Again, it's not clear to me whether that's exploitative or just kind of using the moment. I do know that the organization was able to do a lot of good with that money. It was money the organization really sorely needed to do good. I think there may be a couple of different ways to think about the opportunities we had then. But still, I was pretty happy we were able to use that time as both teachable moment and as a financial fundraiser to help the organization.
ZIERLER: Being back in Southern California and having the perspective yourself of your experiences at Caltech earlier, and many of the ways in which Caltech might've been tone deaf, where there might not have been the infrastructure to support you and people who came from your kind of background, were you paying attention at all to any of the efforts Caltech was making to address those concerns? Have you been keeping tabs? Has it been making good progress as far as you're concerned?
GOINS: I have definitely been keeping tabs of things. I had only come back to campus a couple of times for some of the events. When I got back in 2018, there was discussion of having maybe a display on Black alumni. I forget when it was, it may have been roughly early spring of 2019 when this display happened there on campus. I was kind of around for that. I know that there was a lot more discussion in maybe wanting Caltech to be more visible about featuring its Black alumni. In the same way, I had heard that the students, specifically the Black graduate students, were spending a bit more time to get Caltech to address some of the historical racism, maybe hiring more faculty, increasing the number of undergraduates there on campus, having Minority Student Affairs to have more money so they could do more programming. I've been hearing all of these things rumbling through the networks.
I started a Black alumni Facebook group maybe ten years ago. A few of us have been posting there just to keep track of various things that were happening. But I definitely was hearing some things that were happening on campus. I'm not going to say I attended any meetings on campus about a lot of this. But there were certainly enough grumblings with some of the Black alumni that I could hear what was going on. I can say that I did contact Sarah Sam once or twice, so she was one of the Black graduate students involved with this group called Black Ladies at Caltech, BLAC. She also was one of the few students, I believe probably the only Black student, who was on this renaming committee. Of course, there was all this publicity about her resigning in protest, and I did email her a little bit to figure out what was happening and whether the Black alumni could do more to support her there.
But I can't say I understood all of the fine details of things that were happening at Caltech. I will say that when I first got back in 2018, I was very skeptical that Caltech would change. But this skepticism was founded on me being an undergraduate for four years, being a post-doc for three years, coming back as a staff member, running FSI for one summer, and then even me interviewing alumni going as far back as the 1950s to see how much had changed over the years. The unanimous answer over all of these different experiences was, "Caltech will never change." I will say over the last maybe three years, maybe I've been wrong about that. It does feel that Caltech has made some changes.
I still have a wait-and-see attitude to see how many more. But I have been very happy to see the number of Black faculty at Caltech is larger than it ever has been. I think the numbers may be eight Black faculty now. The number of Black undergraduates at Caltech is larger than it ever has been. Caltech just admitted its largest Black freshman class ever, which I believe is maybe sitting at 30, 40 students. I'm not quite sure. I'm hopeful. I'm hopeful with what I've been seeing. Where I have a hesitance about this is, I've seen similar things in the past, where there's been some progress, but then based on any number of factors, faculty members decide to leave, undergrads decide to transfer, that progress that's been made drops off. The numbers, while they look good to start with, eventually drop to zero.
When I started in 1990, I believe there were maybe 14 Black students that came in. The year after me, 1991, I believe there were maybe 12 Black students that came in. By 1996, I think it was, the Chronicle of Higher Education featured zero Black students in the freshman class. I want to say that happened maybe a second time in maybe the year 2000, 2001, something like this. Early 1990s, there was this feeling of, "Caltech is making a change. Caltech is getting better." And then, a decade later, we had all these reports saying, "Caltech had zero Black students in its freshman class." I'm optimistic that Caltech is making changes now. I've been seeing a lot of internal discussions there on campus with the staff, with the faculty, even with the president. But it's this hesitance of, "I've seen this before, and I'm curious how much of this is going to stick."
ZIERLER: Back to the grant-supported research, the Pomona research in mathematics experience was previously NSF-funded and now is NSA funded, I wonder if the takeaway there is that you saw these infrastructure availabilities at Pomona, and you've really been able to build this dream of yours of making a powerhouse research environment at a very small school that can be supported not just by one federal agency, but by two. I wonder if that's sort of the broad scale takeaway in terms of what you've been able to achieve and what you hope to build on going into the future.
GOINS: That is a good question. I had to think big picture of how I want to scale up what I want to do. This is just maybe some insight in how I decided to play more of the political financial game here. I knew I could transfer the grant from Purdue University to Pomona college, and that was the NSF grant. There were roughly two years left on that grant. We got the grant in 2016, so we ran the summer program for the first time in summer 2017. when I got to Pomona, I decided to not run the program summer 2018, so then technically, the last year of the grant was summer 2019. I decided to try to extend the grant for one year just because we had a lot of money left over. Technically, we really ran the grant for the last time summer 2020. But by then, I started to think, "I want to expand things greatly."
The grant we had up to that point was around $350,000. But I decided I wanted to ask for much more money and ask for about a million dollars from NSF. I realized it was kind of ambitious to literally triple the amount of money you're asking for to run a much more expanded program, so I thought, "Why don't I have a backup plan?" I said, "Let me apply for money from a second agency, just in case, so I'll have the money, and if things don't work out with NSF, I can apply a second time. Hopefully, second time's a charm, everything will work out." As we closed out the funding from the NSF grant I got back in 2016, I applied for funding through the NSA, the National Security Agency.
That was supposed to be a two-year grant as a backup. But it was going to be the same thing we had done with PRIME from before, have a group of students on campus all do research, so on and so forth. We got the grant from NSA, the current grant that we have now, but while we were waiting on that grant, I applied for the big NSF grant roughly for a million dollars. Much to my surprise, we got the NSF grant. We didn't get it for a million dollars, we got it for almost $600,000. But that's the big grant now that I'm going to use to expand prime the way it is. It does look a little bit weird that I started with a National Science Foundation grant, moved over to a National Security Agency grant, and now I'm going back to a National Science Foundation. But that's all because it was part of this big political plan, just from thinking, "There are these different agencies out there. Why don't I just apply for funding from all of them and see what happens?"
I felt very, very fortunate that this all has worked out. What I'll say is, Pomona has been really great at being very supportive about a lot of these things. It's not easy to write a grant. It's not as simple as you kind of write ideas down on paper, and you send it off to this government agency, and then some people look at it, and then they put a stamp on it saying, "This is a great idea. We're going to give you money." Doesn't work like that at all. You have to worry about the internal paperwork of how all this happens. For example, I had to write a 15-page document that outlined why we were going to do this. We had to look up the literature and numbers of how many minorities were getting their PhDs in mathematics, the historical trends and current trends.
We also had to explain the actual research the students were going to do and talk about the more general experience, bringing in outside speakers, taking them on field trips, the facilities they'll have here on campus, the classrooms they'll use. We then had to talk about historically if what we've done in the past made any difference. This meant I had to track down all the students I've ever worked with, figure out how many of them have gone off to grad school, what grad schools they went to, what kind of degrees they had. I really needed to say, "In all of the work we've done over the years, here's the impact the program has made." This is a lot of work you have to do to put together all of this document. It really just isn't as simple as, "They're going to do math. Give us money."
You really have to explain, "Here's why we're doing this, and here's the impact it's going to make, plus here's the impact it's made in the past." Even on top of that, you know to worry about the numbers and how the numbers are going to match up with what's happening at Pomona, you have what's called overhead cost, so Pomona actually gets a little bit of its own money on top of the money I get. This means that Pomona gets something out of this, too. In me getting all these external grants, Pomona also gets money, and some of this is used to help pay for the staff that's here on campus. I know I use some of this extra money to help pay for some other little things like buying t-shirts for the students.
There are also some extra perks that Pomona itself gets out of getting these grants. But it's like a symbiotic relationship. With Pomona helping me to get all these grants, there are great things I can do for the students. But in me getting these grants, I get to help out the larger Pomona community and actually help them to pay for some of the staff members that are here, people I'm never going to see, but they're still kind of helping me behind the scenes.
ZIERLER: Your other grants that are currently in process that emphasize the term African diaspora, I wonder if the takeaway there is that with these grants you're emphasizing that greatness in Black mathematics goes beyond the United States, that there's an African diaspora mathematics community really all over the world, and that you have your sights set globally on what they've been able to achieve.
GOINS: That's definitely right. when it comes to working with students, it's a little bit tricky because a lot of your federal funding agencies, National Science Foundation, National Security Agency, typically restrict the funds to US citizens. I may have students from the diaspora, from other countries, but I need to have students who are currently working in this country. That being said, I can still do programs for faculty members that don't really depend upon country of origin or even the country they're working in now. I've been working with the Mathematical Sciences Research Institute, MSRI, up in Berkeley, California. There, we've put together a program that focuses on encouraging Black faculty, faculty from the African diaspora, to continue to build their research programs.
This means they come into MSRI for two weeks, they're working in these research ensembles, probably about four to six individuals, other Black faculty, and they're all working together to do research. I have been seeing incidents where Black faculty more generally would like to do research, but maybe they aren't feeling as welcome in certain research communities, they might feel shunned, let's say, if they attend a conference. They're rarely invited to give talks, part of these big invited addresses at some of these workshops. Which means there are more and more Black faculty I've been seeing over the years that don't have the opportunity to showcase their work as many of their white colleagues do. As I was saying earlier today, the way that mathematics really works is, new math is being created all the time.
And for this new math to be exposed, people really do need to give talks at seminars, conferences, and workshops. Well, if you aren't being invited to give talks at seminars, conferences, and workshops, no one knows the kind of mathematics that you're doing. This is just the way the math community works. You have to be invited so people know the kind of math you're doing. I've been working with MSRI to help remedy this, to make sure that you have faculty members from the African diaspora that are now working together in groups, building up the research programs so that now they're going out to give talks, to talk about their research, so that more people actually know what it is they're working on.
As part of this whole project, we have a session that takes place at the largest math conference here in the country, called the Joint Mathematics Meetings, where we ask the alum from our research group to give talks here at the session. This means that at these Joint Math Meetings, where there are around 5,000 to 6,000 mathematicians, we have about 20 or so faculty from the African diaspora, people who were a part of this research group, get up and give talks on the research they've been working on for the last several years. I personally love doing this because it really does give Black faculty from all over the world the opportunity to talk about the research they've been working on. I will say I have really been trying to think more about the international community, what Black mathematicians all over the world go through.
One individual I've been learning a lot from is named Nira Chamberlain. He's over in England. He's actually from Jamaica originally. But he's been a huge proponent in Blacks from all over the world who do mathematics. He's been running this conference for the last several years in England called the Black Heroes of Mathematics. Nira was kind enough to invite me to speak at his initial conference two years ago, but the second conference just took place a couple of months ago. I believe that Nira plans to run this conference every year. I love to attend it because he's featuring Black mathematicians who are not from the US. They really are from all over. These are individuals I, myself, would've never been exposed to.
There was another conference that I was invited to speak at that was in the Netherlands. Of course, I didn't actually go to the Netherlands. Everything's been virtual conferences over the last couple years. Unfortunately, I wasn't there. I actually had to present everything over my computer. But this conference was supposed to focus on diversity more generally there in the Netherlands, especially there in the university system. I asked to speak with the Black undergraduates because I have no idea what it means to be Black, but as part of, say, a Dutch culture. We had some really interesting conversations. Some of the students were telling me they grew up in some of the former Dutch colonies, for example, Suriname, which now has a huge influence in Dutch culture.
Other Black students were telling me they actually grew up in the Netherlands. But because they don't look blond-haired, blue-eyed, they really aren't treated like Dutch citizens. I'm starting to learn that the Black experience really is unfortunately the same all over. In chatting with these maybe 20 students or so for about an hour, I honestly thought I was talking with my undergrads at Pomona College. Because we had some really interesting conversations on the terms they like to call themselves. Do they like Black? Is there another term they prefer to use? When they're there in college, do other students consider them to be students from the Netherlands? Do they treat them differently because they're from other countries? What about police brutality? Are they stopped by security when they're in the cities?
Every single thing you can think of, these students in the Netherlands were telling me exactly the same I'm hearing here in the United States. When I use the phrase African diaspora, I really am understanding that unfortunately, there is a universal experience that we do experience. It's been really great for me to learn this over the last couple of years.
ZIERLER: One final question to wrap up this excellent series of conversations we've had. Right now, and looking into the future, your most recent appointment is at Claremont Graduate University. I wonder in what ways having access at the graduate level allows you to continue to pursue your own research interests and to broaden out what you're doing for minority students at the graduate level, not just at the undergraduate level.
GOINS: There have been a lot of huge factors that convinced me to come to Pomona, but one of the huge factors was having the opportunity to take on graduate students. It does feel a little bit strange in that yes, it is true that I left a Research I university to go to a liberal arts college, but Pomona is very unique in how it's situated here. There are the five Claremont colleges–Pomona, Pitzer, Scripps, Harvey Mudd, and Claremont McKenna–but technically, we consider there to be seven Claremont colleges. The extra two would be the Theological Seminary and the Claremont Graduate University. That means every faculty member that's at one of the five Cs can be an affiliate faculty at CGU. This means I can take on grad students, I can teach graduate-level courses.
And when I realized I had the opportunity to do that when I moved here, that just convinced me it was the perfect situation. It looks on the surface like I no longer have the opportunity to teach graduate-level courses and to take on grad students, but that's actually not true at all. I think that's very specifically because of where Pomona is located. I don't know many other liberal arts colleges in the country that would give you that opportunity to take on PhD students. But fortunately, Pomona does have it. I have been trying to think about a much larger picture, and this is just me almost talking off the top of my head because I really haven't figured all of this out. Coming from Purdue, there are a lot of people who do want to listen to the experiences I had having graduate students, serving on the graduate admissions committee, reading graduate applications, and also now working with undergraduates, trying to prepare them for graduate programs.
I want to find a way to leverage that by being an affiliate faculty at the Claremont Graduate University, but more importantly, realizing that I do have a lot of these contacts in the Research I math community. For example, one thing I've been talking with some R1 faculty with recently is this idea of maybe holding a panel discussion, where we would have directors of graduate studies at various R1s to come to a place like Pomona College to sit in a room and tell students, "Here's what we are looking for when we read grad school applications." I don't know if that's really ever been done before, at least in the mathematics community. Typically, you would have maybe some former undergraduates who are now in their grad school programs who may come back to Pomona and talk about when they applied to grad school and that whole experience.
But there's always this general uneasiness of nobody in the room really knows what grad schools are looking for when they read applications. In the same way, at a lot of your Research Is, they've never worked in liberal arts colleges, so they have no idea what undergraduates I liberal arts colleges are going through, the classes they've taken, some of the questions they have about applying to grad schools. I've been wondering, what if you get those two groups together in the same room? Some of the faculty who are at R1s to now talk to undergrads who will be applying to the grad programs, and some of the undergrads who are applying to grad programs now talking to some of these faculty.
What if they can all get together in the room at the same time and talk about this whole experience? I'm really thinking that I can kind of use my unique experience now in both worlds to do things like that that have never been done before to my knowledge. But I feel really fortunate that I think Pomona, being here at the 7Cs, is really the right place to be to do that.
ZIERLER: You've been on a journey your whole career, and it sounds like finally, you're in the perfect spot.
GOINS: I think so. I do.
ZIERLER: Edray, it's been wonderful spending all this time with you. I so deeply appreciative that you were able to share all of your insights and perspective. It's going to be a real treasure for the Caltech Archives, so thank you so much.
GOINS: Yeah, thank you. Thanks for your time.
- The Meaning of Minoritized
- Math as a Human Endeavor
- The Beauty in the Numbers
- A History of African American Excellence in Math
- The Story Behind the Name
- From South LA to Pasadena
- A Meeting that Changed Everything
- Interacting with Extremes
- A Breakthrough at Stanford
- A Grand Tour of Mathematical Institutions
- Galois representations at Purdue
- Diversifying the Field
- NSF Partnership
- Back to California
- Current Opportunities in the Culture of Math