Jim Simons - Science Lives Interview

So you grew up in the '40s and '50s, right? Correct. Outside of Boston. Yeah. Not very far outside. Not far outside. Okay. So I was wondering, when was it that you first became aware of mathematics and what attracted you to it?

Well, I started thinking about mathematics very early, although I didn't think it was mathematics. I thought it was just something that was fun to do. So I learned quickly all the powers of two and was pleased to remember them up to, I don't know, 2000 and whatever. More interesting, I think, was I discovered Zeno's paradox very early when my father told me to my horror one day that a car could run out of gas. And I was really very little. I was down at the beach. I remember very well where I was. And I started thinking to myself, 'Well, how can it? After all, it could always use half, and then use half of that, and then only half of that, and so on. So that would really never run out.' So you weren't kidding when you said you discovered it.

Yeah. I didn't think through the whole problem, perhaps, but you'd never get anywhere either. But nonetheless, I just thought of that continual dividing and leaving a little and dividing and leaving a little. You were how old then? Oh, three maybe. Three. I knew about halves. That's impressive. Yeah. I mean, it was in retrospect. And then one other thing that I remember very well is lying in bed—now, this was, I was somewhat older, but maybe 10—and contemplating the question, the statement, 'pass it on.' Now, you know when you say to someone, 'pass it on,' we all intuitively know what that means. But I lay in bed trying to define it precisely. And I think you actually need induction or something like that.

But one night I distinctly remember falling asleep very satisfied. I had finally completely defined 'pass it on.' But when I woke up, I didn't remember exactly what my definition was. Yeah, this is a well-known experience. And I think I sort of got off that topic after a while. But those were mathematical thoughts. So I always liked math in school. I wasn't terribly good at arithmetic. And I remember distinctly having trouble with long division, remembering the algorithm. But on the other hand, all the ideas were very appealing to me. I didn't know there was a career as a mathematician. I just liked that stuff.

But did it have some special appeal? Did you think of it as something that was different from any other thing?

It was just something I thought about a lot. When I learned formulas for volumes and surface areas in the eighth grade, I remember being very pleased with those formulas. I didn't know how to derive them, but I was pleased that they existed, the formula for the four-thirds pi r cubed or whatever for the volume of a sphere.

That was pretty good.

So by high school I knew I was going to be a scientist of some sort, but I just assumed mathematics. I liked math. I didn't like chemistry. I didn't like physics particularly. I didn't understand why it was what it was all about in a certain sense. But the math was always very clear. I loved plane geometry. I loved learning about proofs and that sort of thing, and spent a lot of time contemplating these various geometry problems.

Did you think that proofs were something that was just special to geometry? Or did you understand that they played a role elsewhere in mathematics?

At first I thought it was just special to geometry. Then I learned sometime in high school that no, there are various things to be proved and so on and definitions. I loved it all. I mean, I really liked it all. And contrary to the wishes of my doctor, who felt that any Jewish boy who was smart at science, math, whatever, should become a doctor—and I couldn't imagine being a doctor—I insisted I would major in mathematics. And still, without really knowing what it was—I mean, I thought it was kind of like, well, whatever—and I went to MIT and skipped the first year of math and started in the second year. And that was okay. But at the end of my freshman year, the second semester, I took a graduate course.

It said 'self-contained.' It was an algebra course. And it was a very interesting experience because I managed to get through the course, but I didn't really—you know, I was 18 years old—I didn't really understand what it was all about somehow. I mean, take the fundamental theorem of homomorphisms. Why would you want to make these sets into elements of a group? What was the point of it all? And then that summer, I read some more algebra, just because I thought I should learn some more. And somehow, within weeks, I remember everything became totally clear. It was just all obvious. It was great. I loved it. I went on and took a lot more algebra follow-on graduate courses in my sophomore year—Galois theory, all that stuff.

It was all terrific. I took a topics in algebra course with Iwasawa in my junior year, which was completely intense. Sometimes I just couldn't get something at first, and it would be very mysterious to me, and then it would click in. And maybe that's typical. I don't really know.

When did you start to get that feeling that mathematics was maybe, in some ways, more real than other things, or perhaps had a timeless quality, or perhaps, because you prove things or discover things, that it had that special something about it?

I'm not sure that I conceptualized that notion of the permanence or the reality of mathematics until I was asked that silly question, which I'll recount again. But mathematics was my life for those years. So it seemed the most natural thing in the world to be always thinking about mathematics. And so when I did leave the field after about twenty years, in my late thirties, and—one of, some business guy, I guess—and I went into business, and the business guy said to me, 'Well, how do you like the real world?' You know, kind of joking around, and I said, 'Well, you know, somehow it seems to me that something like the integers has a great deal more reality than some McDonald's stand or whatever, you know, that's here today and gone tomorrow, and the integers are forever.'

So I think I implicitly, if not explicitly—I think, like most mathematicians, felt that these concepts were really of an eternal nature. And so that was my notion.

Do you think that there was anything that was important about just being a kid and developing into being a mature mathematician who actually did research and so on?

Well, I wasn't brought up in any special way. There were things about my nature that I think lent itself to doing mathematics. Some mathematicians are very fast thinkers and they can solve a problem, look at it, explain it. I'm not one of those. But I do have a capacity to just contemplate things. So they were very worried, my mother told me later, when I went to nursery school. I started nursery school and there was a tree in the backyard. I'd never had an opportunity to climb a tree. And for weeks, as soon as we got out to play, which was most of the time, I would climb that tree, sit on a branch, and watch everybody and think. This was apparently very unnatural. And they were concerned. And my mother told me that I can't sit in that tree anymore, Jimmy.

You have to play with the other children. And I was just fine, fine. I'd play with the other children. But I just enjoyed sitting there thinking. So I was an only child. So I didn't have a brother or sister to chat with all the time. So I did have the capacity just to think. And I sometimes talked to myself, as it turned out, because some of my friends were amused to see me standing talking to myself. So I think that's a quality that, not talking to yourself particularly, but a quality of just being able to get lost in thought that is pretty good for mathematics.

So if we go back to the time that you were at MIT, which includes also part of graduate school, right?

Yeah, because I graduated one year early. And then I stayed one year as a graduate student.

What was the process like for you going from being a student to becoming more of a mathematician? Although I remember you having told me when you get your degree, you're not a finished product. But there's some kind of transition that takes place. And what was it like sort of mentally and psychologically?

It was pretty seamless as far as I could see, because as I got more and more into mathematics, I felt like more and more of a mathematician. So in some sense, I feel I became a mathematician at about 18 when I was starting my sophomore year, and it was a great year for me learning mathematics. I learned a lot that year, and I just felt like, you know, like I was immersed in this subject. I didn't have any ideas for new mathematics until I guess my third or fourth year. Maybe it was in that graduate year, and I remember the first, my first thing I wondered about and how to deal with it, and that is, why the product of harmonic forms was not harmonic. It seemed a pity to me. And so I started thinking about, okay, what can one say about this question?

But I remember in my thesis, which when I was a junior, I had to write a senior, you know, a graduating thesis. It was with Ankeny. And I had an idea of something. What was it about? It was about linear algebra with inner products, the orthogonal group, stuff like that, and reflections and rotations and how you build things with fields other than the reals. And I had an idea how to prove something. I had an idea. This should be true. So I guess that was another mathematical idea. And I think, like a lot of people, I remember exactly where I was when I realized what the trick was to proving that. And I was sitting in a movie that they played at MIT. There was a movie club. You could go and watch movies.

And I was sitting there. And we all remember those moments. I remember that one. But I just sort of eased into it and just felt I was a mathematician.

So did you have particular mentors or role models? And what did that mean? People that inspired you or you thought you wanted to be like them?

You know, that there was something cool about it or anything like that? Certainly there were people who I found very inspiring. I don't think I ever really wanted to be like anyone. It never occurred to me, oh, if I could only be like so-and-so, I would be happier. But Singer was very inspiring. Ambrose was very inspiring to me. I don't know if you remember Ambrose. I remember him a little bit. Ambrose was... You know, they encouraged me.

People who knew Ambrose seemed to think very highly of him.

Yeah. He was a good teacher. He had very strong opinions. So he was helpful. Singer was helpful. I had another thought at that time. So I ran into Barry Mazur. Now, Barry Mazur, I graduated at MIT in three years, but Barry Mazur graduated at MIT in two years. He was quite famous. And I ran into him on the street. And I had just met him in some other context. I don't remember what. Well, I do, but it's not important. And I ran into him late at night in the street. And as I recall, which is probably wrong, but I somehow recall his wearing a pink torn T-shirt. And I was telling him that I was learning Galois theory. And I really liked that. And he said, 'Oh, it's so beautiful.' And he waxed about Galois theory and this and that.

Yeah, one can imagine it. Yeah. And I remember thinking, OK, this guy is undoubtedly better than I am. I figured, OK, I've met a guy who's better than I am. But it didn't bother me in the least, because I felt, OK, I may never be as good as this guy, but I think I can do some good mathematics and have a satisfying experience. But a lot of kids, they think, oh, they're the smartest kid. And I always thought I was the smartest kid around. And then, of course, you learn, oh, maybe you're not the smartest kid around. But it didn't deter me in the least when I came to that conclusion that Barry Mazur was probably a better mathematician than I was.

Did you think that maybe in some ways, though, you had something to offer that he didn't? Oh, sure.

Not to say that he didn't. I felt I had something to offer which would be constructive. And whether or not he was maybe even had more to offer in some ways, I don't know. But I was perfectly content with that, and it turned out I had some pretty good things to offer. But, you know, you learn these things. You're not the smartest guy. None of us is, I suppose, or maybe there's some smartest guy, but it doesn't matter so much, is the point.

What are some of the things you think are important that might not be totally obvious earlier on? I think good taste is very important.

And I remember when I first heard of good taste, because I'd learned what a group was. And I said, 'Oh, a group, see, you put two things together, you got another one,' and so on. I thought, 'Well, how about if you put three things together? Maybe there's a group, maybe there's a definition.' So I made a definition for myself. You put three things together, you get one thing. And then I sort of fiddled around with, what do you do about inverses? And I had a set of rules. And I showed this to Arthur Mattuck, who was my—I was a freshman at the time, I think. It was in the spring of when I was taking this crazy algebra course. And I showed him this, and I said, 'Well, what do you think?' He said, 'Hmm.'

I said, 'Do you have any examples?' I said, 'No, it didn't occur to me.' And he said, 'Taste is very important in mathematics.' And I didn't know altogether what he meant, but I learned. I mean, I think choosing your problems is really important. And trying to do something that you feel is really worthwhile, because it will illuminate, truly illuminate something, is a good characteristic. And imagination. I think taste and imagination are two very important components, along with at least a decent set of analytical skills. And the better they are, of course, the better you'll do, all other things being equal.

After you got your PhD, we met at Harvard during, if I'm correct, the one year that you were a professor there. Yeah, I was there two years, but one year I was just on research, and the next year I was a professor. Right. So that was my senior year. That would have been 1963–64, when you taught the infamous PDE course. Hörmander's course, that's right. Yeah. Certainly ruined me for that subject for the next 10 years. Me too. You must have had some idea about what you were going to do with it, or maybe not. I figured partial differential equations should be important.

I'll teach a course and learn it.

Should be important in geometry. Yeah. That was a great insight, actually. Yeah. Because now it's kind of so common, it's a truism, but it wasn't always so. Right. I mean, people like Yau, for example, certainly played a big role. Oh, for sure. After a year, you resigned, right, and went to IDA. Yeah. Yeah. So why was that?

The family had made an investment. And as a result of that, I had borrowed some money. And in fact, that year that I was teaching at Harvard, that first year, I was also teaching, unbeknownst to anyone, although I had no reason to think I couldn't do this, at Cambridge Junior College. I bet you didn't even know that. Not even I knew that. Not even you knew that. So instead of teaching two courses, I was teaching four. This may explain your performance in the PDE course.

Possibly.

Well, my performance wasn't that bad.

I was at least a week ahead of the class.

I heard that IDA in Princeton paid more, and you could still do mathematics. I don't know. Should we remind everyone what IDA was all about? IDA, it's where they hire people to do secret stuff. They hire only mathematicians, codes and ciphers, that kind of stuff. And the rule there was you could spend half your time doing your own research, and you'd spend half your time—at least half your time—on their stuff, and it seemed reasonable, and I applied for that job and got it. And I was not very happy at Harvard, to tell you the truth, and I was also... My research, I was right in the middle of learning this new field, minimal surfaces, minimal varieties, that sort of thing. It was a time of a little transition in my life.

So I went there, got more money, and it turned out it was a pretty good experience.

Yeah, so for one thing, you actually, I think, had a real success there, right, you and the group? You mean in their work? Yes, which was code cracking.

Yeah, I solved a problem there that had been around for a long time. The field had some outstanding problems in addition to trying to break some secret code or whatever. There were some problems in the whole, some basic problems in the field, issues, problems, I guess, and I solved one of them. I was very pleased. So my work there was good. I wasn't the best code cracker in the world or whatever, but I was pretty good. Anyway, I solved that problem. But I also did a lot of mathematics.

Was this really your... your first exposure to statistics and probability as a tool? Oh, totally, yeah. How much of its potential did you foresee, or what did you think about it?

You know, what I found there—I'd never done anything like this, that, the code cracking part—and it really amounted to coming up with some attack on a particular problem, and then designing that attack, which would end up being a computer program, and then they would run it. And I was no good at all at programming. And in fact, most of the mathematicians there didn't do their own programming. In those days, we had programmers. You designed the algorithm. But I really liked that whole process. I liked everything about it. I liked designing an algorithm. You know, coming up with some attack, designing an efficient algorithm to test it out, and seeing how it came out. I mean, you know, it was like fishing or something.

I don't know. Actually, I don't like fishing because you never catch anything. But here, I felt we might catch something every once in a while. It was a lot of fun. I liked it all. And I'd never seen anything like that. So, yes, you're right. Later on, that experience of making models, looking at data, making models to try to interpret the data was certainly learned there. And if I hadn't been there, I think the business that we built later would never have occurred. I think you were already interested in the stock market, as I recall. I always had this other interest, this financial interest. You know, even as an undergraduate learning mathematics, I wanted to start a movie theater. And I found a woman with a wooden leg.

I'll never forget it. And she was going to be my partner. The only thing is, I didn't have 10 cents. So, I couldn't figure out how to start this movie theater.

Is it right or wrong that you were interested in applying those methods to the stock market as a possibility?

Yes. At IDA, I got interested in that. And, in fact, inveigled some of the people there that we could start a company. That didn't really get off the ground. We came pretty close to starting a company. I had the two best programmers there. And the boss and I, the four of us, we were going to start this company. And I knew a guy who was arranging to put up the money, and we were going to revolutionize Wall Street. At that time, Wall Street had no computers. They did their accounting by card-sorting methods. None of it had been computerized or whatever. And it was clear you could do some research on this stuff. So, in the middle of everything, I was trotting around New York—I was 28, I guess—with this money guy making presentations of this company.

And we needed cash to start. I had a plan. We needed, I think, maybe a million dollars. And all we could raise was $800,000. But I'd made this rule: if I can't get a million, I'm not going to leave this job and go on and do this. Well, we never got the million, so we stopped. "What do you think would have happened if you'd succeeded in getting the million?" It's a good question. I don't think the business was that well conceived in retrospect. And I expect it would have failed. So it's probably a good thing that we didn't get the million. "Well, maybe it was an idea whose time hadn't come yet." It hadn't come. So in the back of my mind, it was always—making some money was always of interest to me. But for long periods, I didn't think about it at all and just did the mathematics.

"So the other thing you were doing while you were there was the minimal varieties work." "Right." "So how did you think about what you were doing while you were doing that? Because for a long time, I think you've told me on other occasions, you were really trying to do basic stuff and put the—formulate things the way they should be formulated and understand it, I think, in a basic way rather than having a goal of solving some outstanding problem."

I had no such goal of solving some outstanding problem. My goal was to understand these objects, minimal varieties, and understand them and what's the—its geometry, how do their variations change, what's the right formula for—an understandable formula for variation, you know, Jacobi fields, conjugate points, all these kinds of things that you learn about geodesics, I wanted to put into a geometric framework for higher-dimensional objects that were, you know, critical points of the area function, of the volume function, whatever. So I just worked along those lines, I looked at examples, Kähler manifolds, you know, I think submanifolds of Kähler manifolds are minimal varieties, looked at various examples.

What happened was I had become friends with Fred Almgren at Princeton, who had solved this Plateau problem and the Bernstein conjecture for one level up, one level higher than two. I guess he had done three, I don't remember.

But, and I looked at his paper, and it mentioned, he said, ah, this thing is a holomorphic quadratic differential, something like this. And I said, holomorphic? I didn't know what it was. I understood, hey, this thing must satisfy, in that case it satisfies some kind of partial differential equation, linear equation. So then I started playing around with the second fundamental form in great generality and saw, hey, it does, it satisfies a nice set of equations. One of them is an equation that was well known. But the other was perhaps not so well known. No, no, the other was a big breakthrough, I think.

I think I remember when you were working on that. It was very complicated because you did it in, I mean, it was an involved computation because you did it in generality. Yeah, I was doing everything in generality. But I remember you saying that it had to work out.

Yeah, it had to work out. And it did work out. Now I had this equation. And I could see that this was a very good tool. And then I decided, OK, now I'm ready to look at this problem and learn what the Italian school had accomplished. So really the singularities were cones of some sort over a minimal variety in one lower dimension. So that gave a beautiful description of a singularity, and the job was to show that those cones basically didn't minimize, and therefore could be not resolved, but those critical points didn't really exist in some sense. You wouldn't, you'd slide by them. And then I had an idea of how to construct the right variation to get by that and show it didn't minimize.

That happened pretty quickly, as I recall, because I was a graduate student and, you know, you were instructing me at that point. Almgren had influenced you at an earlier stage, what you were describing pre the Simons equation, or at least had told you some facts that were... Well, he didn't tell me.

I just read it and saw it in his paper. He just said, here's a paper. And I read that and I saw this thing. And that's when I decided to try to derive such an equation. And then it was not a very long time, maybe a couple of months before, I don't remember now, I was able to solve this problem up through ambient dimension 8 and my example, my variation worked. But one dimension higher wouldn't work anymore. The sign that needed to be positive became negative or whatever.

Yeah, for a particular cone, right?

Yes, I guess that's right. But the general example, the general process broke down in one dimension higher. Now, there might have been another variation that would have done that. I mean, I had a sample, a way to always go further in the minimization process, but not in ambient dimensions bigger than eight. I found this counterexample, this proposed counterexample, so I could see that no matter what you did, any variation in this cone, the S3 cone... Infinitesimally stable. Yeah. Well, locally stable, I guess. Yeah, infinitesimally. Whatever it was, it was stable. And any variation would actually increase area. But I had no idea how to prove it was a global minimum. It was enough already. So I had a lot of material, and then I wrote the paper.

So that's four or five years on that.

Maybe not everyone knows the story of how you came to that, that it came through the combinatorial Pontryagin classes. Right, which you were involved in. Yeah, and actually stayed involved in for a long time.

Well, I had come to Stony Brook. I got fired, you know, from that job.

Oh yeah, I was going to ask you about that.

I'm glad you reminded me.

So how did that happen exactly?

Oh, it was the Vietnam War, you know, and IDA was a Washington outfit with a satellite in Princeton, but all the rest of it, the Institute for Defense Analyses, it had a Weapons Systems Evaluation Division, it had these very warlike sounding units. Our unit, the Communications Research Division, sounded very, very harmless. I think that was the only one that most of the public knew about. In D.C., the other was a bigger operation. But in any event, and in fact, we had nothing whatever to do with the Vietnam War. We were after a bigger game. The IDA was run by Maxwell Taylor, the famous General Maxwell Taylor, who was retired head of Chief of Staff of the services, whatever he was, and a confidant of Kennedy.

And now in his dotage, he was running this IDA. And he wrote a cover story in the New York Times Magazine section of how we're going to win the Vietnam War. We're doing everything right. It's just a matter of time. Blah, blah, blah. Stay the course. We'll win it in no time. Anyway, it was a stupid article. The war was a stupid war. And so I wrote the Times a letter saying not everyone who works for General Taylor subscribes to his views. And I gave my all. It was a good letter. I was very pleased. And they published the letter in the Sunday edition. And then I was on the watch list as far as I could tell, although no one said a word to me. No one said a word to me. Then you couldn't leave well enough alone.

I couldn't. Well, that's right. I couldn't leave well enough alone. Well, someone came and interviewed me. A guy came to interview me about six months later, claimed he was doing a story for Newsweek, Newsweek Magazine, about people who worked for the Defense Department, which I did indirectly, who were opposed to the war. He says, 'They're few and far between. Could I interview you?' What did I know about interviews? So I said, 'Sure, what do you want to know?' So he said, 'Well, I see you're still working there for the Defense Department. You're opposed to the war. How do you approach that?' So I was kind of a wise guy. And I said, 'Well, they had this rule there.' I said, 'You could spend half your time in mathematics and half your time on their work.'

I had elected to spend all my time on mathematics until the war was over, and then when the war was over, I would spend an equal amount of time on their work to catch up, and that would be that. It wasn't even quite true, because I was still finishing up one of their problems. But I was a wise guy. So then I went back to my local boss, and I told him, hey, I gave this interview. He said, what? I said, it's OK. spilling secrets. He said, oh, okay, what did you say? And I told him, he said, okay, I better call Taylor, Maxwell Taylor, tell him about this. So he called Taylor and he picked up the phone and he hung up the phone and he said, you're fired. So I was fired. I was astounded at the whole proceeding, but I was fired.

And three days later, Lyndon Johnson stopped the bombing, announced he was not going to run for another term, and I figured, 'Hey, this whole thing is over.' And I went back to this fellow Dick Leibler, who was the boss, and I said, 'Hey, you know, looks like I was three days on the wrong side of this thing, because now the whole thing is going to be over, and what's the difference?' And he said, 'I don't think it matters.' And so there I was, fired. But I didn't mind it. I had solved this Bernstein conjecture that we just discussed, and so I knew I was going to get a good job somewhere.

How did you suddenly become chair at Stony Brook at such a tender age?

At such a tender age? After having just been fired. They were looking for a chair and had been for five years without success. They were looking at distinguished guys. So we're talking about 1968? 1968, yeah. Distinguished guys and none of them had come along, or at least who were willing to be chairman. So they were kind of desperate, in my opinion, and someone suggested me. You know who that was? It could have been Lenny Charlap. And it was very appealing. I had already worked out something where I'd be half-time at Columbia and half-time at IBM Research, up in wherever they were, up in Yorktown Heights. I thought that would be a nice sort of continuation of what I was presently doing, doing mathematics on one side and IBM.

Sounded interesting. I had that lined up.

Did you have any idea of repeating the half and half? Yeah, well that was a half and half deal.

But then this Stony Brook thing came up and it was fascinating to me. I had never thought about being a chairman. But they really needed to build up a department. And I like people, and I like to hire people. I like to—not hire, I didn't—

Never hired anyone, but I like to work with people and sort of get things going. So you're already—that kind of thing appealed to you at that time, building, building something? Yeah, definitely. Just like when I wanted to start a company a few years earlier, that was—uh, I liked it. But I guess Stony Brook was your first experience actually of— Oh, sure. —of building something like that? Yeah. The guy who interviewed me, the provost, it was Bentley Glass was his name. He said something very funny, you know. He said to me, uh,

Well, Dr. Simons, you're the first person we've interviewed for this job who actually wants it. I said, "Well, I want it." So they took a chance. And it worked out good.

It worked out well. I guess it was a reflection of the times that something like that could happen, almost. I mean, there was much more support for science. Things were much freer at that time that they could, particularly, I guess, in the state. For a little while, they had these big ideas for Stony Brook. Big ideas for Stony Brook. But still, a 30-year-old guy.

Yeah, well, at the time, I didn't feel so young. I mean, I had three children. I had some success. I always felt very responsible. I'd take care of everybody or take care of things. So I didn't feel so young. I didn't feel like, "I'm just a kid here. What do I know what I'm doing?" It seemed fine to me. I wanted to understand characteristic classes, and I never really dealt—I mean, I knew the Chern-Weil homomorphism and that stuff, but I didn't have a good feel for it. So I thought, "Okay, I'm gonna—I gotta learn this stuff." And so I started fiddling around and, you know, maybe you and I talked relatively early in this proceeding. You came to Stony Brook the next year.

Well, I remember your having come to the famous global analysis conference at Berkeley in 1968. Remember that? It was this huge summer institute. Yeah, yeah. And so I remember your having come out there very excited about this problem, the combinatorial Pontryagin class problem, with the idea that you would just do some residue calculation.

I figured, okay, you know, the Euler characteristic has a nice combinatorial formula, why shouldn't the signature? But this was sort of like a, okay, a way to learn the subject. Okay, I'll get this, start with the Chern-Weil formula, and then start flattening out the pieces and seeing what happens. It was all very interesting. It was a great experience. Unfortunately, it didn't end up with a combinatorial formula for the signature. I guess it's—a third of the first Pontryagin class, whatever it is.

Yeah, say for a four-manifold.

I just wanted to work on a four-manifold. I just wanted to study that. In the course of it, I came up with this formula, a three-manifold number, a function of a three-manifold—I guess it was the boundary of the star of a vertex or something like that—and started fooling with that.

So I guess a key point in this is that implicit in what you wanted to do from the beginning were not only the characteristic forms but the transgression forms, right?

Well, if you're going to start trying to integrate the characteristic forms, you're immediately led to the transgression forms because locally it's d of those things.

Subsequent development showed they hadn't been given their proper respect, their just dues, their props.

That's right. It was a convenient way to... lift something to the principal bundle and make it bound. But you needed it to prove the Chern-Weil theory. You needed to show these things are cohomologous. So you need to show they differ by something exact. The thing itself was not taken particularly well.

Yeah, I think it was, you know, thought of as something that came up when you were studying characteristic classes, but not something that was necessarily interesting in its own right, particularly because they weren't closed, of course.

I mean, it's interesting, and universally it turns out they're well-defined up to exact. So you usually think of things closed modulo exact. This was just all forms modulo exact. So they had this property. But sure, I think people hadn't thought about those forms so much. In any event, in the bundle, these forms were restricted to these classical cohomology classes on the fiber. Because when you restrict them to the fiber, they're closed, and everyone knew about trace powers, but that was pretty well known. So in some setting, the transgression forms had a life, for sure.

Yeah, right. I mean, even in topology, in a way, at least the topological idea of transgression certainly existed. Isn't it fair to say that Chern sort of knew these formulas, but it hadn't maybe occurred to him that they were significant as objects in their own right?

When I came to him with a three-manifold result, that here's an invariant of a three-manifold, it's a conformal invariant, and it's only defined mod Z, but that's good enough. And then it's an obstruction to something being conformally immersed in one dimension higher. He was very excited. He was very excited. And I remember the day we were together and I... 'You mean on the plane?' 'On the airplane.' And I made that calculation. If something was codimension, you know, the thing was codimension 1 in $\mathbb{R}^4$... I said, 'Oh, I can calculate this invariant. It just comes out zero.' And he'd say, 'Yeah, but that's great.' I said, 'Oh, maybe you're right.'

So what was it like working with Chern?

For him or with him?

I thought I said with him. Did I misspeak?

He was very up. He taught me some of the more arcane calculus of how to manipulate all these forms, which I—you know, you had invariant polynomials and, you know, in detail how you turn these into characters and all their various properties and so on, which were more than I had known before. And he was very facile at dealing with that stuff. So he'd write down formulas and move the bracket around and so on and say, 'Ah, you see, this is this,' and so on and so forth. So he taught me a lot. And then we wrote our paper together. But already you and I had started doing some work.

Right. Well, I mean, that went back to the approach to the combinatorial Pontryagin also, which didn't, for good reasons, quite work out. But yeah, we had been talking about it for some time, I guess, as it developed.

Well, I kept trying to push down these things. to the base, you could get certain, what we now, anyway, came to call differential characters, but you could have some functions on the cycles in the base that were well-defined, and I gave them a name, and I wrote up that whole paper, a whole paper, and I think even submitted it to the annals. And I even think they accepted it. But in the meantime, you and I started looking at a more abstract version of this stuff. And then I saw, hey, you know, there's better ways to do this. And I remember calling Singer and said, look, I wrote this paper. I think they want it in the annals. But I don't think there's a better way to do it. What do you think? Should I let it get published or not?

And he said, 'You know, who needs a paper that you're going to soon replace?' It turned out 'soon' meant like 30 years, whatever. Well, maybe till it actually appeared, right? We had the famous notes from Stanford from 1973. But I was, if you ask what, it was a high point in mathematics for me. It might sound silly. But I was so pleased with the definition of a differential character. I was really pleased with that notion that you could just define this in an abstract way. And it satisfied this beautiful set of mappings and so on. And then you showed how you could multiply them. You figured out how to do that. I'm really proud of that, the differential character. Well, you should be. Well, maybe.

Maybe I should be. But anyway, so that was a high point for me.

And you also, I think, were very convinced, even at the time, that this was something significant. It was. I was definitely convinced. Although I'm sure you didn't foresee that they would become important in string theory since no one knew about that at the time. I think they still haven't become important enough. No.

But I did tell Yang that these things existed. They were invariants in bundles with connection. And you guys, I said, 'You physicists are all busy with bundles with connection. And gee, maybe these things would be worth something.' But he didn't bite.

I wonder if we could backtrack just a little bit, you know, what your memories are of the atmosphere in the wild and woolly early days at Stony Brook. Well, we had a lot of money.

When I got there, they were flush. We had a lot of parties. We had a lot of parties, but I was able to hire a lot of people was the point, so we brought in a lot of young people. 10 people the first year, I hired 10 people the second year, and we had to move some people out, as you say, who didn't have tenure. We had some great, it was a great bunch of people, and we had a lot of fun. What really made that year was getting Ax to come. And once Ax had agreed, a lot of people could, that was the existence theorem. One could attract a great mathematician to Stony Brook, so others came, and of course you accepted as well that year. Yes, Detlef. And Detlef. Well, Detlef said he'd come if you came, and you said you'd come if he came, but then he said he would only come if Wolfgang came too, and so we ended up with three hires in geometry.

Well, David Ebin also. Oh, David Ebin, yeah, I forgot about that. David came that year, yep. So there were four in geometry and analysis. Ron Douglas came, and Roger Howe. I think Roger Howe was hired. The best set of letters I ever saw on anybody, or at least any

any postdocs. Did you know that I was, when I was at Harvard, I was a grader for a course where he was a student? Oh yeah? I noticed there seemed to be this very smart guy in the course. Yeah. It was the regular advanced calculus course. It wasn't the special Math 55 theoretical course.

But it was great and the administration let me kind of have my way. And we demonstrated good abilities to get good people. And we had a lot of fun.

So I remember one phrase in particular that you used to use at that time about someone either we were trying to get or we had gotten. He's a real guy. Do you remember that? No. One of the people that we were very interested, we used to talk about getting, although it never happened, was Kostant, who I guess you knew going back to the time when you were a graduate student. Yeah, he was my thesis advisor. So what was that like?

Well, it was... So he's an unusual person. He's an unusual person. I learned a lot from him. What was unusual about him? He didn't encourage me in the problem I had picked out to solve. He felt it was too hard, and my approach was wrong. And I think if I had been in his position... So you picked the problem? Yeah.

You picked the problem.

Well, what happened...

This was an algebraic version of the classification of holonomy groups, right, or candidates.

Yeah. Yeah, but it was a direct proof of transitivity, a direct proof of transitivity, and I algebraicized the whole thing. Oh, yeah.

And it was... after they were classified. They'd all been classified. Then it was observed they were all transitive on the unit sphere.

And I had been... He'd given me some papers to read that I thought they were great. Some of his. One was a paper of Hochschild and... It was two guys. Hochschild and a topologist, I can't think. Cohomology of Lie groups and Lie algebras and they really sort of made all that very much come alive, and I learned a lot from that. But I was playing around, and I made a little calculation, and it seemed to lead in the direction of transitivity or non-transitivity or something like that, which I had known was a problem. I didn't know the classification, and I didn't know that these were all transitive. No, I didn't know that. But I... saw this calculation, I mean I made this calculation and I showed it to Kostant and he said, oh, Hunt did something similar.

I said, oh, yeah. And then Kostant mumbled about... Hunt? Gilbert Hunt? Gilbert Hunt. Don't ask me why. I didn't know who Gilbert Hunt was, but he said Hunt had made a similar calculation in some paper. And he said, you know, it's conceivable this could inform the question about this transitivity. And I said, oh, yeah, well, what's that? And then he told me what the problem was. And he said, you know, it's a hard problem. He told me, Singer tried to solve it. I mean, he was saying, this is a hard problem.

But I was intrigued by it, so I just started thinking more, and I came up with a scheme. I came up with a scheme, a whole scheme, and I showed him this scheme. And he, you know, it was kind of following how you analyze Lie algebras, finding a maximal Cartan subalgebra and then looking at that as it acts. You know, you look at that under adjoint representation on the maximal, you know, abelian subalgebra, commutative subalgebra. And then it has roots and weights and all that kind of stuff. You probably remember that. I do, actually. You do. I never fully internalized it. Well, I had fully internalized it at that time because I'd studied that stuff with Singer the year before my one graduate year at MIT.

So I was pretty imbued with roots and weights and that. And I thought, oh, well, maybe you could follow the same general procedure: a maximal, totally geodesic submanifold. Anyway, there was an analogy, and I showed him this, and he was very dubious. I just liked that approach, so I just carried on and did it. I had communicated with Singer once. I wrote him a long letter showing what I was doing, and he wrote back very encouraging.

So you were out in California by this time, in Berkeley? Yeah.

And this was near the end of my first year there as a graduate student. And I only spent two. And then I made a lot of progress, and I came back to Boston in January of the second year there, and I was stuck on one point. I couldn't make something work, and Singer was nice enough to come, and it was a snowstorm. He remembers that better than I do. But anyway, we sat in his office, and I showed him how far I'd gotten, and I said, 'I'm stuck on this point.' And he said, 'Yeah, but you've assumed irreducibility.' I said, 'Oh, yeah.' That was the end of that. I mean, he saw somehow I had—the whole thing was supposed to be, the manifold or the algebra, I think, was supposed to be not a product. It was supposed to be irreducible.

And I had forgotten to use that. And I was trying to prove this thing. And he said, 'Well, it falls immediately from irreducibility.' So that was the break. That was a final breakthrough, at least I thought. When I got back, I found another problem, which I solved one day in the shower. And I don't remember exactly what it was. But anyway, so Kostant was, you know... But I learned a lot.

What was his reaction when you did it?

I guess he was amused, pleased. I don't know. I was a student. I suppose he was happy. I don't remember exactly what his reaction was when I did it, but it certainly wasn't a negative one. It doesn't sound like it was all that positive either. Well, no, I think it was positive. I think it was a positive reaction. It was a long time ago, and I don't really remember. But I remember more his suggesting that this was not the best direction to go. And it may have been good advice, because I think the scheme looked a little harebrained. And he knew it was a very hard problem. And it's not necessarily so advisable to give your thesis students the hardest problem in the world, because then you're going to have them for a long time.

And maybe they ain't going to finish. So I've never criticized him for not, you know, being more encouraging. But I liked it. So that was my thesis. It got published, and I went to MIT to be a Moore instructor.

So you were a Moore instructor before you came to Harvard. Is that what happened? One year.

One year. Then I resigned from that, because I thought I was going to go to South America and work with my friends to make this plastics business. And I soon realized that that was a big mistake. In those days, there was plenty of money around. And Bott put me on his contract at Harvard. So then I went on Bott's contract. And then I could have been an assistant professor either place. And for some reason, I picked Harvard. That's how I met you.

That's right.

So maybe you could talk a little bit about what Singer was like, what your relationship with Singer was like.

Well, I can't talk about Singer without talking about Ambrose first, because it was through Ambrose that I met Singer. So Ambrose was—I met him in my sophomore year, second year of college, and he was teaching analysis. And I had a terrible time with the first semester of analysis. Deltas and epsilons and point-set topology and all that stuff, I couldn't make head or tail of it. I found it boring, hard. And when I took the final for that quarter, for that semester, there were a bunch of problems. I couldn't solve any of them. I really hadn't—I did, but I didn't realize it, hadn't absorbed the material. And I just wrote him a note saying, 'You know, I seem to be able to do other things pretty good.'

I was taking complex variables at the time. I was OK with that. I was doing Galois theory. I was OK with that. I wrote him this note. I said, 'But I haven't understood head or tail of this course.' So he was nice enough to give me a D and let me go on to the next semester, which was basically differential geometry. It was Stokes' theorem, and it was integration and Stokes' theorem and that kind of stuff, which I... So was it differential forms? Differential forms. He defined differential forms and proved Stokes' theorem. I thought that was the greatest thing. I went from understanding nothing to understanding everything. And, oh, by the way, the stuff that I thought I didn't understand in the first semester began to crystallize, and I understood that too, although I never warmed to it, but I did understand it.

And so one day during that semester, I went to Ambrose to talk to him in his office to ask him the following question. And so I said, 'Professor Ambrose, when learning mathematics, is it better to learn a little bit about a lot of things or a lot about a small number of things?' And he looked at me and he said, 'One can make the cliché either way.' That was it. He said no more. And I realized the interview was over, and I left. But I forgave him for that. That was Ambrose.

So did you take anything away from that?

Nothing whatever. Well, I took away that Ambrose was—once, some years later, I was with him in a car in Berkeley. He had come to visit, and we were driving. And we came over a hill just as the sun was rising over San Francisco. And it was very beautiful. And I said, 'Isn't that beautiful?' And he said, 'Thank you.' He was a very literal fellow. But he was very inspiring as a teacher. And then he was working with Singer, and I would begin to see them in Jack and Marian's, a restaurant—Jack and Marian's—late at night. And the two of them, I think, were working on the holonomy theorem at this point, I learned later. And they'd be sitting there, and I wondered, 'Who is this other guy?' Ambrose was an old guy at that point.

He was like 50. And Singer was maybe 35. He seemed senior, but not quite at his dotage. But I thought, what a cool, this is so cool. Here are these two old guys. Their job is to sit in Jack and Marion's at 2 in the morning and do mathematics. I thought that was great. So I got to know Singer. in a year or two later there at MIT, and all those roots and weights and stuff like that. So in my first year as a graduate student, my last year at MIT, I did a reading course with him on the Cartan seminar notes on Lie algebra, Lie groups. I don't know if you know those notes. Inadvertently, some years later, I saw a letter that he had written about me. And it said something like, It was inadvertent. I don't know.

It was lying around somewhere. I don't know how I saw it. I wasn't going through his files. It was just there. I don't remember the circumstance. But I remember the letter and it said, in effect, sometimes this guy seems very dumb, but other times he has terrific insights.

And I remember thinking, 'That's me.'

So Singer was, you know, he's such an outgoing guy and helpful and he became a very good friend.

What does he bring to the table that's made him so... made the mathematics that he's done so important and influential?

Singer is very broadly educated. He started in physics, actually, and then moved into mathematics. And he did functional analysis and C*-algebras and stuff like that.

Right. There's this, I guess it's an article by Kadison. I don't know if you know it, about his early work in function algebras, which is entitled 'Which Singer Is That?' I see. Well, that was that Singer.

It was the same Singer. Then he got into geometry, I think, a little bit later, when he and Ambrose were working together. I don't know exactly what his trajectory was. But the important thing, I think, was that he was very broadly based. He knew a lot of mathematics from different points of view. And certainly, when he got into the index theory area, when he and Atiyah... all that stuff he knew about functional analysis, I think was probably very helpful in the development of that work. So he was a broad guy, always interested in learning something new, and always interested in helping people, as far as I could see. He's a really wonderful guy, as everybody knows.

Well, I recall on another occasion you said Singer is deep. So, you know, even after the index theorem, you had confidence that he would be doing important things. Singer was not the fastest guy. Yeah, very different from Atiyah, for example.

Very different from Atiyah, right. But obviously they made a great couple. Well, Singer had other important collaborations too, I guess. Ambrose for one. Ambrose. McKean and Singer. That's right. Ray. Ray-Singer. Ray. Certainly known about. Yeah, he must have had a lot of collaborators. I don't know. He was a lot of fun to work with.

Do you have any comments on sort of the joys of collaboration?

The last piece of mathematics that I did before retiring from the field was in 1977 in the summer, and I went to a conference. I was already thinking about investing and that sort of thing, but I went to this conference in Japan, which I had accepted a long time ago, and I'd never been to Japan, and that sounded exciting. And I had a good time there, but I had to give a talk. And it was actually pretty amusing because I had some money by then, but I said, okay, while I'm at the conference, I'm going to, you know, be like everybody else. So I had a hotel room that was the size of like three telephone booths or something. I mean, it was really small. And I had to give a talk in the next day or two.

And I didn't know what the hell I was going to talk about. But I'd heard about, I don't know, something to do with Yang-Mills forms. I can't remember. Symmetries. But I do remember getting an idea and showing that there was such, something was unique. There was only one, there could be only one such structure. And I paced around in this little room, and the floor was littered with papers. You know, you drop three papers on the floor, it would have been littered with papers because it was so small a floor. And I came up with this result. I thought, okay, I'll talk about this. And Blaine was there, and Mary Louise, I had just met Mary Louise for the first time. And Blaine saw the talk and liked the result.

And he saw how to generalize it in one thing or another. And a few months later, he said, "Would you mind if we wrote this paper up? And we'll put your name on it along with mine, and I think there was a third person." I don't remember. Probably Jean-Pierre, right? Could have been Jean-Pierre. It could have been. But in any event, there it was. And so that was a joint paper. But really, we didn't collaborate.

I like collaboration.

You know, when I started Renaissance, it was all collaboration. And I really like that, working with somebody else. And you know, sometimes it's frustrating, but when it's going, it's good. Well, you collaborate a lot, right?

Yeah. Yeah. Not exclusively, but a lot.

Yeah.

Yeah. I mean, I find that every collaboration is different. What do you think?

Well, you have to work with different personalities. Right.

Different personalities, different strengths, different relative strengths. From Chern to Dennis Sullivan is a big difference. I thought at some point I would ask you what it's been like having come back to mathematics after quite a hiatus and now working with Dennis, who's an unusual character, to say the least.

He's an unusual character. I tried to hire him, at your suggestion, I think, when I first came to Stony Brook, but he didn't bite. Do you know, I learned a new way, a different way of looking at things. I mean, I've learned a lot from that. And I think he's probably learned a little something from me, because I can do some things that he's not necessarily so good at. But he's a masterful mathematician. And he sees things categorically, and categorically, he's a very big-picture guy.

Right, another guy who's not that fast, I would say. That's right, that's right. At least not that fast in a facile kind of way, although he's pretty fast to get deep insights sometimes.

Yeah, it's been quite positive. We argue a fair amount. I mean, I argue with him more than I... I never argued with Chern. There was nothing to argue about. Did we used to argue? I don't think so. We may have argued a little bit. A little bit, but not much. Not too much. Dennis and I argue quite a lot.

But, you know, we work it out. Dennis doesn't let anything go by, right? If he's not completely sure of something, he wants to stay right there, is my experience.

That's right.

You know how it is in math.

You get a feeling for what's likely to be true and what isn't likely to be true. And you get that intuition from some years of working in a certain regime and doing certain calculations or whatever it is. And you have a feeling, 'No sense doing this. It isn't going to work.' Or you start it a little bit and say, 'No, I can see this is not going to work.' I don't think Dennis... Dennis is not a big calculation guy. His insights are really geometric in a sense that mine are not. I mean, he really sees things in all their... Yeah, I would say geometric and also structural somehow. Yeah, yeah. So he has those things. So he'll sometimes urge me to do some calculation. It's not going to come out. It's just not.

Believe me. But he has a hard time sometimes believing that. But on the other hand... Who's right?

In that particular area, so far I'm right. Yeah, I mean, because I always thought of that as one of your big strengths, in both choosing which calculations to make and then being able to make them.

Yeah, I'm pretty good at that. But usually you need a good idea of how it's going to come out before you really do it, a general idea. So you can see pretty early that there's too much against this. This isn't going to happen and give you a good answer. We argue about that, but it's great fun. I mean, he has tremendous enthusiasm, and I like writing, actually doing the writing once I know what I'm doing. I like to get the notation straight and try to make it as clear. I think I'm a pretty clear writer.

In 1976, you went into business. And I remember I didn't entirely approve of this decision, at least initially. But certainly one would have to say eventually it worked out very well. It worked out. Have you met people in that career who you found extremely impressive? And was it in the same way or in a different way? That's an interesting question.

People on the same level, let's say, but possibly in a different way. Well, once we started hiring scientists into the work, mathematicians, computer scientists, physicists, that took a while to do before we were 100%. I would say no, and I don't think—in my business life, I've certainly met a number of people and have some friends, but I'm never quite as comfortable. So I don't know. I haven't been blown away. You mean even with the scientists?

Oh, with the scientists, some of them have. I've met some of them. They're very smart people, but, you know, maybe in a slightly different way.

You mean the Renaissance people? Yeah. Oh, yeah, they are smart people. Peter Brown is a very smart guy and so on. But I feel comfortable with those people. But I've always felt like something of an outsider, no matter what I was doing. So in mathematics, I was immersed in mathematics. I was a mathematician. But I never felt quite like, 'Oh, I am a member of the mathematics community.' Never really felt that. I always had a foot. Similarly, I certainly never felt I was a member of the business community. I feel like more of an outsider in business than I do—you know, than I did in mathematics, even. On the other hand, I definitely liked the business that I was doing. It was great fun, very satisfying.

We made money in a different way, I think, than anyone had done it before.

How satisfying was that? Because in a way, I think it was really quite an achievement. There's so many people around the world who are investing in the stock market, watching the stock market, all sorts of people. And in a way, the record shows that you at Renaissance were the ones to crack it and say, you know, there are these systematic phenomena that you can make money off of. Yeah. Not just in the stock market, in fact.

Remember, we started in currencies and interest rate instruments and that sort of thing. You know, it was back to doing research. I mean, at first I did it on a fundamental basis, and in fact, we made more money per hour with fundamental trading, at least for certain periods, than I ever would have made with the systematic trading that it became. Gradually I could see that the systematic stuff could have legs. So we started in currencies, interest rate instruments, commodities in general, but then started building systems. And that was—that was the real breakthrough. If I'd stayed with fundamental trading, I would have gotten colitis again or something. It was a big strain. You never know quite where you stand.

You come in one morning, your position is way up. You say, 'Oh, I'm a genius.' And the next day, it's down: 'Oh, I'm a dope.' And the reality is you're not really a genius, you're not really a dope, and maybe you're actually going to make money on this thing. But the volatility was too high. Making models, on the other hand, if you could find some statistically significant factors, that was great. Not only for the satisfaction of making some money, but just the thrill of finding a new predictor. We found lots of predictors over the years. You find a new predictor and it's really terrific. You know, you run the simulation and you see, 'Oh my goodness, this is a real statistical advantage to this particular predictor.'

And it's independent of the other ones and so on. And you build up the system that way. I found that very, very gratifying. The risk control things, I mean, dumb things maybe, but nonetheless, how to model, for example, how to model costs, the right way to model costs—there was something of an intellectual content there.

Yeah, so it sounds like the words even have some similarity to, like, the right way to do minimal varieties.

Yeah, yeah, that's right. We found what I consider the right way to do this modeling, at least one aspect of it. I think we found the right way. And, well, someone can come along and do it better. I don't doubt that that will happen sometime. But we were certainly a pioneer in this. And when we started it, there was nobody else doing that, as far as I could tell.

So how much of this, to come back to something I mentioned earlier, did you foresee a long time ago as a possibility, but when there was less computing power? So I can remember, for example, hearing from you about the problem of speech recognition. Yeah. And it was supposed to be so hard, but now— Still hard. Still hard, but it's something, right? That's right. So I'm just curious as to whether you were able to dream ahead, "Gee, if we had, you know, computers that were a million times faster, we could do something like this," or was it a kind of gradual evolution?

It was more of a gradual evolution. The computers were always adequate to do what we thought would be useful at the time. As we get into faster trading and analyzing more data, but you see that all that came because computers have gotten better. So there's more data available because there's more bandwidth available, there's more storage available, not just in our office but all over the world. So more and more data gets generated, computers get faster, we learn to use that additional data and so on. So I don't ever recall sitting back dreaming of what we could really do if we had a quantum computer. I don't know what the hell we'd do if we had a quantum computer. But by the time we actually had one, we probably had figured it out.

So it's kind of scary. I remember being at IDA, and they were going to get a new machine. It was going to be the biggest machine in the world. And it was going to have a million words of storage. Now, a word was 60 bits. So it was like eight million bytes of storage. I mean, 8 million bytes of storage is nothing. This was coming, and we didn't know how we were going to use all this storage, right? It turned out within three weeks it was absorbed. But I didn't know, what are we going to do with a million words of storage? It's an awful lot of storage. Core—it was called core memory at that time. So maybe I've never had enough imagination to think about how you'd use infinitely fast computers.

Enormous amounts of data exist now, and people are trying to look for ways to process them and extract predictions from them in all sorts of fields. So I wonder if you have any—any thoughts about maybe how dominant—is this a real paradigm shift? How dominant will it become? Will it really change our lives? What role, if any, should math departments play in this? This is something that I have to wrestle with right at the moment and in the coming years.

Well, I don't know what role math departments should play in it, but I do know that there is more and more data coming out and more and more data to analyze. And I learned words that I didn't know. You know, that was a megabyte. I got, okay, a megabyte. Then a gigabyte. Okay. Then a terabyte. I thought, well, that's pretty much. Now it's a petabyte, which is 1,000 terabytes. I can't remember how many zeros all these things have, although we could figure it out. But so here's something I learned just the other day. So at Cold Spring Harbor Laboratories, where they do biological research, and we support some of that stuff, they need petabytes of memory. What in God's name can they do with petabytes of memory?

Well, it turns out the following. You really want to understand, see, our brain has like a trillion cells or more. I mean, our brain has, and all of those have dendrites and they make connections to each other and synapses. It's a huge amount of information that's in a brain, even in a mouse's brain. So I'm going to get to a mouse's brain. So you take a mouse, you sacrifice this mouse on the altar of science, cut off its head, freeze it, and begin to slice the brain. Now, you can slice its brain, this latest incarnation, at 10-micron slices. And each slice will have resolution at a micron. So you'll get a tremendous... Okay, so these dots are... Every micron in this square array, this rectangular array, you have a dot.

And now every 10 microns, you have another slice. And you add all that up. And it turns out it's a hell of a lot. Now, what do they want that for? Because they want to really understand networks. They really want to understand structures, very delicate structures. And this is big stuff. And not only that, it's not one mouse. It's a thousand mice are sacrificing themselves on this altar. So now I've got a thousand of these things, and I want to compare them and make sure everything is lined up. So because there's a statistical difference, you might not know this, but not all mice have exactly the same brain. So there's little differences with mice. And so here's an example of research that's going to be good research.

We're going to learn a lot more than we know. But it's going to just require a huge amount of data and computer processing. I don't know what math departments ought to do about that, but kids need to learn, get comfortable with statistics and one thing or another at some point in their lives.

I wanted to come back a little bit to this period around 1976 when you finally decided you were going to not be a professor anymore and go more or less full-time into business. So yeah, how did that decision come about and what was in your mind when you were making it? Well, it came about because

That business in South America that I alluded to from '62 and when I came back to MIT to teach and I immediately started for some reason started thinking about my friends in South America and how they should do a business and somehow we should invest in it, although I didn't really have any money. And I did go down there and get them going, sort of just spiritually rather than anything. But 12 years later, in '74 or '75, maybe '74, they sold a piece of it and there was some capital. And that capital was largely my family's. But our mutual friend, Charlie Freifeld, invested that. And it did pretty well. And so then I had, anyway, the family had some money. And so I felt two things. One, that money was enough to keep me going for a while.

And I found this whole process of speculation quite interesting. In particular, I had gotten interested in currencies. So I figured, I have a little money. There's something else I'm interested in. I was, as you may recall, very frustrated with the work we were trying to do.

I recall that very well.

You remember that very well. Proving numbers were irrational, which is still not known. But that was supposed to be the punchline of our paper on these differential characters and so on.

Although we did get the application without proving they were irrational, the application we had in mind.

How so?

By using these automorphisms in these examples.

They weren't continuous automorphisms, but automorphisms nonetheless, so you could bring the real classes in and drag them around. That's right, that's right. So we found some rank in that discretized Lie group of homology. But nonetheless, there was bigger game there and we weren't able to really get it. So I was frustrated. I was between wives and had this new opportunity. So it seemed perfectly natural to just do it. Chern told me a few years later, he said, a lot of people said, 'Oh, it's a shame Simons is leaving mathematics,' and so on. And he said, as I think I've told you, he said, 'Well, yes, but after all, he wasn't David Hilbert,' or something to that effect. He needn't have reached that high, but he made the point that somehow the subject would limp along without me, as of course it has.

So I was very excited about this new enterprise.

I felt during those first years that you were really losing something because you weren't hanging around all the time with mathematicians anymore. So from my personal perspective, I thought this was a step down.

Yeah. Marilyn, on the other hand, my wife thought it was a step up. At last she could hang around with people and she'd know what they were talking about. I liked being around mathematicians and that was fine, but I was having fun with new people and just having fun exploring this completely new regime for me. Speculation in currencies, which I found interesting, had just gone off of fixed exchange rates, which they had until the middle '70s. So you couldn't speculate in currencies because they didn't go anywhere. So they were free to trade. And the prices were moving around. And I had some ideas on where they'd go and so on. So it was fun and successful. So I never really looked back. There was never a time

when I looked back and said, 'Oh, I miss all that mathematics.' It was just a new leaf in the book. It wasn't that from time to time I wouldn't think about it. Yeah, I know that. And I would think about it from time to time, maybe do some kind of a calculation. I was mostly always pulled back into the business. And so for almost 30 years, until 2004, I was out of it. I didn't do any mathematics. And then I got back in in 2004 and have been sort of a mathematician again. I mean, you don't stop being a mathematician. Someone asked me a couple of days ago, they were asking me something and I explained, how do you remember all that stuff? I said, 'Well, you just don't forget it. I didn't forget anything.'

As I also said, such a giant store of knowledge I didn't have because I was not the most broadly educated.

But I had something to forget. But I didn't forget anything. Based on intermittent phone calls that I would sometimes get, that you, for one thing, continued to think about the same problems we were stuck on. Yeah, I did. The amazing thing is, 30 years later, in this work with Dennis, you actually kind of solved them. Yeah. At least some of them, not the irrational number. Not the irrational number. So when you started working more actively—so I know first you had some ideas that you came to me with, and I pointed you in the direction of Dennis. I thought he was really the person with whom to discuss these things. So how did that happen?

Well, that was in the winter, really the winter of 2003, the spring of 2004. And what had happened was we had a tragedy in our life. We lost our son, Nicholas. And that put me in a very contemplative mood or mode. And we were spending some time down in Florida. We had taken a house down there for the winter, so we'd have a place to go on weekends because we just didn't want to hang around the house and mope. So we rented a house in Palm Beach and we'd go down there, not only for weekends, but we'd spend a week or two at a time. And I remember sitting outside in the back patio, and I started thinking about mathematics again, this particular question of uniqueness of differential characters, whether the diagram could really characterize the thing.

And I just started working on it, and I found mathematics was sort of a wonderful place to be, because when you're doing that, you're just not thinking about anything else except the problem, and it was like going into a cocoon of some sort. And in fact, I was getting somewhere in that problem. I could see some easy facts that were leading me to think that one could prove uniqueness. And then I came to you, and we fooled around some, and then I was in Nepal again in connection with Nick to set up something in his memory and thinking about the problem, and we had looked at it that what you want to do is map the space into something and pull back to a place where the diagram did uniquely characterize the thing, and then you pull it back and so on.

Some functorial argument like that. But while sitting on the steps or the balcony in this hotel, I started thinking, 'Wait a minute, it's not that you want to map it into something; you want to map something into it.' And I could see how this would work just fine as long as you could realize every homology class by a manifold that was mapped in. The image of its fundamental class would represent all homology. And then I saw quickly how you would prove it there. And then I came back to you and said, 'Is every homology class represented by a manifold?' I think I came back to you and said that. It was funny because very shortly thereafter, Dennis had come to see me to ask me for some advice on something or other—I don't know, personal advice on something to do with his kids.

I don't remember what it was exactly, but he walked into my office and I said, 'Aha, the very man I want to see!'

I actually feel quite proud of having gotten you two guys together. Yeah, you got us together.

And I asked him this question, and he likes to tell the story, he said, 'My boy, sit down. The answer is no, but it's almost true,' and so on and so forth. Immediately, since a multiple of any class could be realized by a manifold, we could see that, okay, the R mod Z uniqueness was there, because then you could just do the thing and it didn't matter if it was a multiple, you're just going to divide by something. So I said, 'Okay, but now that's great.' And I said, 'Is there such a manifold?' And he said, 'Yes.' And I said, 'Can you find it?' He said, 'Oh, no, no, that's hard. That's hard.' So then he started thinking about it. And then he brought in pseudomanifolds, something I'd never heard of, and pseudomanifolds.

Yes, I know them well.

I'm sure you do. And so did he. And he showed, gradually put the pieces together, and how one could really do this theorem using pseudo-manifolds as the representative. So I was extremely pleased with that. And then the uniqueness on the multiplication. Again, I saw some algebraic facts that should lead to that. It sort of made it preposterous: if there were two different ones, you'd have some topological invariant, which would—whoever heard of such an invariant?—and then he threw some algebra at me and said, 'Yes, yes, it can't exist,' so the multiplication is unique. So the whole thing came out. And so that's what got me going. But right at the beginning of this, he was saying, 'Okay, well, fine, but we have to do this for K-theory instead of ordinary homology, cohomology.'

But you had always had this dream about K-theory with connection.

I had. I had. But the thing is, his proposal was different. His proposal was you make characters in the same way, and he had a slightly elaborate way of making characters, which turns out, in the end, to be a perfectly good way of making characters, and that's what we're fussing around with now. But as we went through what you needed to prove this and so on, or to construct this thing and then these things, what it really looked more and more like was what you just needed was bundles with connection with a certain equivalence class on those connections. So I, instead of fussing with the cycles, what about just this? And so that turned out to be a very good representative of the differential cohomology.

And there was one slightly tricky part of it. And even there, one result that you and I had had in our—the famous Stanford notes—about the direct sum and when the direct sum of two connections was equivalent to the—in a certain sense. We weren't saying it quite that way. We were looking to make inverses. It turned out that that was a very useful approach to show that every vector bundle had an inverse and so on—with connection, had an inverse. I got back into it. And sometimes it's good, sometimes it isn't so good.

What, doing math again?

Yeah. On the whole, it's good.

Sometimes it's frustrating, or what?

Yes. Sometimes it's frustrating.

You think this applies only to you, or what? Yeah, I know, I know.

You think you're something special? No, it's not the only thing I've done. You know, I'm juggling all these different activities at the moment.

You're supposed to be retired.

I'm supposed to be retired, that's right, but I ain't.

So what do you have to say about this latest phase? Which, of course, includes the foundation and all the support for science. It includes a lot of things.

I'm involved in a lot of things. But it was not, as it turned out, a joyous transition. So going from math to, you know, even going from math to academics to IDA was smooth and fun. Going from IDA to being a chairman was smooth and fun. Going from chairman to going into business, that was smooth and fun. This has been smooth but not as much fun as I thought it might be because ever since I was the chairman, since I was 30, I had a—I was a leader of something. I had a group of people around me. We were working together. But I had a leadership role. And I really like having a leadership role. And so I ran my company for many years. I was the head guy. And I finally decided that it was time to turn it over to the younger generation.

I was 72, and I—my daughter Audrey was about to graduate college in the city, and that would make us, you know, Audrey, she had some special needs, and so we wanted to, didn't want to do too much traveling without her and so on, but, and she graduated, and I retired. And now I have to try to figure out how to live in this new state where, yes, we have the foundation, but it's an enterprise that funds others rather than sort of organizing a bunch of guys and, 'Let's solve this problem.' We're paying other people to solve problems.

But still, I mean, you're involved, as I understand it, with evaluating the proposals. Sure. And you're, I'm sure, deciding what it is you should be supporting.

Well, even that, to some extent, yes. But when you're giving out individual grants, let's say for research in neuroscience, in which I'm not an expert, I don't have any say, and I don't want to have any say in how those grants get given out. Sometimes if it's a very big one, they'll come to me or we'll say, 'Well, maybe we should cut this back a little bit,' or whatever. But basically, I'm not in the position to make those judgments. Now, for certain other grants, I am. I work with Marilyn, my wife. But it's still a kind of a working with gloves on, if you know what I'm saying. I'm not sitting down with a pencil doing something very concrete or even suggesting some new predictor, 'Let's get the guys together and talk about the possibility of this or that.'

I'm not really doing that. I have responsibilities at the university. I'm trying to help Stony Brook get on its feet. I have a battery company that I'm trying to make sure succeeds. Math for America, which we might talk about, is an organization I got started about seven years ago and I want to see that succeed. But in every case, there's someone else who's doing the work and I am watching over them. You might say, 'Well, that's being a leader, right?' But not quite, because they have so much autonomy, intentionally so, that it's not like I'm interacting

know every couple of days and say you know maybe we should tilt it this way maybe we should tilt it that way so it's certainly understand what you're saying but i mean on the other hand couldn't you argue that i mean which is neither here nor there that you have so much more scope now in in this way i mean you can really sort of influence uh the way basic science develops in in the country i can't and you know and you are and we are and that's all fine

And I enjoy that. But there's still a hollow spot that needs to get filled. And it will. I mean, I will adjust to this.

So just doing math at this point doesn't fill it?

When the math is really going good, by the way, it does. Because then, like this morning, if we hadn't been doing this interview, there was a calculation I really wanted to make. Don't look at me. It wasn't my idea. Well, here we are. But I discovered something yesterday that I think is very interesting. You know, I think it's interesting. It probably won't be, but I think it's interesting. And this came out of a discussion with Blaine Lawson.

Oh, no kidding.

Because I wanted to look at the Dirac operator, but when the connection in the tangent bundle preserved the Riemannian structure, but it was not the Riemannian connection. There was some other connection in the tangent bundle preserving that. And you can write down a Dirac operator, and I wondered if that would satisfy the Atiyah-Singer-Patodi theorem, that version of the Dirac operator, when you did it with respect to a connection that was not the Riemannian connection, but it did preserve the inner product. And over the phone, he said he thought that would work out okay, and we started to do calculation, and then he said, oh, we've got to show it's symmetric. And it turns out it's not symmetric, in general.

On the other hand, there is a class of connections for which it is symmetric. For which is it symmetric? The Dirac operator, yeah. There's a class of connections for which this operator is symmetric. And it has to do with, there's obviously torsion, because otherwise it would be the Riemannian connection, because this is connections which already preserve the metric. So there's a property of torsion, that if the torsion satisfies a certain property... then the Dirac operator... then the Dirac operator is symmetric. I think it's a torsion. It's a symmetry... must be. It can't be anything else, right? Because the torsion, the difference... Anyway, so I was excited to try to... make this precise, see just what it was, and start learning about this family of connections.

So I was very pleased. Very Jim-like.

A very Jim-like enterprise.

Yeah. Well, there it was. So doing that, but then I had to give an interview. I have a meeting. So all day long, I'm not going to be able to make that calculation. And probably by tonight, I'll be too sleepy. But I will get it done. So yes, when it's going good, it definitely fills every void.

So is that the only possibility? Or could the other activities be augmented in some way that you would have more hands-on involvement? We're thinking hard about that.

I'm thinking hard about that. We're also thinking hard about the direction of the foundation. The foundation is growing. We're bringing more capital into it. Where, what's its ultimate disposition, disposition, direction?

Yeah, that was one of the things I had in mind to ask you about, actually.

Yeah, well, it's a good question. You can ask me right now.

Okay, consider yourself asked.

Well, you know, it's a sizable foundation. It's going to get a fair amount more sizable. And, you know, what should we do that's different and of high quality? But how should we organize it so I and Marilyn get the most pleasure out of this and yet we're not just another foundation, you know, giving away money for worthwhile things somehow.

Yeah. Well, I mean, already you're not that, I would say.

Well, already we have our own staff and that's good. But it's—I'd like to bring some more work actually in-house. Is that a possibility? Can we bring some research in-house? Can we move almost in the direction of a research institute where, yes, we'll support outside research at other places, but we'll also build an internal component along that? What kind of research, what kind of project should we focus on? Right now we have a big autism project. That's very exciting, very focused. Other things are a little more pedestrian. So the future of the foundation, I think will occupy me and perhaps begin to fill that sort of hollow spot that still exists. You know, it's a feeling of irrelevance. You know, I was telling Marilyn, you know, I said, 'I feel irrelevant.'

Well, it's, as Dennis once said, in a related context, different, but maybe some analogy is carrying things out maybe to enough decimal points. So when my father retired, he got very depressed. "Your father?" Yeah, yeah. So he had 100 men under him in his job, so he was the chief engineer at a big engineering firm. They did a lot of work in the state. I think basically it was a difficult adjustment. He didn't have a foundation to go to. He said he felt useless now. Now, you have all this stuff that you're doing, and still somehow, if there's some void there that you feel, this doesn't bode well for the rest of us, those who might consider retiring.

But on the other hand, you see, in mathematics, you don't ever have to retire.

I mean, you can just keep doing it. Just keep knocking your head against the wall until you drop dead. I wanted to actually get into science, science education, what it means to the country, and why it's important. And this is obviously an aspect of it that you think is important. So maybe you could talk about Math for America, what are the ideas behind it, and how it's working, and so on, and where you hope it will go.

...is that the country is facing a big challenge, and I think it doesn't really understand the depth and even the breadth of that challenge. Quantitative methods are more and more pervading the economy, whether it's a new computer or a new gene. The techniques required to work in such an economy are more and more dependent on quantitative methods. At the same time, the fact that that's the case means that people who are good at that stuff, fewer and fewer of them will want to teach. Why? Because they can make so much more. It's not only more money, but more respect and everything to do something else. When I was a kid, if you really liked mathematics and you were pretty good at it, you could become an engineer, I suppose, or an accountant.

But there weren't a million jobs. There were no computers. We just mathematicized everything. Teaching high school math was a nice job for a lot of people. You liked kids, you had your summers off, and you could be doing mathematics.

I know that you've made this point in particular as it pertains to women. "It's also true for women." Particularly true, right?

Yes, although it turns out that the statistics show that the job expansion has been an even more important factor. But a lot of women had no choice whatsoever if they liked math and wanted to do something in math as a career. I'm not talking about being a big-time researcher, but just, you know, you like math. So a woman could have been a bookkeeper or a teacher. They couldn't even be engineers in those days. Women were verboten from the engineering business. So a lot of smart women were teaching math. So we had pretty good people teaching mathematics. I certainly had some good knowledgeable teachers when I was going to high school. I also had the football coach, who wasn't so knowledgeable, but he was just one example.

The others were pretty good examples. So they're great teachers. But we're competing with the whole world here, and we're losing this competition because we're not training our people properly. So the last time we were challenged was with Sputnik. 1957, Sputnik went up, and all of a sudden everyone was afraid the Russians will next be on the moon throwing Molotov cocktails at us or whatever it was, and there was a tremendous rush to improve and to compete in this race. And it was perceived, quite correctly, that our store of scientists was too low, and we didn't have—our best universities didn't have big enough departments in math and physics, perhaps, or electrical engineering. And so there was a big push at a national level to address this issue. And my year, I got a PhD in 1961, it was something of the order of a hundred people got PhDs in mathematics that year in the United States. Now, ten years later,

was 1,400. And that increase was largely due to this huge effort that the federal government put in promoting people. Of course. Of course, I remember this very well. You do. The National Science Foundation was being built up, and the National Defense Education Act was created. And as probably you know, or possibly you know, I was a beneficiary of the National Education Act. And when I went out to Berkeley, it was the first year of it. And I had a fellowship, one of these very lucrative fellowships. And I was going to go to Berkeley anyway. But nonetheless, this was a very generous fellowship, relieved me of the usual teaching responsibilities that, almost completely, that a teaching assistant would have to do.

And I was the first person in the United States to get his degree under the National Defense Education Act, for some reason or other. And I got a nice letter from Abraham Ribicoff, who was the Secretary of HEW and so on. It was because I'd already had a year of graduate school and I finished two years later, so I got my degree. I always had a soft spot in my heart for that program. It was a great program, and it was created in the face of a threat. Now I look around, and 15 years ago I started looking around and say, 'Well, we have a threat now. It's not military; it's economic. And it's not one country; it's every country. It's every country. They're all trying to eat our lunch, eat each other's lunch.'

These other countries are preparing themselves for this by teaching their kids properly.

So what went wrong here, actually?

I don't know what went wrong. Most people don't really see there's a problem. It's easy to see where there's a problem when there's this little basketball, you know, orbiting around your head and someone points out, 'There it goes again. Holy shit, you know, what are we going to do about that?' But we don't have that. It's just this sort of malaise. So, well, you know, we bring in these smart Chinese kids on H-1B visas, and that's okay, and so on and so forth. And, oh, most people think their schools are pretty good. I'm not talking about the disadvantaged kids who have a special set of problems. But the average American family, I've been told time and time again, thinks their school district is pretty good, their kids are getting a good education.

Now, they're not. Because fewer and fewer, let's say, of the mathematics teachers in high school actually know mathematics. A minor problem. They don't really know the subject. They don't know well enough to be teaching the high school kids. Now, the parents can't tell that. They don't know. The kid comes home and says, 'Gee, I don't think my teacher knows quadratic equations exactly. She seems to be having a problem.' The mother says, 'Come on. Who are you kidding? Look, that's very hard. That stuff is very hard. You know it's hard. I can't help you, but I'm sure your teacher knows how to solve it. You just have to study harder.'

How could the parent, if the kid's teacher can't read—

Or doesn't read well, the parent convinces them, "My God, she can't read. This is terrible. I'm complaining." But, "She doesn't know minus b plus or minus the square root of whatever it is, a squared minus 2ab. Gee, we've got to do something about that." Or b squared minus 4ac, as a matter of fact. I didn't want to say anything. You didn't want to say anything. Square root. Square root. I said square root. I threw in the plus or minus. I got the square root. 2a. But all over 2a, yes. Our students in high school, not by eighth grade—we compare in the median to our competitive countries—but by 12th grade, we're right at the bottom. So people see the statistics. "Oh, well, you know, maybe we need smaller class size."

Maybe we need computers in the classroom. Maybe we need a better curriculum. But it hasn't completely dawned on people that what we need are teachers who know the subject. And a teacher who knows the subject can make up for a large class size. You can make up for no computers in the classroom. I think, you know, it can make up for a lot of things.

Do you think it would be enough to fix the problem? Or are there also societal problems?

I don't know. I think if there are... Well, what kind of societal problems?

You could make science and math seem more glamorous, for example.

Sure.

By inviting people to the White House, let's say, who had gotten some distinction, not just championship sports teams. It would cost nothing. You know, some way to make it seem more exciting and glamorous is one example. I'm sure that the quality of the teachers is a very important thing, and it's something that you could address in a focused way as Math for America is doing. But, you know, you wonder, is it enough?

You could make math and science more glamorous. There are various facets to the problem, and I can't say that more knowledgeable and inspiring teachers in the classroom will solve the whole problem. But it will go a very long way toward solving the problem, and hopefully other things can change it at the same time. But I felt this should be a national program. We should take it with the same seriousness that we took the NDEA, National Defense Education Act, and create a program. When my friend Chuck Schumer became Senator, I assisted in his campaign, and he was grateful. And I went down to Washington as soon as he was inaugurated, or went in—not inaugurated, whatever you do when you're a Senator.

And I said, "OK, here's my program. You know, we've got to do this. We've got this big problem." He says, "Oh, it's a wonderful idea." And nothing happened. And nothing whatever happened. It was one of many wonderful ideas he probably heard that hour. Everyone comes with their wonderful idea. So after batting around and talking to people and so on, after a couple of years, we got the idea, "Let's just do it ourselves as a pilot here in New York, make it good, maybe start some branches in other cities." And then with the proof of concept, get the government to make a program, and that's the course that we're on. And it's—and it's slow going, but it's not... So where are you on that course exactly? Well, we're on a course to make New York considerably bigger over the next few years. There'll be—we're aiming for... The government participation? No, that we'll just do privately. Maybe if the government comes along, it would be great. But I think we understood that at some point they—they had approved something, but they didn't fund it, or what was it? They funded it. They got a little program passed, but most of the money was wasted.

And it wasn't a program exactly along the lines. It was so general that people could interpret it all kinds of ways. So little things got started in different places. Some of our programs got money from that bill. But it was a modest bill and not really well focused and buried. Almost all of the money we spend at the federal level on education is spent on the disadvantaged. It's spent on getting the ship upright. It's listing. The poorer kids are not learning as well as the—well, let's help the poor kids. Almost all that money. But in the meantime, we may get the ship level, but it's sinking. I mean, so there's more than one dimension to this problem. So it's going down, and we're busy getting it level.

Of course, I think it's important to get it level. It's important to help the disadvantaged. But the Department of Education has a $65 billion budget. And the amount that's put into something like Math for America or National Teaching Corps is zero, or close to it. And how much?

I'm just curious. Two billion? Two billion.

Two billion a year to have 20% of the math and science teachers in the United States enlisted in a math science teaching corps. And that would be quite transformational, because they would inspire the other teachers. They would inspire school districts to get more such people. And you have to pay people more and you have to make the job more better in terms of respect. So it turns out it does not take a fortune. You don't have to make them as rich as they would if they worked for Google. But you have to pay them more and make them feel they're part of something that's relevant and exciting. And they'll inspire the kids. Just like I was inspired by Walter Taylor with plane geometry in the 10th grade.

You know, he was inspiring. And he knew the subject. He knew the subject. That's what we're doing. It's slow going, but we're making progress.

I think that it's frustrating at every level, not just this level, because mathematics is so fundamental and it doesn't require big laboratories. Right. You know, it's in a way such a bargain and yet it's hard to get it funded at what I would consider an appropriate level. Yeah.

Well, you know, everyone thinks of his own. I'm sure you could get historians to talk about their field and how it's a pity that people don't know enough history and we all should know history and I'm sure we should. But we don't have a shortage of historians in the workplace. When we bring in people on H-1B visas, it's not because we need people with history degrees. It's because we need people with computer science degrees and that sort of thing. So we have a real shortage here. And I agree. It's not a big trick.

Tell us a little more specifically about how Math for America works. What are the details of the program?

Well, it's addressing two issues. Recruiting people into the field and retaining them once they're there. So you could put up front inducements to get someone to take a job. But once that's gone, they're not going to stay in the job unless it's a good one. So you could say, okay, we're going to give you a scholarship to train in high school to be a math, in college to be a math teacher. And isn't that great? And you'll get a scholarship, but you have to teach for three years. Oh, fine. So they're trained, yes, I'm a math teacher. Then they go in after three years and say, this job stinks. It doesn't pay very much. I have to deal with the argumentative principle or whatever it is. Teaching is hard.

As it turns out, in particular in your early years, there's a very rapid fall-off rate, turnover, in particular among math and science teachers. They come in and they go out. So it's not merely inducing people to come in. It's making the job good enough so that they stay in. So how does it work? People who are entering the field, we advertise, we approach them. If they're interested, we give them a test. And then we interview them, and if they look like they'd be suitable for the classroom and know math, we give them a math test that's called the Praxis exam. It's not perfect, but it's pretty good. They pass that, and they come into the corps. What do they get? They get a fellowship for the first year, $30,000, which is pretty much what a graduate fellowship is these days.

$30,000, and they would pay their tuition in an intense 15-month course. Because they don't have teachers. They didn't study education. They only studied math or physics or whatever that prepared them for these things. They go in for 15 months to an intense course. They learn the ed stuff that they're supposed to learn to get a master's degree.

Are they also learning math stuff, or you only take people who are at an appropriate level?

No, we encourage them to take more math, and they do. They do. That's part of it. Then they have to teach for four years, and they get stipends, say averaging $16,000, $17,000 a year on top of that pay. So that makes the first part of the job good and so on, but then how do you keep them there? Well, then there's a master teacher corps. And that's for people who already are teachers and say for four or five years and who've demonstrated good teaching skills and can also pass the test. We bring in those teachers either from the ranks of teachers who happen to be distinguished in that respect, and there are some, or the fellows then transition to that if they have done well in their first four years of teaching.

So there's two entry points. You can be an existing teacher with a number of years under your belt, take the test. If you pass it, you become a member of this elite corps. You get an extra $15,000 a year. It's a very successful program. People love it. The only problem is, can you find enough teachers who are already in the ranks who really know the field to keep them? And the answer is no. Those people serve as examples. They serve as inducement to someone entering the field. Oh yeah, maybe I could be a master teacher if I could carry on. And the master teachers help mentor the fellows, help mentor the more junior teachers. So that's basically how it works. And there's a team, or not a team, but there's

advising that goes on during the person's first couple years in teaching for the fellows. And we have events. We have dinners. In this building, people come in for seminars and things like that. Almost bonding situations. They feel great. They feel great about being teachers. And they feel great about being a member of this teacher corps here in New York. And so we'll build that up and use that as an example. But we think that's about the right way to do it.

And so the commitment is ongoing, I guess, as long as they're doing this, they get the supplement. They get the supplement and remain

members of this corps. And what I'd like to have, as I said, is about 20%. If we had 20% of the teachers of math and science in New York City, it would be about 2,000.

About 2,000. And what percent is it now?

Right now, there's only 350 in the corps, but we're going to build it up to 1,000 over the next four years. So 350 here in New York.

And what do the other teachers think about these teachers? They're perfectly happy.

They're happy.

Yeah. Do any of them want to go back and get the further training and attempt to join it, or is it more bringing new talent?

No. You mean existing? Yeah, existing teachers. Do they see this as a way, for example? Most of our Master Teachers are coming from existing teachers. From existing teachers. And an existing teacher could say, take the exam, fail it, and say, 'Gee, I need to learn some more math.' One way or another, learn it, take some courses or whatever, and try the exam again. And if he or she has learned enough, and they pass the interview process, which is fairly rigorous and good recommendations, they could join. So far it's going very well. Will we run out of people who are already in positions to make the members of the Corps? Surely. That's why we need to keep bringing in new folks. And the unions haven't resisted?

The unions don't care. It's something on top. It's something on top. Their bosses aren't paying. It's not coming out of the school district's money. And so someone's gotten a reward from it. From God, well, how can we complain about it? So the unions are OK with it.

Is it getting enough positive publicity?

No. I would say no. That's one of the things we've got to work on, getting more publicity. But it's getting pretty well known here in New York. But it definitely needs publicity. It bothers me so to see something that is so obvious not done. We had a financial collapse in 2008. Here's another example. Everyone's been running around like chickens with their heads cut off. Where did we go wrong? What were the problems? Blah, blah, blah. How did all this happen? We have to punish the hedge funds. We have to punish the banks. We have to do this. We have to do that. It was all outrageous. We all got swindled. Maybe. But the real problem was that the rating agencies put the wrong ratings on the bonds.

They put wrong ratings on the bonds, then people would buy the bonds. People would buy the bonds, people would create the mortgages of which these bonds were, these instruments were created. So the whole chain just worked its way up because there was no policeman in the street. So if all the police leave New York City, there'd be a big crime wave. Then everyone would say, 'Those criminals, they're terrible, let's punish the criminals.' Well, we've always punished the criminals, but the best thing is to have some police that keep them from being criminals in the first place, right? The police took a holiday. Is anything happening to the rating agencies? Is there any reform being made in the rating agencies to make sure this won't happen again?

No, or very little.

Why not? It's not politically interesting. It's not interesting to the newspapers. They never even heard of a rating agency. The average person would go right to sleep if they heard the rating agencies aren't doing their job. But you hear the big bankers are getting big bucks. That attracts the news or the politicians. So the key problem that created this mess is not being addressed. And when I see that, it's just very aggravating. And I talk to people and they say, 'Yes, you're right, we should do something.' But I'm not doing anything. Some people think teaching is a calling. And that the idea that teachers have to get paid, of special subjects, have to get paid a whole lot more is grating. Some people think, 'Wow, Miss Jones was a perfectly good teacher years ago, and Miss Jones, how come all of a sudden we've got to pay the teachers more?'

Sort of a reasonable thing to say, except times have changed, and these folks are in demand. And the unions want only flat salaries. They do not want any difference between a history teacher, an English teacher, a gym teacher, or a math teacher. So they're ignoring the law of supply and demand. So you get used to certain things. The unions are used to a flat thing. People are used to teachers are humble folks who don't get paid too much. And I'm not talking about college professors or guys like you. Your average teacher. So people have it in their mind. We know that doctors get paid a lot. We've come to accept that. They didn't always, I guess. But, you know, it's expensive to train, blah, blah, blah.

Though, interestingly, now even doctors are complaining that the insurance costs are so high.

Well, that's another matter, and it's absolutely true. So we can't right every wrong. The tort lawyers are opposed to limits on these payments, so the insurance companies have to charge a lot, and everybody suffers. So that's a wrong needing righting. But you have to look around and say, okay, there's a lot of wrongs. Is there some that I could do something about? I can't do anything about that. There's a chemistry, lithium-sulfur chemistry. These two elements are very reactive and when they react with each other create a tremendous amount of energy per unit weight. So if one wants batteries as we need that are light for automobiles but don't weigh like a lead-acid battery, you can schlep them around, but they're so heavy, you can't do anything.

And the lithium-ion batteries are still not light enough. They don't compare to the energy density of gasoline.

So I think you explained to me one point is getting the energy out quickly for acceleration.

Well, you want to get it out quickly, but the biggest—okay, so 17 years ago, some technology came out of Brookhaven Labs to make lithium-sulfur batteries, and they formed a company, and we backed that company. For 17 years, we have been trying to make these batteries practical. And the main objection to its practicality is the very nature of this intense reaction destroys its own container. So it's like having a gorilla on the football field. Boy, he's wonderful, right? He can tackle three guys at once and so on. But on the other hand, you've got to teach him the rules. If he doesn't follow the rules, it's no good. He'll run off and hit people in the stadium. No, no. You've got to stay on the field.

You know, so it's like that. So we've got a gorilla in a can, and we've got to tame him. And that means protecting all of the innards of these batteries against this fierce chemical reaction, which, when it's under control, is doing a wonderful job. And we're pretty much there. We have a nice grant from the Energy Department. We're about to become partners with a big German chemical company, and we're hoping that within about four or five years, these batteries... So these batteries have enough specific energy so they can nicely compete with gasoline. And they're cheap to build, and yes, they have a reasonably fast discharge rate, so that's not an issue. Just have to learn to build them so that they don't...

...eat themselves up. Eating themselves up doesn't mean causing an explosion. It just means you don't get as many recharge cycles. Every time you recharge a battery, a little of it is hurt. That's why you only get so many recharges. But we're only getting 50 or 75, and we need several hundred recharges before it's really practical. I'm really interested in electric cars. I love the whole idea, I think. I mean, I could go on on this subject. Do you realize that 70% of the petroleum produced in the world is for transport, is for cars?

I can accept that.

It's not a majority of the energy consumed, but it's 70% of the petroleum. So now if you have electric cars, you're going to way, way cut down the amount of petroleum needed. You may boost up needs for coal to generate the electricity. That's another matter. But presumably, we can find a way to deal with that. But if you're only using half as much oil, if the country is, if the world is, all these problems in the Middle East are going to kind of go away. I mean, they won't be our problems anymore. Maybe they'll be their problems. That's a nice thought. That's a great thought. I mean, imagine if oil consumption was just cut in half. We'd be able to produce our own. We wouldn't really need to import.

It would be fantastic. I love electric cars. So hopefully, that's our battery business. 17 years I've been at it. And we're doing a deal, I think, with this German company, and we looked out at royalty schedules and said, 'Okay'—this was just yesterday, all right—'if we do this deal, all royalties are going to end in 2032.' It was going to be 2030. I said, '2030? I'm going to be 92.' But we even got two more years, so... We'll be good until I'm 94. But so, you know, I think it's going to happen. Yeah, I mean, there are other people working on it. Tons, but no one's working on lithium-sulfur. We have all the intellectual property on lithium-sulfur. Now, there are people who say it will never work.

It's too energetic. It's too whatever it is. You know, no one else has been able to do it.

But we have.

So I think it's going to work.

As far as the planet as a whole is concerned, are you optimistic or not?

As a citizen of the world, I see pretty good social progress around the world. I see the Chinese and the Indian economies growing very fast. These were countries—that's 40% or 35% of the world—which 10 years ago was pretty submerged and now is coming out. Absolutely.

The populations are growing fast.

The populations are growing fast, but they really are making progress—great progress—and I think that's great. I think that's great. So soon, maybe in my lifetime, substantial majority of the world will be not Third World. Third World will really be a minority. So that's good. Whether we'll blow ourselves up in time, I don't know. Will global warming, climate change, catch us unaware and ruin the planet? I don't know. But I'm reasonably optimistic for the world. I think we'll deal with these issues and there'll be enough intelligence. I'm less optimistic for the United States. I'm not optimistic for the United States. I think we have perfected the art of blocking anything. So the way things seem to work, you know, whether it's—I mean, I can't get an awning on my building, this building—

Oh, no, you see, you have to go before the board of—what do you call it?—the trust, I don't know what you call it, these buildings that are historic sites. This is a historic site. I don't know whatever happened here that makes it a historic site, but it's a historic site, and they don't allow awnings unless special permission, and it takes six months to get permission to have an awning. I mean, you know, so we've perfected the art of inaction. And I don't see anything really changing. I don't see leadership emerging that is going to propel us in an effective way into this century. Right now, all the thought is our debt is too big. Okay, our debt is too big. You know, the biggest debt we ever had relative to GNP was when?

I guess in World War II. Right after. Right after World War II. It was considerably bigger relative to GNP, GDP, whatever you call it, than it is today. Well, we must have paid off that debt, right? Wrong. We never paid off a penny. We grew the denominator. So the numerator, which was very big, stayed and the denominator got bigger and bigger, and after 10, 15 years that ratio was right back in the box. We grew the economy. But we're not thinking about that.

Well, is it possible some crisis could change things?

I don't see it. I don't know what crisis could change things. We want to pay down the debt. We don't want to invest in infrastructure. We don't want to invest in serious education, which is part of infrastructure. I just don't see it. It's so depressing. But maybe we'll get better leadership and maybe something good will happen.

Do you think you have any role you could play?

No, but you're wrong.

By now you're, let's say, more well-known than you once were. For example, you have this long list of impressive achievements, you made a lot of money, which people tend to respect, you're very articulate, amusing, etc., uh, forceful, logical. Go on Saturday Night Live? Do you think, for example—ah, that's it. Yeah. Is there something, you know, as a wise elder statesman who cracks a lot of jokes and so on, whatever, you know, by saying these things enough and in a public enough way, is it conceivable that that, you know, that people might listen for whatever non-intrinsic or intrinsic reason?

I can't say it's impossible, but that could be effective. But I—I'm not very optimistic that I could make that. I haven't really given it much thought. What could I do to make that difference on that scale? I don't know. I don't know. The problems are so pervasive. The parties are so at each other's throats. Worse than it's ever been, in terms of politics first, politics second, politics third, policy fourth, maybe. I agree with that. And so how do you break that kind of a logjam? How do you get people focused on reality and not Tea Party kind of stuff? I don't know. And there are people who go on the air, and there are smart people who say this and that, maybe even amuse people, but I don't know how much people are really going to be moved by such a performance or series of performances.

I mean, this guy Friedman, he writes these books. He says, 'We're falling apart. Look at China. We have to do this. We have to do that.' He's a pretty good writer. He puts out these books, The World Is Flat or The World Is Square, whatever it is. Is it making any difference? Not discernibly. Why would I make such a difference? The two of you are rather different.

I mean, I don't know.

Well, you're a good writer. You're a funny guy.

I'll take this up with myself.

Yes, please do that.

Report back to me.

So this was when you testified before Waxman?

Before Congress. That's right. Before Congress. It was in 2009, I believe, in the wake of everything. And it was just before the election. And he decided to get the five top hedge fund guys to testify before his committee. And he just took the list of who made the most money, or something, and I was on the list, and George Soros that year was on the list, and this one and that one. There were five of us. And this was a time shortly before the election, people were trying to score all kinds of points. There were some awful such hearings where people were really excoriated. Now the fact is that the hedge funds had very little to do with this, if anything. But it's always fun to beat up on rich people, especially in front of a television audience that will include your constituents.

So I was very nervous about this. I didn't want to be excoriated. But I was asked to appear and I was going to appear. And we started preparing. But Soros said, 'No.' Soros said, 'I will appear, but after the election, not before.' And as soon as I heard that, I said, 'Me too. He's not going to get me up here until after the election.' And then everyone raised their hand and said, 'Me too.' So they agreed to hold it off until after the election because they weren't going to get their band of—they could subpoena us all, but that's getting ugly and so on. I guess they didn't want to do that. So they said, 'Okay, after the election.' And I really thought that would be the end of it because I thought, since once the election was passed, what's the point of putting on the show?

But in fact, they did, and it appeared they were trying to gather information. They were not rough. I was prepared for anything. I was prepared for the worst treatment. And I had two lawyers, and they were training me, and I was practicing. 'If they ask this, you can say that, but if they then follow up with this, you have to back up with that,' and so on and so forth. My head was swimming in what I should and shouldn't do or could or couldn't say and so on, you know. You know, I was prepared. They'd say, 'Oh, you're a very rich man, Mr. Simons. Exactly how much did you report as income in the last year?' I don't want to talk about how much I reported as income. None of their business. Income tax is your own business.

You know, or there were a million directions they could have followed, which I would have found intrusive and inappropriate. So I had to be taught how to—well, 'If they ask that, then you can say this,' and so on and so forth. Anyway, we went in there prepared to be excoriated, and we weren't. And I was blessed by having George Soros on my right, because the way they did it, they wouldn't go down the line. They'd pose a question, and then they'd say, 'Okay, what do you think, Mr. Soros? What do you think? What do you think?'

Soros, George Soros likes to talk. So they'd start with him. He'd go on and on and on and on and on. And finally he would stop and it was my turn. And I, because I hoped he would talk so long they'd drop the question altogether and so on. But he didn't. And then I could say something. And I had the record for the shortest answer, which was 'yes,' following a great lecture by George. And I just said, 'Yes.' And they liked that. But they were nice to us. And then afterwards... Why do you think that was? Were they impressed? I think... they didn't want to offend some people, many of whom were political supporters. I mean, you know, we backed some of their efforts at times. The election was over, and maybe they really did want to learn something.

It's hard to say. And I worked hard. I wrote a—you're supposed to have a written statement, which you don't necessarily have to follow, but you're supposed to submit a written statement, which I did. And it was a good statement, and it appeared on the web. But I was so glad that that was over. I was so glad.

I remember one thing that you said, which I thought was very good, and that was that they should make an effort to keep people in their homes. Yeah, that was the first thing I said.

We haven't done a good job at that.

The banks are sitting with these mortgages, which they haven't necessarily written down yet. They're not so eager to do that. So things linger. The mortgages are what I would call in weak hands. But if the banks were to sell their mortgages to you or me, we'd buy them at $0.20 on the dollar. Then we go to the homeowner, and now we're in good shape. You could pay us back at the rate of 30 cents on the dollar. I make 50% on my investment. And he gets his thing cut. Now the bank takes a shellacking, but the bank had taken the shellacking anyway. It was all just sort of pushing it off and pretending. And we're doing a lot of pushing off and pretending. So I figured the banks ought to be dealt with, get that paper into strong hands, and then

The owners of the paper can then negotiate with the homeowners and make deals. Sometimes they take the deal. Sometimes they don't. They walk away. They don't want to do that. But at least you give people a chance. And usually you can keep them in their homes. I thought that was very important, but we really haven't done that. And there's all this stuff in foreclosure, and it's the best thing for a house. So is the problem really that the banks don't want to do it? The banks are not eager. Because it means having to write this piece of paper down and thus showing their balance sheet goes down. So the banks aren't really eager to do it. They're being pushed to do it. That was my idea, keep people in their homes.

But we didn't do a good job at that. I always believe in taking, if there's going to be a hit, take it. And then go on about your business. But sometimes you just want to keep pushing it out into the future. Which, you know, sometimes is good.