Jim Simons: Math, Codes, Hunting Talent, Stocks, & Science

Hi, I'm Lawrence Krauss, and welcome to the Origins Podcast. This week, my guest is a true Renaissance individual, Jim Simons, who's had at least three amazing careers. He's most well known to the public as the billionaire founder of Renaissance Technologies, a hedge fund firm which established the modern era of what are called quants, quantitative analysis and data mining in order to do stock trading. But Jim's had a distinguished career in mathematics before that, in fact, created something which has become very important in physics. And I first heard of Jim as a physicist for his contributions that had affected our understanding of what are called gauge fields. And we talk about that in our discussion.

Jim was not just an accomplished mathematician. He had a very interesting career as a codebreaker and then moved to become chair of the department at Stony Brook, the mathematics department at Stony Brook, building a very distinguished department there before switching careers completely and moving into creating what is now Renaissance Technologies. Most of the discussions with Jim have focused, of course, on his stock career, but I wanted to talk about the influences that led him to be a mathematician and to think about the, create the tools that would later on be used to help him in his current career. And we discussed everything from the nature of mathematics and science to the importance of empirical data and its use and also to how the techniques that he's used in stock trading may be relevant to the kind of things that AI is using now and some of the implications of that for the future.

It was a wide-ranging and fascinating discussion. We also touched on Jim's interest in supporting science through the Simons Foundation and his interest in public understanding of science. In fact, I first got to know Jim when I lectured at the World Science Festival, one of the things he supports. So I hope you'll enjoy this remarkable conversation with a remarkable individual, and I hope you'll get some new insights into Jim Simons. For those of you watching this on YouTube, I hope you'll subscribe to the podcast on YouTube. Only a few percent of the people who actually watch our program subscribe to it on YouTube. And by subscribing to it, you'll learn about new podcasts and you'll be able to participate in other aspects of our podcast and our foundation.

Also, if you would be interested in supporting the Foundation directly through a Patreon subscription, that would be very helpful. If you have a Patreon subscription, you can watch these podcasts without advertisements and also to participate in other things like our monthly live Q&A with me on a variety of subjects and other programs that we're involved in. So I hope you enjoy the podcast, and I hope you'll help support us through either subscribing to us on YouTube or subscribing to us on Patreon. Thanks again. Well, Jim, thank you so much for taking the time to join me on this podcast. It's a real pleasure to see you again and a real privilege to be able to talk to you. So thanks for coming.

Okay. Well, happy to do it, I think.

Well, we'll see in the end if you do it. I already have benefited tremendously from this without even initially talking to you about it because you'll see that I actually learned that you had a huge impact on my life without knowing that you had until I began to research more about you before doing this. We've talked a number of times over the years, and I knew some things, but it was fascinating to learn more. You know, I've also watched some interviews with you, and I want to try and do, you know, our discussion to be somewhat different. And I hope it will be covering some different things. But this is the Origins Podcast, and I do want to go over your origins. And I've noticed you say a number of times that you always liked math, that you always liked math as a child.

But I haven't heard you say why. What was it about math that...

What was it about math that made me like it? I don't have the famous, the faintest idea. I just I just liked it. I liked counting. I liked doubling 248 16 all the way up to 1028 or whatever it is. That was far enough for me. But I would do that often actually.

And so when you say often, how—when you were, how young? Just when you first learned to count?

Three or four, when I'd learned to count.

And you knew it was math. I mean, the point is that you recognized it as mathematics.

Well, I—I didn't know mathematics. I knew counting. Uh, but, uh, I did something very early in my life that, uh, showed I must have some ability. Maybe I was four years old and we were driving. I was riding with my father and he says he has to go to the gas station to get gas. I said, 'Well, why do you need to get gas?' He says, 'Well, we could run out.' And I thought for a minute and I said, 'Well, you shouldn't be able to run out. You just use half of what's in the tank. Then you use half of that, and half of that, and half of that, and half of that, and you'll never run out.' That was like Zeno's paradox.

Yeah, you had rediscovered Zeno's paradox at age—

I did. On the other hand, it didn't occur to me, 'Yes, but we wouldn't get very far.'

Exactly. Well, no, in fact, okay. Now I've heard you mention the Zeno, this Zeno's paradox and discovering it when you're young, which is fascinating. The—and the fact that it hadn't occurred to you that you wouldn't get very far, but one thing I hadn't heard, and I wanted to ask you about that specific story—so I'm glad you brought it up—was: who—did anyone give you the resolution? I mean, did Dad say anything, or did anyone... When did you come to realize that that paradox was sort of solvable, or at least finite? I mean, was it much later, or...?

I don't remember. I don't remember.

Well, let me go back then to actually you interacting with your dad there, because I wanted to talk about the influence your parents may or may not have had on you in terms of your interest in math or science or anything else. Your father was a businessman, or no?

Yeah, well, he was in business. He was first... He worked for 20th Century Fox all his young life, actually. He... He graduated eighth grade. And then, uh, I think he actually took a job with them delivering films or something. Uh, and he went to night school, but he kept falling asleep. So he didn't finish night school at all. So he was with 20th Century Fox in those days. Um, well, in those days, he became a salesman after a while. And in those days, the company, the movie company, would have five films that they were peddling at a time. And you had to take all five. So the theaters had to take all five. Now, luckily, they had Shirley Temple.

Yes, sir.

Everybody wanted Shirley Temple. So as long as the five had a Shirley Temple in it, which it didn't always, of course, they would take all five. So he drove around later in New England. And I have a distinct memory, and I was quite little, of my mother leaning over me in the crib saying, 'I hope your father is going to be all right.' And I think that was the hurricane. There was a very big hurricane in New England. And I think that that was the hurricane and he was out on the road somewhere. But anyway, he did, he drove around and then he became the sales manager. And, uh, so he could stay home and, uh, you know, work, work from the office at home. And then, and he did okay. My grandfather, who had a shoe factory and was a wealthy guy—

In Boston or in Massachusetts?

In Massachusetts. It was in Haverhill. The factory was in Haverhill, which was north part of Massachusetts. And he told them, oh, he would do fine and he'd get a piece of the business. So my father took the job, but he really didn't like it. He really didn't like it. And as for getting a piece of the business, it turned out my grandfather made a lot of money, but, uh, he also spent it as fast as he made it, uh, on horses. And he was quite a womanizer as it turned out. I didn't know that when I was young, but he, uh, you know, he liked the ladies. So, uh, my father was, uh, just kept working for him. He probably got a raise of some sort, but, uh, he really didn't like the job, but he, uh, well, that was it.

He didn't like the job, but he stuck with it for quite a while. Finally, my grandfather sold the shoe factory and he went to work for the guy who bought it. And, uh, so he was, my father was in the shoe business for many years.

Interesting. So was my father, in a different way. My father just sold shoes, didn't make them. Oh, well. So he had an eighth-grade education when he went out to work, and then he tried to do night school. So, he never had a high school degree or anything like that?

He took a course once at Harvard, an extension course or something. That was all. Maybe that was in business, or I don't know what the course was. Okay.

Now, your mother, did she have any more education than him, or no?

Yeah, yeah. My mother had a high school education. In those days, not so many women went to college. Sure. And she didn't go to college, but she did go to art school. She was a pretty good painter. And she went to art school and some kind of finishing school, I think, whatever they call it. But she didn't go to college. And I was an only child. Not for want of trying. But my mother had four miscarriages after I was born. Wow. And turned out that there was something wrong with her uterus, and she had to have what's called a hysterectomy, which—which they remove the uterus and you can't have any more children. And so, of course, I didn't know this at the time, uh, that she had a hysterectomy. I knew she went to the hospital, and, uh, I missed her. Kids weren't allowed in the hospital at that time, but my father took me to the back of the hospital.

And my mother came to the window, and that gave me confidence that my mother was still around.

Okay, now this is interesting because I was wondering whether either of them encouraged—well, look, first of all, I assume—neither of my parents finished high school, and I was a young Jewish kid, and they wanted me to be a professional. I would be surprised. They wanted me to get an education in particular. They wanted me to get an education. So I'm assuming the same thing for you. Did they encourage you to—they wanted you to get an education because they had not?

Oh, definitely. Uh, they wanted me to get an education. And, um, well, I went—I grew up in Brookline, Mass., which is a suburb of Boston. And, uh, we lived in an apartment building and, uh, in fact, uh, about three or four months ago, I got a yen to go back to Brookline and walk around and see what it was. And Marilyn, my wife, came with me. And the first place we went to was the apartment building in which I grew up. And I hoped that, uh, I could see it again. We rang a superintendent's bell, but no response. So we just went up to the door and, uh, buzzed the number. Uh, she made some noises, but we couldn't make it. So we just walked up the two flights. It was on the third floor, but we were already on the first floor.

And knocked on the door, and she opened it. We explained who we were, and she was delighted to let us in.

Oh, wow.

So if I'd been alone, she might have been a little more dubious, but since I had my wife...

Yeah, sure. Well, look—sorry, go on.

So, I grew up in Brookline, and... but in the... and I went through the ninth grade at Brookline High, but then... my parents bought a house in Newton, a small house, and... That was great. I loved that little house. But one thing: it had two bathrooms.

It's very important for a teenager, I guess.

When I was a little kid, you know, sometimes I'd come running home because I needed to use the bathroom and someone was in it. Here I was, whoa, two bathrooms! One will always be free. And then I went to Newton High School. And Newton High School actually started in sophomore year because they had junior highs—Brookline did. So I entered Newton High School, and it's a very good high school.

Sure.

I got a good education there. And, and, of course, I really liked math. And I had a terrific math teacher.

I was going to ask if you had, if you had good math teachers, uh, if—I mean, one—we'll get, uh, getting ahead of myself, but one of the many things you've done is support Math for America and, and the importance of good teachers. So I wondered—I've heard a variety of things. Some people do very well with no good teachers, but, but, um, uh, you had good teachers that encouraged you, eh?

Yeah, he encouraged me. Uh, it was, he taught plane geometry.

You know, there's theorems and proofs. Yeah, I love that stuff. Me too. Yeah, it was fun. Yeah. Uh, did you—can I ask you that, just to raise the question? One of the things that was fun—geometry was probably the most fun, I think, maybe in high school. But one of the reasons was, and I don't know if that's ever happened to you, but, um, there'd be proofs you'd have to give for certain things, and they'd be on quizzes sometimes. And it was always such a thrill when—when I happened to come up with the proof, which was not the proof that was in the book or that the teacher was expecting. And it's such a reinforcement when you realize, 'Hey, I've done something different.' Did that happen to you?

I don't recall that. I don't recall that happening to me. It certainly may have. This was when Advanced Placement was just starting. And Newton High was a guinea pig for that. So it was called the Kenyon Plan. And so I think I got some calculus even as a junior.

And then as a senior. And, well, I just loved it. And I tutored math. To young kids? Yeah, to kids who didn't do so well. I tutored. And it paid pretty well. And I really enjoyed tutoring. It was very satisfying when, let's say, I'm thinking of a girl in particular, when she took her test, she did okay. And she certainly wouldn't have done okay if I hadn't been tutoring her. And it still wasn't true with the guy. So I did some tutoring and I worked in a, I always wanted to work. I always wanted and, uh, had a funny experience over Christmas. I think it was this sophomore year. It was my sophomore year, which was my first year. There was a store garden supply store called Brex, not so far from the house.

And, um, they hired me, uh, to work in the stock room after, uh, after school. But I was terrible in the stock room because there was no rhyme or reason of where the stock was kept. It wasn't alphabetical or anything like that. I was supposed to bring up stock to the main floor or put it away. And the couple who ran that stock room was a little frustrated with my inabilities. So they said, 'Okay, your job is now floor sweeping.' Okay.

That you could do.

I loved that job because I could just push the sawdust around, sweep the floor, and think. And I loved just thinking. So at the end of the season, they talked to me. We sat down. They said, 'Well, what are you going to do when you grow up?' And I said, 'Oh, I'm going to study mathematics at MIT.' They laughed so hard.

They didn't see that. They didn't see the connection that those of us who are academics clearly see between pushing a broom around and thinking, and sitting at a desk and thinking.

Yeah, right. So they laughed. But I did go to MIT and study mathematics.

And you never—I think you never went back and sort of said, 'I told you so,' to them? No, I did not.

The next year I got a nice job as a soda jerk Uh, in a drug store, uh, work there, uh, from three o'clock in the afternoon till six. And I really liked that job. Oh yeah. 65 cents an hour. And, uh, I got my first girlfriend there, a girl who she came in to buy something. I said it's a calendar. And I always work with my arm, my shirt rolled up.

Just above my elbows. And she said, she was kidding around. She said, "Don't your elbows get cold?" I said, "Well, no." And the next day, she came in with elbow warmers that she had knitted. Two woolen triangles just to slip over my elbows with some straps that you could strap them. So I thought, "I think this girl likes me."

I figured, yeah, yeah, that was a pretty good guess.

She became my first high school girlfriend.

Oh, that's a lovely story. Did you get to also drink all the profits? Not all your profits, but I suppose you were allowed as many sodas as you wanted while you were working there?

Yes, I could. But I didn't like sodas, but I had ice cream. I could have ice cream. Funny thing happened there. Well, a couple of funny things. A woman came into the store and she wasn't soda fountain. She wanted some aspirin. I think she wanted three things. And I knew what they cost. And I added it up in my head and said, "Okay, it's $4.95," or whatever it was. And the owner of the store came rushing out and said, "Didn't you do that on the cash register?" because there was an adding function. I said, "No, I just did it in my head." Well, he did it on the cash register, and he got the same answer I did. From then on, when doctors came in—because he loved doctors because he made most of his money giving prescriptions—and he would call me over and say, "Watch this."

And then he'd rattle off three or four numbers. Maybe they were even big numbers. "How much is that?" And well, I gave an answer. Sometimes it was right, sometimes it was wrong, but no one knew what was right or wrong. And so he touted me as a genius.

Oh, that's nice. Well, you mentioned doctors, and I want to get there in a second because when we get to your—well, let's go back to your parents for a second. So they wanted you to be educated. Did they want you to be a doctor? Did they ever—did they encourage an interest in science or math? They knew you were interested in it. Did your parents specifically encourage that?

The one who wanted me to be a doctor was our doctor.

Yeah, that's what I heard, actually. Your doctor wanted you to be a doctor.

Right, right. The doctor wanted me to be a doctor. He knew I was a smart boy. And a doctor is a great job. And I didn't want to be a doctor. But I said, "You know, I want to be a scientist of some sort." I knew enough to know that. And he and he said, "Yeah, but you can't make any money that way." Well, I showed him.

That's right.

It took a long time.

Yeah, no, it's interesting, because my family doctor wanted me—my parents wanted me to be a doctor, that's why, and my brother to be a lawyer, and he became a lawyer, and then there was more pressure on me. And my family doctor, who was a person I revered, actually, because I was—because my mother had made, I would say, the mistake of encouraging me to, wanting me to be a doctor and telling me that doctors were scientists, and that got me interested in science.

Yeah, well, doctor, well...

To some extent. And to some extent they were, but you were much wiser than me. You knew right away you didn't want to be. It took me a long time. I was probably in my second-to-last year of high school before I suddenly realized that I liked science and that doctors weren't necessarily scientists. So it was a big blow for my mother. But in your case, it was just that it was your family doctor. But you know, you knew you wanted to do math and you knew you wanted to go to MIT. You even told them.

I thought I'd go to MIT. I also applied to the University of Chicago, where I was accepted. And I applied to Princeton, where they didn't accept me, and Brown, where they didn't accept me. But MIT and the University of Chicago are two places that were better than Brown.

Yeah. In math especially.

Yeah. I decided to go to MIT. It was close to home.

Is that the reason? I was wondering whether it was because it was close to home.

It was close to home, and I went to MIT, and I graduated in three years, actually, because I had taken Calculus I in high school, so I skipped that. At MIT in those days, if you studied a course, you didn't take the course, but if you studied it on your own and passed the final, you'd get credit for the course. So, uh, I did that in a few cases, and I took a course in summer school. And so I graduated in three years, and I—and I took a lot of math, even in my freshman year. In the second semester, I took a graduate course, which said 'no prerequisites.' So I said, 'Oh, great.' And it was abstract algebra, which is what the course was. And, well, I passed it, but I found it confusing. I didn't really understand why they were doing some of the things that they were doing.

But that summer I got a book on the subject, and within a week or two it clarified, became totally clear why they were doing these things. And so, uh, I took the subsequent courses in the next two, you know, two years, they were all on, which got tougher and tougher. And, uh, I think I was the only undergraduate, uh, in those courses. But, uh, so I took a lot of math there.

Now, you know, by the way, I should add that, you know, I think that policy—well, I know they have that policy, at least when I did my PhD at MIT, and that for me was a saving grace, this policy of not having to take the classes. They had these qualifying exams for your PhD, and the general rule was you took two years of courses and then took the qualifying exams. But they let you take the qualifying exams, even if you hadn't taken the courses. And I gambled. I thought I had an education—Canadian, I thought it was good, I thought I could fill in the holes. And I passed those exams. And that allowed me to... And what did you study at MIT? I did my PhD in physics, although at the time it was mathematical physics, because we'll get to that.

Because I did my undergraduate degree in mathematics and one in physics. And in fact, I want to ask you about that, because I want to ask you: why math and not physics for you? I didn't like physics. Why didn't you like physics?

I didn't like physics because, in some sense, I didn't... Let's take the notion of a force. You know, what is a force? You know, if they had written down a vector field.

Yeah, over the real world.

Something, but I just, I didn't like physics. I had to take a physics course.

Sure, yeah, yeah.

You know—I didn't like physics.

The reason I'm asking is it fascinates me because when I was an undergraduate, I also did history, but then my university, the most challenging course was you could do two degrees at once if you did mathematics and physics. I thought, okay, I'll do that. It was up in Canada. I thought, OK, I'll take that because it's challenging.

No, for my PhD. As an undergrad, I was in Canada. I went to MIT for my PhD. And so I took math. And I took math with all these very good young math students and physics. And it was a revelation to me. Well, first of all, interestingly enough, what you said resonated. I did very well in math. But it was an abstract algebra course when I realized, and I got an A in it, I remember, but I realized I had no idea why they were doing what they were doing. And that was when I realized that I wasn't, you know, that if I hadn't realized already that I wasn't a mathematician, that I could do math well, but I couldn't see where to go next. And whereas in physics, it was quite the opposite. And what was a revelation to me was there were a few kids in that math group who were much better mathematicians than me.

And I thought for them, physics would be a breeze because for me, physics and mathematics at the time seemed identical, and these kids couldn't do—I found the physics courses very difficult, and it flabbergasted me that I thought a good mathematician should automatically be a good physicist, and it wasn't the case. It was a surprise to me. Sometimes the case, but sometimes isn't. Anyway, I did not like physics, but amazingly, some of the math that I did later in life—of course, we'll get there. I knew you first for Chern-Simons, I guess a lot of people did, but I want to get there slowly. You say you didn't like physics, but you said something in an interview somewhere that fascinated me because, again, I guess I resonate with a number of the things you said in a number of different areas.

But you said, you know, I was going to ask why geometry rather than algebra or number theory, or what was it about geometry? And that's the fundamental question. But let me preface a little. At one point, you talked about Stokes' theorem and how beautiful it was. And it is, to me, one of the most... To me, it's what encouraged me to be a physicist. The beauty of Stokes' theorem, that you could understand the details that were going inside a volume by understanding what just happened—you know, measuring things in the boundary and measuring, basically, counting field lines going out of the boundary. It was beautiful. And I thought that's the beauty of physics. But obviously for you, that was the beauty of mathematics.

But you did say—was it Stokes' theorem or something like it that encouraged you to—why geometry and not the other areas of mathematics?

Right. Well, I didn't like number theory particularly, and algebra I was good at, but when I started learning differential geometry, I think it was there that we learned about differential forms and the modern version of Stokes' theorem. I was just blown away. And I knew that I wanted to study differential geometry. That was what I wanted to study. That's beautiful. So I graduated in three years, but I stayed as a graduate student for another year, and I worked with a guy named Singer.

I know Isadore Singer. Yeah, I know him.

And he taught me Lie groups and Lie algebras and that kind of thing. I loved it all.

Yeah.

But then they suggested that since Chern was leaving the University of Chicago to go teach at Berkeley, I should go to Berkeley and work under Chern because he was the great man in differential geometry. So I said, okay, and I got a nice fellowship. And I went to Berkeley. Regrettably, Chern was celebrating his first year at Berkeley by taking a sabbatical year.

Probably part of the deal he made. Probably was.

So, uh, yeah. Yeah. So, um, so I worked with a different guy, and it worked out fine.

Bertram Kostant, right? Kostant. Now, did he later on move to MIT? Yeah, because I thought I knew him when I was at MIT. I don't know whether I sat in a class from him, because we'll get to this. Geometry of Gauge Theories was what caused me to want to go in to do my PhD at MIT. So yeah, Kostant, I knew him. Yeah.

I, yeah, we, we hit it off pretty well. And, uh, and, and there was, uh, and I, I just started diddling around with some playing around with some theorems that I was creating. And, uh, he, he told me, 'Oh, that's interesting, it might apply to this problem.' Uh, that was an open problem, uh, but he said, 'But don't try that because Singer couldn't do it and Borel couldn't do it. So I don't think you're going to be able to do it.' But that got me going.

Of course, that challenge, especially if you're young and ambitious.

Yeah, I just got further and further on it. And I actually... shared what I was doing with Singer by mail, and he encouraged me. Oh, that's good. He was encouraging. And I got pretty far. I got pretty far on it. And that winter, we were going to go back to Boston. I had gotten married while I was in Berkeley, and so we went back to Boston to... see our parents and all the rest. But I was stuck in this theorem that I was trying to prove. And I was stuck. And so Singer and I agreed to meet at his office. There was a tremendous blizzard that day. But so we sat down and he said, 'Okay, where are you stuck?' And I said, 'I'm stuck here.' And he looked and said, 'But you haven't used your own hypothesis.' I said, 'Oh,' about whatever it was.

And I said, 'Oh.' And I instantly became unstuck. Because I could see, oh, if I'd used that part of the hypothesis, it was that—well, I can't remember the word. But anyway, so that was great, and I got unstuck, but it still took me a couple of minutes.

It was about minimal surfaces or something?

No, that was later.

Okay, sorry.

No, this was about holonomy groups.

Oh, holonomy groups. Okay, yeah, that's right. Okay. And Singer was very supportive. I mean, again, I remember as a physics student, it was terrifying for me to go approach a mathematician with a question. He was very supportive and not intimidating as a teacher. And as a human being, at least in my experience, he was a great guy.

I just wrote, uh, someone is compiling, uh, uh, a volume of, of sorts about Singer. And I just finished writing my piece. And, uh, but Singer, uh, he, he was, he was a good friend. Um, we didn't, we didn't really work together, uh, except when he was teaching me, uh, Lie groups, that stuff. But, uh, we were friends and, um, at a certain point I learned through C. N. Yang, the Aharonov-Bohm, do you know the Aharonov-Bohm?

Okay, I guess everyone knows that, although when it was first... Oh, it wasn't known for a long time.

I mean, it wasn't appreciated, I think, for its importance until much later.

It wasn't believed.

Oh, that's... Okay, yeah, yeah. Because it seemed... You're right. It seemed like it flew in the face of conventional wisdom.

Yeah. How could it be? So a number of people did the experiment. They got the same answer. And then I think something in... some part of physics, I'm trying to think of a name, the area of physics, could prove it. It came out of, it could be proved by, I can't think of what the...

It doesn't matter. I mean, yeah, quantum theory, quantum phases, well, anyway, it's ubiquitous.

Yeah, well, so I learned that from Yang, and Singer was in New York that year. I think he was at Rockefeller. And so we had dinner and I showed him this Aharonov-Bohm experiment. And he was thrilled by it. And I think because in his older age, he would, he was doing physics.

Exactly. I was going to say, unlike you, I was going to ask if he had that impact on you, because he was a mathematician who, when I knew him, was definitely interested in physics, but he didn't pass that down on to you when he was teaching you.

No, not at all. But I think this inspired him, because you could model it as a flat vector bundle that had holonomy, and it was his... Sure. But that was the electron. And so I think he and Atiyah started doing things.

Yeah, the Atiyah index, the Atiyah-Singer index theorem became very important. It was related to that in a sense.

Oh, yeah, but he had already done that.

Yeah, yeah, but they exploited that kind of thinking. Well, you know, I was going to do this later, but since you talked about Yang, I have to jump ahead because I heard about... your time, well, we'll get to when you were chair and, uh, eventually, um, and in your experience teaching Yang and, and, and others math and, and physics, and that's when I really, I have to say this now, that's when I realized the incredible impact you had on me, because when I was an undergraduate up in Canada, I went down to Toronto—I wasn't in Toronto, I went down to Toronto—and I went to hear some public lectures by Frank Yang. And Yang at that time was talking about the geometry of gauge theories, fiber bundles. And it was a revelation to me.

And that's what I decided I wanted to work on. And actually, that's what I proposed that I wanted to work on and what eventually I think got me accepted to do my PhD at MIT. And for a long time I actually worked on, that was what I thought I'd be working on, which is the geometry of gauge theories. And I remember, I mean, there was a physicist, Roman Jackiw, who was originally my supervisor, who was a physicist, very interested in mathematics at the time. But that became very interesting. And I remember even later on, Steven Weinberg, who you probably know, he was a wonderful man. But when he learned, I remember I was in his class, and when he learned that I knew about geometry of gauge theories, I was so...

It's very humbling, but very exciting. He invited me to his house. He basically pried me for information. And as this humble graduate student to have this Nobel Prize winning physicist just wanted to learn everything about it. It was fascinating. But now I realize I have you to thank for it because I think Yang's interest in geometry, in fiber bundles and the geometry of gauge theories came from you. Is that not right?

I think so. Yes. He asked me for a book. So I gave him Steenrod's book. But it was very hard for him to read. That was a tough book for a mathematician to read, let alone him. But he did then understand. He invited me, asked me to give a course, a seminar over lunch to his students. Institute. So I did the smartest class I ever had. Well, terrific physicists. And, and I would—I said, you know, in physics, you call it this, we call it this. And I try to get them not to use so many indices or indices. Oh, you know, these indices.

Yeah.

So, so forth. So it was a nice—yes, I gave maybe six of these lunch things. And then they gave me a present, which was a giant dictionary. One of those, it takes two arms because I'm a terrible—and they realized, maybe we'll give him a dictionary.

Nowadays, you don't have to be a good speller, thanks to computers, but in those early days, you had to be. Yeah, the indices is one interesting thing. I'll tell you something else about Weinberg, which is interesting, you may not have heard, because I took many of my graduate courses from Steve, and Steve was, you know, there were indices everywhere. And in fact, his first book on general relativity is full of indices. And that's how I learned general relativity. I picked up his book and read it. Actually, I took it first as a math course, as a graduate course when I was an undergrad, not from physicists. But then later on in life, when he redid his book on relativity, he basically said, you know, okay, differential forms are the way to really picture it.

So he eventually came around himself to recognizing differential forms as a way to think about it.

Differential forms was a very interesting invention, actually. That and the d-operator was all very, very beautiful. And that's, of course, the way, that's what I learned at MIT with Stokes' theorem. It was formulated with different tools.

Yeah, I didn't hear it as formulated as differential form until much later. Of course, I learned it from physics, and then it was only later. And that's, I guess that's what got me turned on to thinking about the math of being associated with physics. Now, you, so, okay, so, Kostant, you went back to MIT for a while. Yes, at the same time as Kostant did. Oh, you moved together. Oh, interesting.

Yes. Ah, okay. I was a Moore Instructor, and he—they gave him tenure, so I think he was an associate professor at MIT.

And then you went to Harvard from there? And is that right, after you were at MIT?

Sure. Yes and no. I did go to Harvard. It turned out that I got interested in business in that first year, because I had some friends in Colombia, South America, two in particular, who had gone to MIT. And they were down there, they were doing different things. But I was certain that if they got together, they could make a good company, a manufacturing company of some sort. I had been to Colombia, but when I graduated MIT, I guess you probably know the story. Yeah.

I knew you took a motorcycle or scooter trip or something like that.

We took motor scooters. They had just come into vogue. And we had Lambrettas, I remember. Wow. It was Boston to Buenos Aires or bust.

That's, uh, amazing that you'd think of doing that on a scooter. Yeah, well, we got halfway. We got to Bogotá. That's still a heck—by the way, I have to ask, that's still a long way to go on a scooter. I had a motorcycle, and this wasn't comfortable enough, but I can't imagine going thousands of miles on a scooter. We did. I almost died at one point, but, uh, I didn't. And, um, and we ended up in Bogotá, and, uh—

Well, the Jewish community in Bogotá was astounded at us. So we would get invited to this and that and so on. Oh, that's nice. What I learned about Colombia then was that if something had been imported and then you manufactured it there, imports would be blocked. So you can, you could get a, uh, a monopoly.

Oh, I see.

Cause that was to encourage manufacturing in Colombia.

So anyway, in the middle of my first year at MIT, I went down for a week or so to Bogotá and said, 'I'm not going to leave until you found a business.' Well, we found a business, uh, while I was there. And, uh, it was to manufacture vinyl floor tile. And that was not imported in, so we thought that would be good. So I scraped together a little money, and I managed to, from my uncle, rich uncle I had, and my father, and so I had 10% of the business. And then I thought, maybe I'll go down there and work at that. This was after my first year as a Moore instructor. But I realized I don't want to do that. I don't want to do that. I want to keep doing math. But I had given up the Moore instructorship.

But Bob, whom I knew, said—oh, he was at Harvard—'I'll put you on the contract.' He had an NSF contract or whatever. So I had, I was at Harvard for a year, just, I didn't have to teach. And then they made me an assistant professor. And that's when I was starting to work on minimal, minimal surfaces and varieties. And, but, the business wasn't working out so well, and I owed money, and I wanted to pay it off, and I learned about this place in Princeton called the Institute for Defense Analyses. It was a code-cracking, highly classified place, and they hired mathematicians.

And they paid more, presumably.

What?

And they paid more, presumably, than being an assistant professor.

They paid considerably more, considerably more, and I got the job and moved to Princeton, and I was there for four years. Much of that time was working on this minimal variety area.

I understand you were allowed to spend half-time on math and half-time on classified, in principle, code-cracking analyses about things that you weren't always aware of exactly what you were doing.

I learned about computers there. They had a huge one for the day. It was equal to all the computing power in New Jersey when it came in. Wow.

Was that your first experience? I was going to ask you that. It was on my list here. Was that your first direct experience of working with computers?

Well, yes and no. Yes, it was, but... I didn't know how to program. And when I tried to learn, I was a terrible programmer because I have kind of a bad memory for local things. And I was a terrible programmer, but they had good programmers there.

But you were good at algorithms, but not implementing them in programming languages. I mean, algorithms is something you enjoyed, right? Developing algorithms.

Very much. And I did one thing for them, which was very good. There was a longstanding problem in the field and I came up with an algorithm which would solve that problem. At least it would get the answer thousands of times faster than they could. So that was really a good contribution.

Yeah, sure, sure. Were you allowed to publish that or was that classified at the time?

It was classified and it's still classified. The NSA, uh, National Security Agency, uh, built a special-purpose computer to implement the algorithm.

Oh, that's neat.

And I found years and years later, they were still using that. So 9/11 period, they were still using that, uh, my algorithm. So, but, but I, uh, you know, I left.

Well, now I want to get to your leaving, because I try to pick things from which I learned from your background that I think are interesting. But before we get there, because I think the shift from Harvard to Princeton, at one point, and maybe this was just an offhand remark to someone, you said that you found Harvard to be stuffy and a stuffy environment compared to MIT. And it's interesting because I did my PhD at MIT, and then I went to Harvard to something called the Society of Fellows, which you must be aware of because the Simons Foundation has something called the Society of Fellows. So I don't know if it's named after the Harvard one. It seems very familiar when I was just looking at it.

But I found the transition from MIT, which is kind of a practical, hard-working, no-nonsense kind of place, to Harvard to be a very interesting transition because I did find Harvard much more, and the Society, of course, is one of the more pretentious groups at Harvard, and it was a difficult transition for me. So I was intrigued to find out that you found something similar.

Yeah, I really didn't like Harvard, and I don't know why, really, but I found it stuffy. But that was quite an honor to become a Junior Fellow at Harvard for you.

Well, it was an honor for me. Yeah, I was shocked and surprised.

And it was actually... Was it in math or was it in physics?

It was in physics. At that point, I'd done my PhD in physics. There were some really good mathematicians there, too. But in fact, I was going to ask—it seemed to me based on... Well, I don't know how it was, but you could have... I'm surprised that you weren't... considered for that. I don't know if that was operating then, but I think it was. Yeah, it was. It was operating, um, the Society of Fellows. It was an alternative—maybe you'd already gotten your PhD—it was at that time, for many people, was an alternative to doing a PhD. By the time I got—became a Junior Fellow, um, at least in the sciences, most people already had their PhDs. In the humanities, the many people who had it didn't have a PhD. And I have to say, by the way, that kind of honor—I don't know if you've... maybe it didn't happen—it was very difficult for me because...

I was in that community of MIT-Harvard, which in the physics community was small enough so that I used to take my courses at Harvard, and there were seminars back and forth. But I was a nobody as a graduate student. I mean, I was who I was, but no one knew. And then the minute I got appointed Junior Fellow, suddenly all of the faculty at Harvard knew who I was. And I had not done anything of significance that I was aware of. And it was a very difficult thing to have a very prestigious position and at the time feel like... Did you have your PhD already? Well, I had been named a Junior Fellow before I got my PhD, but by the time I began, I had my PhD. But, but it's still, it was very difficult to be surrounded by people and have this expectation that I was—so that I was something special when I hadn't really, in my mind, done anything special at all.

And I found it took me about a half a year before I got over that. There's a syndrome or whatever it's called where you don't feel competent and you feel—I feel like—it felt like I was fooling everybody.

But you didn't have to teach, I think.

No, that was the best part. I didn't have to teach. And the other thing that for me that encouraged me—and I say this because I know that the Simons Foundation and your own interests are wide, not just supporting science, but also supporting popularization for science, which is obviously something I've been quite interested in for much of my life—the thing that the Society encouraged me was to go beyond just physics. So while I was there, I actually, I decided I wanted to write some books more generally on science and culture. And it was while I was there that I actually got my first contract to write a book. I didn't actually write that book, particular book, for later on. But the idea was that you should be free to do whatever you wanted for three years and unencumbered by anything.

And which, which is, I understand, the purpose of your Simons Fellowships. And it's a wonderful—it's a wonderful thing for young people now. And I guess I'll say this for the young people who are out there that, you know, there's so much pressure on people right now. And, and normally you had a postdoc and you have one or two years and you have to try and produce and show things to get your next job, and to have some time, a three-year period, which is a substantial amount of time where at least for the two—first two years, you're not really under any pressure except to think, is a very valuable thing. It's almost as valuable probably as pushing a broom around. Anyway, in any case, it was, yeah, it was a fortunate thing.

And I actually worked, and interestingly enough, when I heard you mention Bott, at that time, when I was at Harvard and Bott—Bott's group, Raoul's, Bott's group was there—was, I remember sitting in a class for him when I was doing my, my Junior Fellowship because I thought it was a time I should try and learn some math as well. And, and he was very interested in, in, in geometry and physics as well. Both he and Singer became very interested in physics or potentially interested in physics.

I don't think at that time they were doing any physics. I think that later.

Well, you mean later than when I was, or you? Say it again. I mean, when I was there, they were interested in physics. But you're saying when you were—when you were talking to them, they weren't interested in physics.

Yes, I don't think they were that interested in physics. I mean, Singer and Atiyah. The index, index theorem, which is, which is not physics—maybe used in physics—but the index theorem was a great, a great result.

So was Chern-Simons, which was pure mathematics and of course became, you know, that's before. Yeah, that's how I first obviously knew of you as a, before I knew that, but the Simons Foundation, about your work in business, and you've talked eloquently, I think, very importantly about how, you know, it turned out to be very useful in gauge theories and trying to understand the topological properties of gauge theories. And then eventually became, in fact, a whole new area of of mathematical physics called Chern-Simons theories. But but the important thing was that you had no notion at the time of developing it that would have any application whatsoever. Right.

In physics. Absolutely no, no, none. I didn't, I didn't know any physics, or very little. Uh, but, uh, I thought the math was, uh, was beautiful.

It is.

I, I got the—that was when I was a chair at, uh, at Stony Brook. And I decided I wanted to learn, really learn characteristic classes, uh, thoroughly. So I set myself a, a problem, um, you know, there's a combinatorial formula for the Euler characteristic, vertices minus, you know, yeah, I know, vertices, edges, and faces and so on. I wanted to come up with such a thing for what's called the signature of a four-manifold. And it's a, it's a nice construction. But I wanted to see if I could make a combinatorial version of that. And I started to work on it and I got pretty far, but then I got stuck on one term, which did not yield to anything, but it did turn out that it was a function on a three-manifold, which had very interesting properties.

And that was the roots of Chern-Simons with that three manifold example. And it was really quite a wonderful thing, this function. It was a conformal invariant of a Riemannian manifold. It was a conformal invariant. It was, uh, it was only defined modulo the integers. So, you know, 0.08 and one point, you know, 0.8 and 1.8 were the same. So it was, uh, so it took values. You could think of it as taking values in a circle, but, uh, anyway, I was interested in mod Z and, uh, I showed that, um, I went to calculate it. for a three manifold sitting inside, immersed anyway, in four space. And I calculated the answer and it came out to be zero. Zero mod Z. It came out to be zero. And I thought, wow.

Then I calculated it for three-dimensional projective space and it came out to be a half. So then I realized, okay, so three dimensional projector space cannot be conformally immersed in our four. And anyway, I showed this stuff to Chern and he, he just said, well, we could do this in all dimensions and uh, not just three. And I was a little dubious, but uh, we started working together and he was right. And uh, So that that became Chern-Simons, but it never entered my head that it would apply to physics.

Yeah, no, it's I think that's I mean, there are wonderful examples like that that I think are incredibly important. And by the way, you know, it enters physics in a number of areas. But but in particular, trying to understand—for the listeners who aren't experts, gauge theories describe all the known forces of nature, really, and the fields that we now think of as electricity and magnetism and even gravity. And trying to understand the mathematics of these, it turns out what's called the topological properties, or the properties that don't depend on sort of detailed natures of the spaces, are very important in telling, and useful to understand processes in physics called instantons. And so, that this classification of Chern-Simons, and something, the integral, which is something called—it has an index, is

is very important. But it was important, as you say, from a mathematician's point of view, because of its mathematical beauty, without any knowledge at the time of gauge theories or what it would work on. I'll jump ahead because I suspect we're not going to get to the end of everything I want to get anyway, so I want to at least get some of these important questions. Nowadays, there is a great, over the last, well, say, in government in particular—and this has been true since I guess I've been a professional scientist—this push for applied funding for applied problems to solve, you know, to solve problems, and less interest from the point of view of politicians and sometimes, unfortunately, from the point of view of the public, in fundamental, curiosity-driven research.

What people don't realize is that very few profoundly important applications have ever come out of people directly thinking about those applications, but rather came out of people like you working on something that was fascinating with no idea that later on it would have an application. I wonder if you could comment on that. I guess you have the luxury, in some sense, of funding with your foundation potentially this, but in terms of the government and the pressures of the public to say, "No, we want you to solve this applied problem." And, you know, if they'd wanted faster computers back then, they would have had faster pulleys and wheels until someone developed a transistor related to something totally independent.

Well, yes, we support primarily—although in one area we have a study on autism, which is applied, yeah, treatments and so on—but the rest is, uh, is just basic science. And, uh, and yeah, I love basic science. And you're right. My favorite story is I.I. Rabi. Yep, so he invented or discovered, uh, nuclear magnetic resonance. And he won the Nobel Prize. And you know what it is.

Yeah.

Or whatever.

Yeah, people use it all the time now to see their bodies.

Well, exactly. He won the Nobel Prize. A few years later, two guys came along, I think they were German, and realized you could analyze materials with this. And they won the Nobel Prize. And subsequently... and another two people, one of whom was at Stony Brook, realized that you could take pictures. Now, they didn't want to call it nuclear magnetic resonance. They didn't want the word nuclear. It would frighten people. So they called it magnetic resonance imaging. Now, I don't think I.I. Rabi—he probably wasn't alive by then—but whatever, it dawned on him that there were machines implementing what he discovered all over the world. Thousands and thousands of machines that could look at your shoulder or whatever.

I'll add to that story for you a little bit, because Rabi was one of the more influential physicists of his generation and had many great students. And he influenced many people. And one of the people who then took... followed up on that field was a wonderful physicist named Ed Purcell, who was at Harvard. And actually, by the way, he was one of the people who interviewed me for the Society of Fellows. But he was an amazing man. Every time I talked to him, I wanted to grow up and be a physicist. He was an experimental physicist. He won the Nobel Prize specifically for magnetic resonance, nuclear magnetic resonance, the details of which had followed up on Rabi. He and Bloch, who was at Stanford.

And when asked at the time, Ed Purcell was asked at the time when he won the Nobel Prize what the utility of this would be. And he said he didn't necessarily think it would have any wide-scale application. It was a very important phenomenon in physics.

But I thought it was I.I. Rabi who discovered it.

Well, I mean, nothing is there. It's all incremental, right? So Rabi did a tremendously important work in understanding the importance of magnetic moments in atomic systems, for which, in the spectroscopy of fundamental atomic systems, and so that's what he won the work for. And then the people who'd actually used it for nuclear magnetic resonance to, to, to allow you to do a new kind of spectroscopy to follow up on the spectroscopy of Rabi were Purcell and Bloch and others. But, but I remember those guys specifically said at the time of the Nobel Prize, I remember at least Purcell said he never thought it would have an application. And, and he, and, you know, I know the name Purcell.

I never met him, but I know him.

It's a pity. He was a wonderful man. He actually wrote a great introductory book in electromagnetism, which was one of the best at the time. But he was just fascinating. Like Schwinger, and in my opinion, the important thing that I hope most senior scientists realize is that just conveying your fundamental excitement and interest is perhaps the best thing you can do for young people in a way that, you know, young people are terrified by important people and people they look up to. And just being willing to talk to them and convey your excitement is probably the most important thing you can do as a mentor and a teacher, because I certainly know it. For me, that was a profoundly—that, you know, just having people who would take me seriously enough to convey their excitement was a tremendous motivator.

I agree.

Yeah, it's—and we're lucky to have such people. And, but let's—I want—there's a few I want to jump through because obviously we're going to—we're not going to have time to do everything. And I'll even get to your business career, which has been not so bad. But, but, but I was fascinated to learn. I knew you'd done the time at the Institute for Advanced Study, and I knew then you had become chair at Stony Brook, and I was interested in that transition. And I did hear you somewhere talking about the story related to Vietnam, that you got basically fired by IDA for protesting the Vietnam War. Is that not true?

Well, yes, it's true. Maxwell Taylor, you might remember that.

Sure, yeah.

He headed not only IDA, but there were various other kinds of units in this Institute for Defense Analyses. And he wrote a cover story in the New York Times about how well we were doing in Vietnam and we have to stay the course and blah, blah, blah. And I thought the Vietnam War was the stupidest thing we had ever done. So I wrote a letter to the editor saying, 'Not everyone who works for General Taylor agrees with his views, and here are my views.' And so they published a letter, and I thought there might be repercussions, but there weren't any. But then a few months later, a guy came around and he told me he was a stringer for Newsweek magazine, and he was doing a story on people who worked for the Defense Department, which I indirectly did, who were opposed to the war.

And he said, 'I'm having a hard time finding people. Can I interview you?' Well, I was 29 years old. No one had asked to interview me. So I said, 'Sure, you can interview me.' So he said, 'Well, how are you approaching this?' And I said, 'Well, here we're supposed to do at least half our time on their stuff, but you could do half your time on your stuff. So until the war is over, I'm going to only work on my stuff. And when it's over, I'll only work on their stuff until it evens out.' Which was not completely true, but it was kind of true. And then I went to see my local boss, which was the only intelligent thing I had done that day, and told him I gave this interview. He said, 'What did you say?' I said, 'Well, I said,'

'...half and half,' and so on. So he says, 'I got to call Taylor.' So he went into his office. He called Taylor. He came out in five minutes and said, 'You're fired.'

Wow.

I said, 'Fired?' I said, 'You can't fire me. My title is permanent member.' And he said, 'Well, do you know the difference between a permanent member and a temporary member?' 'No,' I said. He said, 'A temporary member has a contract.'

But I wasn't worried at all because I had recently finished a work on minimal varieties. And that paper, 50 years from then, is still cited. Sure, it had almost 1,900 citations.

Wow.

And for a math paper, that's a lot.

That's a lot, yeah.

And so it was really a very good paper. I was very proud of it. And I knew that I could get an academic job. I wasn't worried about supporting my three children.

Now, let me ask you this question. It's a hypothetical one, but because that's a great segue, because we'll talk about moving back into academia. And it's nice to have had that security knowing in the background that maybe that—I don't know, that didn't weigh on your decision. Let me just ask the question: Would you have done it again if you'd known the consequences of what you said? Or would you have held back?

Well, that's a good question. Uh, I probably would have preferred not to get fired. So, uh, in that sense, but as I said, I—it, it didn't worry me very much. It didn't worry me very much because I knew I could get a decent academic job that might not pay as much as—uh, uh, and I, I had some offers, but then Stony Brook came along and asked if I wanted to chair the department, and that sounded kind of exciting.

We'll get there because, again, I can relate because I did almost the exact same thing at almost the exact same age. But before you get there, I read a quote from you or I heard a quote from you somewhere saying, 'Everyone should be fired once.'

Yes, everyone should have that experience, as long as you don't make a habit of it. That's what I say.

Okay, but let's parse that for a second, because I actually also think it's kind of a useful thing for people to do. And maybe it was just a fun remark, but it can be very useful. Maybe it was just an offhand remark, but I'd ask you to elaborate on that. What's the utility about being fired? Because I think it's useful to suddenly be, in one way or another, forced to do something else.

Well, I don't know. I just blurted that out.

Oh, okay. I didn't know if there was more to it than that, and I couldn't resist asking. But it's a great remark. It's a great remark, yeah. And maybe that's why I heard it. It's a good soundbite. You moved to Stony Brook, and how old were you, like 40? No, 30. Only 30. Okay, so you're much younger. You know, I moved to become chair of a department. I was—I taught at Yale and I moved. At that point, I was 38, but I moved to become chairman of a department which was—had had a reasonable history, but was at sort of a low point at Case Western Reserve in Cleveland. And the physics department. Yeah, the physics department. And—but yeah, no, I was in the physics department at Yale and then I moved to become—I left that to become chair of a much, uh, smaller department in some sense at Case Western Reserve. It's a university in Cleveland, yeah. And, uh, and, um, it's a good school. It's a good school, and the department had had a distinguished history. Michelson was its first professor of—Michelson. And, um, but, um, and I had ended up having that same position he did, but, but, uh—

It was invigorating. And people—there were a number of reasons I chose. I was kind of young and people said, 'Why did you want to move into administration?' But I had this opportunity to have 12 new faculty positions to hire, to build a department, to create something new. And it was very attractive to me. So I wanted to ask you about that, about your experience and what attracted you to be a chair. Because if you're young, people say, 'Avoid administration. You know, don't do it.'

Well, I just thought it would be fun. The pay was pretty good. And the department was weakish, so I knew there could be improvement. And I just thought it would be fun. And it turned out I was a very good recruiter. I love recruiting. Me too. You like it? Yeah. It's really fun to find great people and lure them to your operation. So I did two things in those few years. I started what became Chern-Simons. But I also, the first year, I hired 10 people. The second year, I hired 10 people.

Wow.

And had to fire a few who didn't have tenure. And we built a very, very good department, especially in differential geometry. But we'd also hired a guy named Jim Axe, who was—I don't know if you remember that name. Yes. He had won the Cole Prize. He was an algebraist. And he was the most famous guy we had.

You hired from Cornell or something? You lured him away from Cornell?

He was at Cornell. And I lured him away from there. But then we hired a lot of very, very good people. And the department became... you know, a very good, very good department.

Yeah. And that's a great—that's a very satisfying thing. Let me—let me ask you another personal question, I guess, because—because it was my experience, and I don't know if it was yours when you're a young academic trying to make your way up, and of course you sort of left for a while, so maybe this is different. You're really always thinking about yourself and how to, you know, your own problems, your own academic problems, the things you want to do, the research thing you want to do. And it's not really an altruistic field in that sense. And when I became chair, it was not only a thrill to be able to recruit good people and to recognize talent, which in retrospect is a very satisfying thing to know that you've helped a young person that's talented, but I also found it very surprising how fulfilling it was for me to help other people.

Do what—do what they wanted to do well. And, and I don't know if you had that experience, to, to be able to, to find that you're actually helping other people build a career and be excellent. Is that—was—did you find that, uh— Well, I found it more when I went into business. I, I was going to—I, I was going to ask that only because I realized that one of the—I'm jumping ahead because I thought maybe that, that experience might have primed you, because as far as I can tell, and unlike most of the interviews with you, which I assume are largely about your incredible success as a quant, but is that one of the reasons you were so successful, it seems to me, if I try and distill this, is being able to bring in really talented people and let them run with their talent.

Yes, and let them run. You have to have good taste in selecting people. And, uh, but then you don't sit on them. You, you let them do their thing. And, uh, that's, uh, that's very satisfying. And again, when I went into business, um, that was even more important, uh, in a certain sense. And, I hired some terrific people there and let them, as you say, do their thing.

But do you think your experience as chair helped prime you for that or not? I mean, the sense of hiring faculty and saying, "Okay, we think you're good. Now do good things."

It did. I mean, I learned how to manage people.

Which is very difficult and something you don't learn as an academic as a rule.

Right. And so I left Stony Brook, I think, after eight years. And that's when I went into business. But I had learned to manage people and I was good at that.

Well, recognizing talent and encouraging them to do the best thing is great at managing people. Sometimes, unfortunately, there's the minutia of other things that get in the way, but that's the heart of a good... It obviously worked for you. You—and fortunately, you were—you actually were able to build—look, let me, let me put this—well, let me—there's, as far as I can tell, again, I've tried to, to think about your life, having read—been studying it lately, three factors probably are important. But one, I, I learned, one was that you, you, you had sold this company that had started, uh, way back when in Colombia, and so you had a cushion. You had a—you weren't—you had a monetary cushion. You weren't quitting your job, in some sense, with worrying about feeding the family.

I did. And in fact, if—that business was sold, and for quite a lot of money. And my friends said from Colombia, "Okay, now we have all this money. We want you to help invest it." I don't know anything about investing, but I said, "Okay, I'll do that." And I found a guy, a mathematician who had gone into the commodities business. And I went and talked to him to see what he was doing. And he seemed to really know what he was doing. So I said, "Okay, we're going to give you X dollars. You can have 10% of the profits, and, uh, we want you to, uh, make some money for us." And I said, "But if you lose too much, you have to stop." And he said, "What's too much?" I said, "Well, if you're down 30%, you have to stop."

But as I was walking out the door, I said, "And if you make a tremendous amount of money, you have to stop." "How much is that?" I said, "If you multiply our—the fund by a factor of 10 after your fees, then you have to stop." Well, he couldn't argue with that. But the remarkable thing was that after a few steps that he took that didn't work, he got into something and made a fortune. And nine months—nine months later, he had multiplied our money by a factor of 10.

Wow.

And, uh, much of that was in a Bermuda trust that had been set up for me by, uh, the father-in-law of one of the two boys, because he was very appreciative that I'd gotten this business going in the first place. He owned half the business, and he, uh, he—he took a hundred thousand dollars and put it in a Bermuda trust for my family. And so that hundred thousand was invested with Charlie, and that became a million. So now I'm—so, uh, uh, so I don't know how we get into that, but, uh—

No, well, the fact that, oh, yeah, I got into it by saying I knew you'd had a little, you'd had a cushion financially, which would, which allowed, which makes it a little easier to switch, to quit academia, I think, obviously. But the other thing was that you had, so that was certainly a help. There's no doubt about it. And it might have been a harder decision if you were going paycheck to paycheck. But also, you also had a cushion of intellectual excellence. You were able to build on the investment you'd made in humanity. As far as I can see, you brought in, let's see, someone you knew, a very important person from the Institute for Defense Analyses, who'd been involved in creating a very important algorithm, which led to speech recognition, right?

Baum, is his name or something? Baum. Yeah. And then also Ax, your great hire from, from... So you were able to say, 'Oh, I've got these really good people, already know they're really good, and, and I can bring them in.' That must have been important.

It was, it was important. And at a certain point, we were doing fundamental trading. Mm-hmm. Initially, and that worked out OK. Wait a minute. I should go?

We had 10 minutes left. 10 minutes or so?

Yeah, 10 or 15 minutes, yeah. Yeah, maybe 15 minutes. Thank you. I don't know where I was. It was fundamental trading, but finally we got into making models, and they worked better, and ever since it was model making.

And your experience in algorithms, obviously algorithms became very important, as did machine learning. I mean, were you directly exposed to machine learning, or is that something that was brought in by your colleagues?

Machine learning didn't exist in those days as a notion. I think machine learning has only been around for about 10 years or 15 years. No, we didn't do machine learning.

But the idea of, in some sense, looking at, having a vast storehouse of data that you could analyze and look for patterns. Yes. That became a central feature, obviously, of what... That's what we did.

We had a tremendous amount of data, historical data, tick data even. The tick, we had a ton of that. And the way it worked is, a guy would think, 'Oh, well, maybe, uh, this would be a predictive signal,' and he'd cook up something and then we could test it, back-test it, uh, for the previous 10 years to see, 'Does this really work?' And, and, uh, and, uh, if it was statistically significant, it would go into the system. So that's the way it worked, and it probably still works that way.

It still works that way. It's called black box, right? And I'm intrigued by that because, in some sense, I've done a lot of discussions with people in the past and written about AI, but the idea that, basically, patterns can be discerned that you might not discern yourself, but by looking at data enough—and that's how Tesla can look and find, you know, in principle, hopefully, that someone's not a pedestrian, but a stoplight—is that a black box can come up with saying, 'This is what you should do,' but it never tells you why you should do it. Absolutely. And it's frustrating for people, and I understand early on it was a natural tendency for you guys not to believe it, to say, 'Look, we have an intuition.'

Why should we trust this machine telling us to do X when there's no rational reason that we can think of doing it?

I didn't worry about that. If it worked, it worked. But we had very strong conditions—the signal versus the noise, I guess. Predictive signals, and they have to have enough statistical significance to put them into the system. They're tested all the time. Sometimes the signal disappears after a while, so you take it out of the system. But you know, it's just a continuing, growing thing.

Well, in retrospect, of course, it seems eminently sensible. By the way, I've had three, four of my PhD students from Yale one year went to work as quants on Wall Street because they, you know, the mathematics was not that different than what they were doing and the pay was a lot better.

But none of them came to Renaissance?

You know, the interesting question is, no, I don't think so. They were being hired by, you know, and I don't know if any of them eventually came to Renaissance. They were being hired by the big management for, you know, all the big banks and things that were hiring people like crazy.

Places like that.

Yeah, I know. But anyway, they, you know, the funny thing is, I, I later, I heard, I remember a year after three of them were on, uh, on Wall Street, they were, they met and they were sitting there at, and they were at work, and they, and then they would end up talking about gauge theories, and, and then someone said, 'Hold on. Hey, wait, wait. That's not what we do anymore.' But, but, but, but what I wanted to ask you about is this interesting—it's fascinating that you had the capability to say you didn't worry about whether it defied intuition. Because many people, I think, would not be able to do that. And I was going to ask you a side question. There's no doubt that as machine learning gets better, medical diagnostics will be ultimately, rationally taken over, I think, by machine learning.

But looking at vast amounts of data and making clinical recommendations on the basis of it. But, but the question that's interesting is, will people be willing to take—so if a black box says, 'Do this,' but doesn't give you the biochemical reason or the rational reasoning, whether people will be willing to take medical instructions from a black box, basically.

That is a very good question. It never occurred to me. And I think the medical community, it would be very difficult for them to implement some treatment, which they didn't understand at all why it should work.

Even if it's the best treatment.

Yeah. Well, exactly. I mean, for example, acupuncture—some people believe in acupuncture, but there's no analysis that says, 'Oh, this is why acupuncture should work. We should all do acupuncture.' So most people stay away from it, even though it might work in some cases. I don't know.

It might. I haven't seen evidence of it, but I know that people swear by it, but then people swear by a lot of things for which there's no evidence. It's a human characteristic. Okay, well, I'm glad we got to that question because I think it's an interesting one. I mean, the difference is, I think why it'll be much harder is that if you're wrong in your algorithm, you lose some money. If you're wrong in your clinical recommendation, you may lose a life, and one seems a little more difficult than the other, I think. And maybe it's easier to take losing money than the life. Since we don't have much time, there's a few other areas I wanted to hit, and I'll just pick on one of them. You know, I'm a great admirer of many things you've done, and not just the math, but the things you've chosen to do in your life.

And that's how, by the way, we first met, I think, was when I lectured at the World Science Festival, probably early on. I remember you and your wife came to a number of the lectures. We had a number of good talks.

We support that organization.

Yeah, I know you do, and we've chatted about it, and as I've built other organizations, I've hoped at some point the Simons Foundation would fund that, but that's not the reason we're doing that. The thing I want to talk about is one of the things the Simons Foundation funds is the Flatiron Institute of Computational Sciences. Which, of course, in some sense I can see why you personally would think that's incredibly important because it's been important in many ways in your own...

I am as proud of the Flatiron Institute as I am for anything else I ever did. I'm really proud of it. It's terrific.

You know, that answers my question I was going to ask. My last question was what you're most proud of. Well, are you as proud of that as Chern-Simons or the minimal varieties? Yeah.

Well, I'm pretty proud of that. Chern-Simons, well, yes, because I came up with its roots at the beginning. And then with Chern, of course, we expanded it a great deal. But I thought, what I came to him with was very good, so I'm pretty proud of that.

Well, you've a lot to be proud of. I mean, you don't have to rank them. I mean, I'm glad to see that the Flatiron Institute is up there, but I wanted to ask you a question. It funds, it supports computational biology, computational astrophysics, computational quantum mechanics, computational mathematics.

Not quantum mechanics, quantum physics.

Oh, quantum physics, thank you. Computational mathematics and computational neuroscience. If you had, okay, just let me ask you, there's no reason, this is just a guess, speculative, which of those areas do you think is going to pay off the most? And we'll do another interview in 50 years and see.

Well, they're all paying off. I can't really tell. The astrophysics unit has published the most papers, but that's not necessarily a measure.

Yeah.

That was run by David Spergel.

Who's now the head of the foundation.

The head of the foundation.

Who I've written papers with, by the way. Was I? Yes. Yeah. And when I was a junior fellow, he was a graduate student at Harvard.

I see. Well, so I don't know which unit is going to pay off the most, but they interact with each other, and in particular, computational mathematics, which was relatively a new unit, is great because it's like glue. They help all the other units. Some of the postdocs there are joint with quantum physics or astrophysics or something. So that's headed by Leslie Greengard, whom you've undoubtedly heard of, and he started the thing. It was called SCDA, Simons Center for Data Analysis, and that worked out so well. It was tilted to the biological side because Leslie also has an MD, but it really went well. And then we thought, well, maybe we'll start astrophysics. Spergel gave a workshop, organized a workshop to see if it was a good idea to do this astrophysics. That would have been the second unit.

And I took him aside after the thing and said, "I'll do this if you head it." And, "I gotta think about that." But after a couple of months, he agreed to head it. And he's done a great job. And we have great leadership in each of the units. Absolutely stupendous leadership.

That's important.

It's totally important. And with good taste. So there's very many good people there.

You have many skills, one of which has clearly been knowing talent and nurturing it, which I think has been obviously very important for you in every area of your career. Look, I know you have to go. I have one last question because I don't want to keep you. Actually, I would love to talk for another hour or two, but I've really enjoyed this. I hope you have. But speaking of the support of the Flatiron Institute and the Simons Foundation, there is now a trend, in some sense, to almost return to the Renaissance times of patrons. As governments cut back on their support of research because of economic concerns or demands, one is finding more and more extremely wealthy individuals like yourself and Yuri Milner supporting some things and others, that we're getting almost a time of patrons again.

Where it, it seems to be that the opportunities for supporting especially foundational research is now coming directly from individuals of great wealth and not from the government, which, which was really only fairly recent—government-supported research has only been since the Second World War in the United States, the big science. I'm wondering what your take is on that and its future. And is it a good thing or a bad thing?

Well, it can't be a bad thing for someone to patronize science. That can't be bad.

It can't be bad, I agree.

But I think it's really important that the government does more. Schumer has a bill that would boost science considerably. We'll see if the bill passes. But I think it's great that there are patrons of science. In fact, we have an organization called the Science Philanthropy Alliance, which consists of people who would like to support science—philanthropists. So I think that's great. But I also think that the government ought to do more. And China is doing much more.

Yeah, one is seeing much more in China and Asia. One was seeing it in Singapore and in Korea. And that was of great concern, of course, watching the United States having its support of fundamental research decreasing. And I agree with you, it can't be bad. The only bad thing could be if governments say, 'Oh, look, they're doing it. Now we don't have to do it.' And that would be the bad thing.

Or would it be a bad thing?

Yeah, and so that is the message I want to give, is that we shouldn't use this. We should benefit from it and the demonstration. And I think, if anything, use it as a demonstration that individuals like yourself can spur really important results with merely a few billion dollars spent at the time. And it used to be a billion dollars was a lot of money. And so governments can do a lot with very little. But we have all benefited from your career as a mathematician, an intellectual scientist, and then as a supporter of science. I say this not just as a scientist, but someone whose whole being has been built around trying to improve people's understanding of science and the scientific enterprise.

And so I particularly appreciate what you've done. And so it's been a great... It's, it's always been—the times we've talked, it's been a pleasure, but this has been a real thrill for me, and I, I really thank you for the time you've taken. I, I enjoy it. I didn't—I enjoyed it. You're a good questioner and a very interesting guy yourself. Well, you've done a lot of interesting things, I'm sure. Well, I hope. Thanks a lot, and I hope we have a chance to, to do this maybe once again online, and I certainly hope, um, to do it offline, maybe next time in New York. I hope you enjoyed today's conversation. You can continue the discussion with us on social media and gain access to exclusive bonus content by supporting us through Patreon.

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