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Isadore M. Singer

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[MUSIC PLAYING]

INTERVIEWER: So this is the 150th anniversary celebration interview with Professor Isadore Singer. And let me start by asking, where you were born? Where'd you grow up?

SINGER: I was born in Detroit, Michigan. I'll start over again.

INTERVIEWER: Okay.

SINGER: Where was I born? I was born in Detroit, Michigan, in 1924, and I grew up there. My parents came from Poland and emigrated to Toronto, Canada, where they met and married. And then they came to Detroit in 1923.

INTERVIEWER: And what did your parents do? Did they also work?

SINGER: My father was a printer and my mother a seamstress. When they arrived, my father tells a story that the printers' union was on strike. And they asked him not to break the strike and gave him $5 a day not to do that, and he agreed. He wrote his mother back in Poland that it is, in fact, true that the streets of the United States were paved with gold.

We were very poor during the Depression. It's a vivid memory for me, and so I'm particularly concerned about people who are out of jobs now, because my father was out of a job for a year or so. And we suffered badly at that time.

INTERVIEWER: Were there any particular events or influences in your childhood that you think helped you to choose the career path you chose?

SINGER: No. You know, I was an all-A student all the time. Mostly, I found school boring. I preferred playing baseball and stuff like that. I was more interested in athletics than I was in anything going on at school. I read a great deal.

Things did come to an end about my junior year in high school. I had a very good English teacher, and I had a very good chemistry teacher. So a periodic table struck me as something very exciting, and the English teacher got me to read lots of good books-- Dostoyevsky, War and Peace. My oldest daughter's named Natasha after Natasha in War and Peace. So those two things had a big impact on me and woke me up to the excitement of science. I became president of the Science Club very quickly and gave lectures on relativity already as a senior in high school.

INTERVIEWER: How did you decide on the University of Michigan?

SINGER: They had a competition, and I either came first or second in this competition, and therefore, I won a scholarship to the University of Michigan. What that meant was I had tuition paid. Tuition was $50 a semester. As I say, we were very poor, and I was originally going to go to Wayne University and live at home. But my mother said, you can't. You can't give up $50 twice a year. So I went to Michigan as a result.

I lived in a co-op. In the co-op I lived in, you paid $2.25 a week for room and board. And I remember the vivid discussion about getting up to $2.50 a week, which we did.

INTERVIEWER: It must be staggering to look at tuition prices now.

SINGER: Absolutely. It's shocking, actually. But of course, there are a lot of amenities that one doesn't take into account. We didn't have any at all. In fact, I survived by having three jobs at any one time and also by selling my football tickets, which I could sell illegally for $5 a ticket. That lasted two weeks for me.

At any rate, the war started when I was a freshman. And I enlisted in the Signal Corps, because they said they would allow me to continue school until I finished, as long as I took courses in electrical engineering, which I did. Because they wanted me to become a radar officer when I finally got in the army. I might add that I rushed through school because I didn't really believe that they would let me go the full four years, and I got my degree in 2 and 1/2 years.

INTERVIEWER: That must have been difficult.

SINGER: Well, I've gotten used to being at MIT, with everything going on and so many things to do.

INTERVIEWER: So what is it that drew you to physics, do you think?

SINGER: Because of my lectures on relativity in high school, I felt that I didn't really understand the question what the issue was, even though I spoke about it. And so I wanted to learn more about relativity, and I I'd heard about quantum mechanics. And so I wanted to learn that, as well.

Actually, when I got to Michigan, I hadn't decided whether to major in physics or in English literature. And what happened was that I found students in the poetry class understood poetry, many of them, instinctively, easily, and I struggled with it. But when I took physics, I was the one who understood what was going on very quickly, and that decided me as to what path I should take.

INTERVIEWER: That's a good way to make the decision.

SINGER: That's what I think the first couple of years at a university is all about.

INTERVIEWER: And then how did the interests shift from physics to math?

SINGER: That's kind of complicated. As I say, I finished early, went into the army. Was in the army for 2 and 1/2 years. But after a year and a half, when I was destined for was greater officer in the European sector. And that was about ended, and we were all moved to go to the Pacific. I was still concerned that, as an undergraduate, I didn't understand relativity or quantum mechanics.

And I had heard about extension courses at the University of Chicago. So on my way, everybody-- it was called redeployment at that time, all of us moving from the East Coast to the West. I stopped in Chicago and went up to the fourth floor of the building. And there was-- I've forgotten his name. [INAUDIBLE], I think. At any rate, he told me he did have extension courses in geometry and then group theory, which was needed for quantum mechanics.

And so I enrolled in them, and I took them with me. I ended up in the Philippines and ended up running a communications school for the Filipino army when I was out there. And I would get these letters from-- corrected papers of mine. I studied all the time. My friends played poker, and I did my homework.

But to answer your question, how did I get into math, what happened was since all the textbooks for these correspondence courses were from the University of Chicago, I thought that would be the place to go. And I was, indeed, accepted in the math department, because I thought I wanted more math to understand the physics of quantum mechanics and relativity, which was, in fact, the right instinct.

But that first year in math was so wonderful and so beautiful, whereas listening in on the quantum mechanics course, it was still the same-- a rough course, I would say. Then I felt mathematics was really my field. And I was right, because it was a mathematical instinct that told me the way they were teaching quantum mechanics was not right. That is, in fact, true as far as I'm concerned.

INTERVIEWER: You decided to stay at the University of Chicago for your doctorate.

SINGER: Yes.

INTERVIEWER: Why?

SINGER: Well, that first year was so wonderful. And remember, I didn't have a great background in math. But a lot of friends supported me and taught me the material I didn't know. I rapidly caught up. And the faculty was just terrific there. Brought new people in-- Andre Weil, one of the world's great mathematicians. Chern, SS Chern, came the last year, who influenced me greatly in differential geometry. And we became very good friends over a long period of time. So that was the place to be.

INTERVIEWER: So would you consider him a mentor?

SINGER: My two mentors were Chern, certainly, and Irving Segal, who was my thesis advisor and eventually came to MIT. I learned a great deal from both of them.

INTERVIEWER: I wonder if you'd talk a little bit more about Irving Segal?

SINGER: About Irving Segal?

INTERVIEWER: Mm-hmm.

SINGER: Well, he was a wonderful and lousy teacher at the same time. We were excited about what he was doing, because he was lecturing on the forefront of analysis and functional analysis. But he got stuck about halfway through every lecture, and he spent the rest of the lecture trying to straighten it out. So that makes him a lousy teacher. He didn't get very far in any one day.

But I'd go home and would try and solve the problem he was stuck with. And I'd either have my solution or I didn't know how to do it, so I was very eager to see what he was going to do at the next meeting in the class. And I could compare my solution with his, if I had one, or I could see where he did something that I hadn't understood. And so it was essentially doing research every time on your own. So that's one way in which he was a very exciting teacher.

Also, he stayed late at night. And most of us, as students, stayed late at night. His door was always open. So late at night, I could go in, and it wasn't a matter of talking about my dissertation. If we did, that was for about five minutes. But we'd spend the rest of the time talking about mathematics and the importance of functional analysis. So that's how he influenced me a great deal and gave me a very good background in analysis.

Chern came the last year I was there. And his field is differential geometry. And I only listened to his course and took notes, but I immediately felt that I was in the wrong field, I was so taken by his geometric view and the instruments he used in order to reflect that geometric view. And it was too late for me to make any changes, but you'll see that it had a great impact on me and on MIT when we get to it.

INTERVIEWER: So how did you come to MIT?

SINGER: Well, when I got my degree, I had two offers. One to the Institute for Advanced Study to be with-- what's the matter with me? I've forgotten. And MIT, I had an offer. And that offer was $50 more than the one from the Institute for Advanced Study. So, naturally, I took it. I had a family already, and that was the thing to do.

INTERVIEWER: Do you remember what your first impressions were of MIT?

SINGER: I'm so glad you asked me about my first impression. So you said you liked stories, and I'm going to tell you one I've often spoke about. In fact, I'm going to reminisce, because I'm retiring June 30th. And I arrived at MIT July 1, 1950. So that's 60 years, with some time away. But July 1, we'll celebrate the 60 years, and I'm about to tell you the first day.

So I came over across-- I was staying in Back Bay-- across the river and went to Building 2 to meet Ted Martin, who was the chairman. And he had one secretary, Ruth Goodwin. Went into the office. There was a guy reading The Globe. And I told Ruth who I was. He put down his paper and said, I'm Ambrose. Singer, we've got a seminar going on Lie groups. Come on, let's go.

I said, but I have to see Professor Martin. He said, oh, that'll keep. Come on. So I went to the seminar, and I met a number of people who got to be good friends, some mathematicians of note. George White, particularly, in topology. And then we went back and I did talk to the chair, and Ambrose waited for me. And then he said, we meet for coffee at 11:00 PM. I'll pick you up. Where do you stay?

So he did pick me up that night around 11:00, and we went to this terrible coffee shop-- Hayes Bickford in the middle of nowhere in Boston. And there, I met the same group who were in the seminar. And Kate Whitehead, George Whitehead's wife, was there, and also a mathematician. And we talked for a bit. And then I thought Ambrose was going to take me home.

He did not. He simply showed me what Boston was about, drove around for a long time, and dropped me off about 3:00 in the morning. And I went up to this apartment that I had been given for a few days. You have to remember that I hadn't been home, because I'd left for the university. I then spent three years in the army, and I then spent 3 and 1/2 years at the University of Chicago, so I really had no home.

I went up to my bedroom and said, I'm home. This is my home. And that's my first day at MIT.

INTERVIEWER: Do you remember-- so you had had experience at two other universities. Was there anything that struck you as different when you got on the campus and kind of got to know the students and the faculty and the culture here?

SINGER: Not immediately, but as time went on, I saw a considerable difference between the two places. One of the important things at Chicago was it was a graduate school. For us, undergraduate teaching was done by another division of the university. As a graduate student, we saw very little of undergraduates, brilliant as they were. I would mostly see them in the locker room or in some sport or another and had very little contact with them. I did no teaching there.

MIT was entirely different. It was an important and enormous load or responsibility of teaching undergraduates. And that has been done with great aplomb, as far as I'm concerned. So MIT was a place where you did research, but teaching was extremely important.

INTERVIEWER: Was there anything about it that was a surprise when you've sort of got to know undergraduates?

SINGER: Was there a surprise at MIT?

INTERVIEWER: Either in their attitude or what you found you got from the relationship or anything like that?

SINGER: Well, it took a while for me to think in those terms, I must say. What happened was that Ambrose asked me what Chern had done in his course. And he wanted me to discuss it and explain it to everybody. He was a stickler for details. So I ended up more or less lecturing on differential geometry to him, learning it with him, and reorganizing it into a more modern language than Chern used.

We gave courses in it. Students wrote books about it. And so MIT became a center for a differential geometry on the basis of what we tried to do with, really, the notes of my course from Chicago. Now, as to the difference, the feeling that I had was that I could-- there was a kind of freedom. I could give a course immediately on new material to undergraduates.

And recently, in fact, because I was looking for some old notes, I was really shocked at how much large undergraduate teaching I did at the time with the freedom of reorganizing the course. I gave a course in-- it was called Algebra Matrix Theory, and I just changed it completely into a modern form. And I still have former students who are now well-known mathematicians who remind me, whenever we meet, that I had given this remarkable course with a huge audience-- 2190, the big room.

I gave lectures in there frequently, and I was allowed to do that-- criticized, of course, by some old timers. But there was a freedom to change courses. So as to adapt to modern times. I must tell you that the '50s was a period of great development in mathematics. And so between seminars, reorganizing courses, and keeping up with what was happening-- topology, geometry. A lot of things were happening at that time.

We had many seminars. We could immediately put them in the coursework, and we were allowed a freedom to do that that I had not known before, but only because I wasn't-- you know, I couldn't do that at Chicago, because I was a student. Whereas, here, I wasn't a student anymore. And that was really-- those were exciting times.

INTERVIEWER: Is there a particular reason the '50s was such a busy time for mathematics?

SINGER: Yeah, because the war ended.

INTERVIEWER: Just the influx of people?

SINGER: Well, there were a number of very good French mathematicians who were prisoners of war or conscientious objectors, and they were one of the leaders in this development. So we got a lot of new stuff coming out of France. And then there was Chern and what he was doing and what he had done and the implications of it. So a lot of things were happening that were brand new. The '50s were very special.

INTERVIEWER: So can we sort of walk through the various areas of interest that you've had over the years, starting with differential geometry? Will you talk about the work you've done in that and maybe why it's particularly interesting to you, why it's captured your attention?

SINGER: I think what I really like in mathematics is the connections between different fields. And geometry captured my attention because it combined topology with geometric insight. And you needed analysis, which I learned from Irving Segal, in order to-- well, what we call in order to get existence theorems. In order to solve certain equations which came up from geometry, you needed some strength in analysis in order to solve those equations. And I like that combination of all three things, and that's what attracted me to geometry.

And in fact, again, what we did at MIT was all the courses that needed these backgrounds in other fields, Ambrose and I revised. And we revised the geometry course, as well, to be modern. And I think, among them all, the geometry course is pretty much what it was when we revised them-- by then, the '60s.

INTERVIEWER: I assume they had not been revised for a while before that.

SINGER: That's right. They were pretty old-fashioned. This was an opportunity of Young Turks coming in and doing some new things.

INTERVIEWER: It was your impression that the mathematics department was a little behind the times when you arrived?

SINGER: I don't know. The only department I had been acquainted with was Chicago, and it certainly was not behind the times. I guess maybe MIT was a little and we were the first-- Ambrose was the leader, I must say. It was his energy that said we should do this, that, and the other thing. And I provided some of the energy to help him along.

And so it did need some modernization in the '50s, though we had terrific people like George Whitehead. And Norbert Wiener was still there, but he was doing his own thing. And his main contributions to mathematics were already finished by then.

INTERVIEWER: Well, that's probably why they hired you.

SINGER: Pardon?

INTERVIEWER: That's probably why they hired-- bring someone the University of Chicago newer stuff to MIT.

SINGER: Well, it took a while, you know? I always kid the department. They had a program of instructors, Moore instructors, and I was a Moore instructor there from '50 to '52. But they did not keep me on. It was only supposed to be a two-year appointment, and most of us left. And I went to UCLA. But I say they sent me to the minor leagues for training, and they did.

And it was good for me, actually, and I came back four years later. And that's really when I started revising the department. And I think Ambrose and Whitehead, who were here, were very eager to have me come back, and that's why the department decided to have me come back.

INTERVIEWER: What about the area of partial differential equations?

SINGER: That's part of what I call analysis, and those equations are what come up in differential geometry many times. And it's solving those equations that are critical for many problems in geometry.

INTERVIEWER: And I have mathematical physics?

SINGER: Yes, that came later. Mathematical physics-- my interest in mathematical physics started with something called self-dual solutions, to partial differential equations. And those self-dual equations were much simpler than the usual ones you find in what's called gauge theory. And I was struck by the physicists Polyakov and company coming up with these geometric solutions to equations. And we mathematicians had not seen them.

And I felt that it was a blind spot on our part not to have understood that these equations could be simplified this way. And then I got interested in saying, well, why do they want these? What's happening? And this has to do with what's called gauge theory in physics, which turns out to be something of mathematics-- fiber bundles that we knew in geometry. So I was struck by what they had done, struck about this dictionary called the Wu-Yang Dictionary, that related mathematical terms in geometry to physics terms in gauge theory.

And so I wanted to know where all this was leading to, and I started to seminar and a course on the connections between math and physics. Now, I did not do that here. In '77, I decided, for personal reasons, to go to the West Coast, and I went to Berkeley. And I spent seven years at Berkeley. MIT was not happy about that, and what they did is ask me to retire and make sure that I could return easily and come out of retirement.

So I started the seminar in Berkeley. And every year, I got a call from MIT to ask me to come back. And I got very impatient with Berkeley. And when they made the critical call, I said, yes, I'm coming. I'm coming home. And I did.

INTERVIEWER: What was different about the atmosphere or culture at Berkeley that didn't fit as well as the MIT one?

SINGER: As I said, I went there for personal reasons, not for scientific reasons. But there, I did witness a change in culture. It's as if the younger people felt that there were some connections between math and physics that hadn't been explored, and they were excited about my running a course and giving a seminar. And three of my best students are students that I had at Berkeley who got involved in this connection between geometry and mathematics and case theory and physics, wrote her thesis about these matters. And all three of them are very close friends who I know.

INTERVIEWER: So why did you ultimately decide to come back?

SINGER: Berkeley, politically, I didn't care for mixture. And the University, although it had some brilliant people, by and large, there were people who were still involved in-- I don't know-- revolutionary times, political issues. And they had more to say at the University than the really brilliant people who were there. And ultimately, I got impatient with all that politics interfering with real science.

And it was one of those days where I was fuming that MIT called me again and asked me to come back, and I did.

INTERVIEWER: Is this a good time to talk about your theorem and how that came about?

SINGER: Yes. But I'd like to have one more-- we're talking about stories. My wife and two daughters were very unhappy about moving east. And they always said that they wanted to go back, especially my children, my two daughters. Well, it now happens that daughter Emily is biotech editor of technology reviews here, and my other daughter, Annabel, received her PhD in brain and cognitive sciences at the University of California San Francisco and elected to be a postdoc here at MIT. So now they're both here, and I see them frequently.

INTERVIEWER: So you knew best after all.

SINGER: I wouldn't know, but it's worked out.

INTERVIEWER: So how did your collaboration and your theorem develop? Can you tell me that story?

SINGER: Yes. I got to know Michael Atiyah when I was at the Institute for Advanced Study in 1955. That was a very good year. We had a lot of top mathematicians there, and I got to know Michael well. And there was a change in my family circumstances, and I was on sabbatical. And I needed to go to someplace where English was spoken. And so I called Michael. He himself had just arrived at Oxford, and I asked whether there was a place for me. And he simply said, come. We'll arrange it.

So my wife and I and son moved to Oxford. And after I got settled in the first day, I was warming myself by one of those fires. And he came up and he asked me a question, which was a question in his field. Why was the A-roof genus an integer for spin manifolds? That was the question. And I looked at him and I said, Michael, why are you asking me that question? You know the answer to that. Really probing him that he had some other reason for asking it.

He said, well, yes, I do know the answer. But I feel there's a deeper reason for it. I liked that answer. And although I was working on another problem, I spent the spring in the gardens of Oxford colleges sitting on benches thinking about that problem. And finally, I thought I knew the answer to it. And it involved the Dirac operator, Dirac's equation for a spinning electron, which I knew for other reasons, and involved differential equations and analysis and some geometry.

So the next day, I came to Michael's office and said, look, Michael, I think you're getting an integer because it's the number of solutions to this equation. Moreover, if we do a little bit of juggling, you'll see that all the equations that give you integers as answers can all be described in terms of these geometric operators. You're just counting the number of solutions, and that's why you're getting integers.

It just took overnight for Michael to say, yeah, we can write down a formula for all that. And that started our collaboration on the index theorem. And actually, nine months from the time he asked me the question, at that time we had a complete proof of the index theorem.

INTERVIEWER: You had a new baby.

SINGER: What a baby. It grew into really something-- very robust development.

INTERVIEWER: So as someone you know without a science background, is there a way you can explain the theorem in kind of lay terms? And I understand if that's not possible.

SINGER: Well, it's difficult to do. I can just give you motivation for it, to some extent. You're trying to solve an equation, and you want to find the solution. Something called the phantom alternative, where you look at the number of solutions and you also look at the number of different ways you cannot get a solution. And you compare the difference of the two. What you'd really like is to have that equal to zero, and that difference is called the index of this equation.

You'd like it to be the zero, because then it would say that existence implies uniqueness, and uniqueness implies existence. Existence is-- well, any rate, those are the two integers. If they're equal, then you know, as I said, existence implies uniqueness. Uniqueness implies existence. Well, it's much easier to show uniqueness than there is existence.

So if you know it's zero, you only have to solve half the problem. And you only solve the easier half of the problem. And that was the original motivation for defining or saying what you meant by the index. And the reason our theorem was so exciting, aside from the fact that it combined a lot of different fields, is it gave you an answer in geometric terms-- the number of solutions, or the number of holes in this particular, you see.

So it put geometry into this partial differential equation answer. And that's what made it exciting.

INTERVIEWER: Can you explain how that led to this sort of breakdown between fields, between physics and math, for example?

SINGER: Well, there are two questions, I think, when you say the breakdown between. One is in mathematics itself. This had such impact because we were using geometry, topology, a little algebraic geometry, and analysis all together to get a very striking solution. So that broke down barriers between fields a great deal. And because it was so striking, those barriers have stayed down all this time, except for people who were very fixed in a given subject.

Physics is another matter, because string theory came along. And it turns out, they needed some aspects of mathematics in order to solve their problem, what's called K-theory. And ultimately, they needed the index theorem and K-theory to be able to answer some questions in string theory. And so it turns out, very quickly, young physicists move rapidly and absorb mathematics very rapidly.

So they became experts in K-theory and the index theorem very quickly. And asked penetrating questions about the subject, again, very quickly. It's interesting that Atiyah and I wrote our last paper in '84, and it was on the applications of index theorem to string theory. Anomalies, let's call, a cancellation of anomalies in physics. And we had a geometric way or mathematical way of explaining how those anomalies came about and how to eliminate them, and that's what physicists wanted.

INTERVIEWER: Do you think it was-- you know, was it your particular exposure and background in geometry, starting at the University of Chicago, that helped you to see this in a different way? Do you know what it was that allowed you to figure this out when no one else had done it up to that point?

SINGER: Well, I would say what allowed me to make progress on all these things was, as I said originally, I loved the interconnections between fields. I found that most exciting. So I was well trained at Chicago between the analysis and geometry that I had learned there.

And we had a very good topology group headed by George Whitehead. And I learned a lot of topology then. So it was those connections that allow me to put them together when needed. I mean, it just happened. You're sitting on a park bench-- it's the old story-- and suddenly it clicked.

INTERVIEWER: Yeah, it's a great image. Because as you pass people in a park and you see them on a park bench, you don't figure they're necessarily thinking about science-changing theorems, but--

SINGER: Well, I was noted for sitting on a park bench with pencil and a pad of ruled paper all the time.

INTERVIEWER: As you look forward, do you have expectations for other things that you think this will help to explain or unlock in the future? Or could it be anything?

SINGER: Well, it turns out that index theory is used in a number of different ways in physics. I hesitated because there's a subject called noncommutative geometry, which is too complicated to explain here. But I feel that index theory has influenced that. And I want to use some aspects of non-Euclidean geometry in the future to explain some things that are going on with black holes.

So I'm still interested in physics and problems in physics, but I want to use more sophisticated methods than are presently available in physics to attack those problems. It's one of the reasons I am retiring, is so I can focus on that material without any complications.

INTERVIEWER: By sort of uniting physics and mathematics in a way that they hadn't been before, what kinds of issues have people subsequently been able to deal with that they couldn't have dealt with without that closer connection?

SINGER: Well, for example, index theory is used to explain entropy and black holes. To compute certain kinds of black holes and their entropy, you have to use a number of solutions to a differential equation for the entropy. So there's an application that was kind of unexpected. Steve Hawking talked about entropy in a recent video on TV. I think I'm hesitating, because I'm just going to repeat myself.

I think there are parts of mathematics, like noncommutative geometry, that have had some impact on physics, but I think it'll have more so on black holes. And that's one of many subjects I want to look into in the near future. There are some aspects of topology-- it's gotten very sophisticated, again, partly because of index theory-- that tries to combine string theory with rather axiomatic topology, I would call it.

And I think that's going to have some impact on physics, as well. These are coming subjects that I'm just guessing about, really.

INTERVIEWER: But back when you came up with the index theorem, you didn't really know, at that point, all of the ramifications that it would have?

SINGER: No. That theorem was-- you know, 40 years of it. It's always been robust. Even now, we're working on-- my colleagues and I-- I'm going to come back to talk to them-- are working on some aspects of a rather sophisticated index theorem that nobody's played with before.

INTERVIEWER: That must be quite an accomplishment, to feel that you have sort of a long-term contribution that keeps kind of giving birth to new--

SINGER: Yes. I'm very lucky in that way.

INTERVIEWER: I read that you've made some comments about the frustration of communicating with younger mathematicians about jargon.

SINGER: Yes.

INTERVIEWER: I wonder if you could explain that.

SINGER: Every field has its terminology-- not just in mathematics, but whatever. You're not really in the field until you understand the jargon. In mathematics, that jargon plays an important role, particularly for young people to feel they're part of the field. Whereas, as an old timer, naturally, I'm not good at learning other languages anyway, so I am unhappy with that jargon. And I'm unhappy when young people try and explain something in that jargon.

And so, if anything, I just trying to eliminate and ask, now, what are you really talking about? Can you put it in more straightforward terms or give me an example of what you mean? So I'm impatient about that, and not just with young people, but it's true with many experts. For example, the difference between a good colloquium lecture and a poor one is whether the speaker uses jargon or not.

INTERVIEWER: And as someone who works in communications, I completely agree with you. It's the difference between talking to impress or talking to communicate.

SINGER: Yes.

INTERVIEWER: And there is a difference.

SINGER: Absolutely.

INTERVIEWER: Let me ask a little about some of your other work. You were chair of the Committee of Science and Public Policy at the National Academy of Science.

SINGER: Yes.

INTERVIEWER: Can you talk a little about that?

SINGER: That was a very exciting period for me, my period in Washington, and that's part of what I did. We attacked a number of problems. One of the things we did was describe-- I think it was the first report on what to do with nuclear waste that we had. I had one experience where, with the internet and computers just breaking out, I had a meeting where we discussed privacy matters and the threat to privacy with what was coming.

But I was way ahead of my time. Nobody on the committee really went along with that as going to happen. I mention that because now we're quite concerned about that privacy. But I was, I don't know, 20-odd years ahead of the game. But the important thing for me was I met so many brilliant, creative people there, and it was exciting to be with them all the time. And they made me aware of how creative human beings can be and how constructive they can be.

We were very careful-- my secretary and I-- in choosing people who might serve. And we had terrific people. And to tell you another story, you know, I knew Jerry Wiesner from first year I was here. He was running the electronic lab at the time. And I came to see him because I had an idea, based on Norbert Wiener, of putting a multiple probe on the optic nerve and using it as a television set for people who were blind.

And they looked at me then and said, well, we can only put one probe in now. But if you want to come and work in my laboratory, you have a job, which is how we met and talked. But anyway, when he was president of MIT, I went to see him about something else. And he congratulated me on being the chair. And I was sheepishly saying it would take away from my research.

And he said, no, it won't, Is. The experience and the broadening that you'll get then, when you go back to mathematics, you'll have an entirely different view about what you want to do and how you want to do it. He was absolutely right.

INTERVIEWER: How did it change? How did that view change by your experience?

SINGER: I simply instead of focusing on the technical aspects of the problem I was working on, I just took a step back and said, do I want to do this? Why do I want to do this? Where does it fit in my view of mathematics? And often, that changed how I went about things.

INTERVIEWER: How about your experience of being on the White House Science Council?

SINGER: That was very exciting. I can't speak much about that. I think much of it is still confidential. But again, that was a learning experience. Again, there were terrific people on that-- Paul Gray, for example. And we have to talk about the various presidents of MIT. We haven't talked much about MIT, per se, but we should.

INTERVIEWER: We will.

SINGER: Okay. We didn't focus on much of Reagan's program as president for the country. It was mostly problems international that one was concerned with, I can't go into. But I will mention one that came up at that time. That's when one discovered AIDS. And we had to discuss with the science advisor how he would approach the president with this horrendous problem.

And President Reagan was very positive about the whole thing. He said, well-- what we suggested is he get a committee to look into it and make recommendations. And he said immediately he had no prejudices of any sort. Yes, let's do that immediately, and let's see what we come up with. And the first thing they came up with, which was important, was to emphasize cleanliness was the first recommendation of the committee.

And I think they did a very good job. You know, that's an example of something that came our way from time to time.

INTERVIEWER: Was it important to you to just sort of put in this time in the public sector?

SINGER: The part in the academy was important. I learned a great deal there. And being on the White House Science Council was just one of those things that I felt, well, I feel I'm a pretty level-headed guy. If I can be useful to them-- I don't know why they want a mathematician, but if I can be useful to them, then, by all means, I have to do it, just as a citizen more than anything.

And in fact, I remember the science advisor one morning, after a heavy meeting the night before, coming in and said, Is, your suggestion solves the problem. How can you be so smart? You're just a mathematician. I said, so? You could see the role of mathematics in that heady environment.

INTERVIEWER: Did you get any sort of different perspective from that experience in DC that you brought back in and it somehow contributed to what you did back at MIT? Or was it more an issue of personal growth?

SINGER: I don't think it's growth, but I think there is a different perspective. For example, as I've mentioned, I served in the armed forces her almost three years. And I had a certain perspective about the armed forces. I like my freedom, and in that respect, I hated being incarcerated, so to speak. But I gained a healthy respect for the armed forces, the generals I talked to who came to various meetings who were necessary.

I had lunch with a general whose responsibility would be to push the button if we were going to use nuclear weapons. And I said to myself then that their choice was impeccable. In general, I concluded that their choice of people and how they go about it is remarkable-- much better than the way we choose people for tenure and stuff like that. They were remarkable.

And the generals, I'd have lunch with from time to time. Often, we would have to go to the cafeteria because there wasn't enough food around for them. You know, the White House Council would have lunch, but nobody else could who was visiting. And I elected to go to the cafeteria with our visitors, often. I have a lot of respect for the military on the basis of what I learned at that time. And I got a better feeling for the chain of command that occurs in the White House at that time.

INTERVIEWER: Is the difference-- and this is only a guess on my part. Is the difference that they're able to look at and evaluate more almost intangible qualities than might be involved in the decision for tenure? They're looking more at what the person contributes as an individual.

SINGER: I don't know the answer to that. I can only say that there's so many little things that made me come to the conclusion. For example, the aid to the science advisor, Jake [INAUDIBLE], had been in charge of a nuclear submarine before that. Well, you can imagine when we were to meet, there was always one crisis-- I mentioned one or two-- coming up all the time.

I don't think I've ever met a person as cool as he was. There was no crisis that he couldn't have something constructive to say about how to handle it, and all in a cool manner. And as I said, that was the feeling I had about the general, who would have to push the bomb. It's those individuals and their personalities that led me to believe that the selection process must be awfully good.

Sheila Widnall, I think, will confirm that, because she was Secretary of the Navy, was it? And I think she'll confirm that sense of selection that they have that's better than ours.

INTERVIEWER: You were a Sloan Fellow and a Guggenheim Fellow two times. Is there anything about the experience, that opportunity, that you'd want to talk about?

SINGER: Could you repeat the question?

INTERVIEWER: You were a Sloan Fellow--

SINGER: Yes.

INTERVIEWER: --and a Guggenheim Fellow two times.

SINGER: Yes.

INTERVIEWER: What does that experience add?

SINGER: Well, the main thing is freedom. I think all research people want the freedom to do their work. And they gave me a great deal of freedom so that I could just do what I wanted. And I'm very indebted to those foundations for allowing me the freedom to do what I wanted.

INTERVIEWER: Freedom is a theme.

SINGER: It's the theme, yes.

INTERVIEWER: You've been teaching first semester calculus all along, haven't you?

SINGER: Not all along. That's very interesting. Well, since you brought up teaching, I had occasion-- I was looking for old notes of mine of a lecture I gave a long time ago. What I found was a series of courses that I had given in large classrooms and the revision of the subjects-- including, at the beginning, teaching calculus. We all taught calculus at that time. But for many years, I only taught graduate courses or the high-level undergraduate courses.

I don't know what possessed me, but I decided to be a TA in the first calculus course to freshmen. I think I did it because my good friend ran the whole program one year. I think what motivated me was I was too far removed from MIT on the undergraduate level. And this gave me a chance to come back. And in fact, it was a wonderful experience the two years that I did it, making contact with freshmen again.

They liked my lecturing. And in fact, whoever ran the program had instructors who were from abroad to come in and listen to how I handled the course. One of the important things that happened-- Arthur Mattuck was in charge of the calculus program. He is a fantastically good lecturer-- showman, really.

And he arranged, at one time I was doing that, that we TAs would not be responsible for final exams or making up problems or grading. And that changed our relationship with the undergraduates, with the freshmen, because we were now their friend and not judging them. And I'd often come in and say, well, what did so-and-so do this year, this time? They'd say, and I'd say, well, that's not the way to go about it. I think, really, to see it, you do it this way.

So there was that sense of freedom that I could say what I wanted it. And the students understood that I was there to help them and not to judge. I'm repeating myself. And that was an entirely good relationship. Moreover, I got to know some of the students quite well. And in every class, freshman class, at least two of the students could be world-famous scientists, engineers, anything they wanted to do. They were that good.

Many of them elected to do other things. So it was very personal experience for me, and I had made friends. I saw kids who seemed to have nothing grow to show a great deal. And that made it such a exciting, different experience. It made me feel part of MIT that I hadn't felt for many years. Everybody was surprised that I did it a couple of times.

INTERVIEWER: Do you have a philosophy of teaching? Or how does sort of teaching integrate with your other work?

SINGER: Teaching is integrated with my other work in the sense that I never think of research in quotation marks. All I want to do is understand what's going on. And the motivation for understanding is when I understand it, then I can explain it to somebody. So there's a link for me between doing research-- doing research means understanding something that I don't understand, and maybe it turns out nobody else understands. And when I do understand it, the link is I want to tell them about it.

So therefore, in a sense, I'm a good teacher. I can put myself in the position of a student. I know what they don't understand, and now, if I know them well enough, I can kind of explain what they don't understand in terms that they can comprehend. So it's that empathy that I have that makes me a good teacher.

INTERVIEWER: Do you learn from your students?

SINGER: Rarely. On the graduate level, I have learned a lot from my graduate students. On the undergraduate level, no.

INTERVIEWER: You've had a number of visiting appointments at UCLA and Columbia and Princeton, and you were at Berkeley. When you go off and spend time at other academic institutions, does that come back in any way and benefit MIT? Is there a value from those experiences?

SINGER: Well, of course, all experiences are valuable. Every day is valuable. But no, I'm impressed with MIT. We do things right-- not just in the math department. I'm really impressed with how constructive everybody is here. And I think we do a better job than anywhere else that I know. So I haven't learned anything from other schools that we need to know at MIT.

INTERVIEWER: Well, that's an important lesson right there.

SINGER: Yes, I think so.

INTERVIEWER: Were you surprised to be chosen an Institute Professor?

SINGER: Yes.

INTERVIEWER: Tell me why.

SINGER: Well, it just never occurred to me. I talked to Paul Gray about it recently. And he said one of the joys for him as president was to notify people. And he talked about one case where the professor came in shaking and said immediately, what have I done wrong? What have I done wrong?

And I confessed to Paul that when I came to see him, that was what I felt, that I had been called in because I'd done something wrong. But I kept my mouth shut. So I was shocked, delighted, of course, when he told me.

INTERVIEWER: How has it changed the nature of your relationship with MIT, if at all?

SINGER: It changed my relationship with the math department a lot, because it meant I reported directly to the provost and that I was free to do what I wanted. And again, that freedom meant a great deal to me. My math physics seminar was mostly on my mind. And I spent most of my time making sure that that ran well.

And more recently, we had a new seminar called New Opportunities for Mathematics in Other Fields, where we got visitors from other fields to talk about possible connections with mathematics. I did that for a year and a half, and that was very exciting, also. Again, I learned a great deal from these people. We'd go out to dinner, and I'd be talking to people who are experts in an entirely different field, and that was exciting.

INTERVIEWER: That's what I'm doing over here. It's great fun.

SINGER: Yes. Okay.

INTERVIEWER: You have a list of some incredibly prestigious awards and honors, and I'm wondering if any in particular have meant more than the others or were very meaningful to you?

SINGER: Well, the Abel Prize was the most prestigious. And I think, because of that, it means more to me. You know, the Atiyah-Singer index theorem-- Michael and I won the prize together. The Atiyah-Singer index theorem did have an impact over some 40 years. It's still having an impact.

And to have that recognized and recognized throughout the world, not just in the mathematical world, I thought was very important for mathematics and certainly important for me in the sense that I feel-- I don't know. I can't express how I feel about it.

INTERVIEWER: Let's talk about MIT.

SINGER: Yes?

INTERVIEWER: Why have you stayed here so long? What is it about your career interests, your research interests that have meshed so well with the environment here?

SINGER: Why have I stayed here so long? I think I'll expand on it, but the direct answer is, it's the best place to be. And the issue is why. We talked about freedom, and that's part of it. But I think the-- let me put it this way. The Japanese have a game, and when they want to evaluate what a person is or their character, the game is to say one word to do that. For x, its energy. For someone else, it's depth.

For me, the one word for MIT is generosity. It's a generous place. For me, it's been a generous place. Freedom is part of that generosity. It's a place where I grew up scientifically. Remind you of my background-- I came as a grad student after almost three years in the army. I was way behind. I came here and got involved in what we were doing. And gradually, as time went-- and you know, I had to go away, and then I came back.

Gradually, as time went on, even before the index theorem, it sort of became clear-- we went out to lunch, did one thing or another, that questions would come up. And after a while, I'd say, well, maybe we were looking at it wrong. Maybe we should look at it this way. And it changed our picture of the issue. And after a time, there'd be a discussion and there'd be silence, and everybody would turn to me.

And it's in that sense that I kind of grew up at MIT. And then I had the freedom, soon enough, to do what I wanted, even before the index theorem because I was a good lecturer. I would do things differently than others, and that was much appreciated. That generosity shows up in a lot of ways.

OpenCourseWare, as my great example, started as a recommendation by some faculty members and others working hard on their courses so it would aid their administration, finding funds to have it happen. That's a great reflection of MIT, per se, as to what we're about. And I've always found the administration very eager to allow faculty and students the freedom to do something constructive and different. There was no reason to leave a place as wonderful as that.

INTERVIEWER: I guess maybe we should-- let's talk about the presidents.

SINGER: All right.

INTERVIEWER: And I'll leave it to you. Who would you like to speak about or make a comment about?

SINGER: Well, I've been fortunate in getting to know them all pretty well. Howard Johnson comes to mind because of his death such a short time ago. I got to know him because we had student unrest here, you know, for a period of time. I wrote him a note saying that on the basis of what I knew about Berkeley, he would be wise if he kept in contact with the faculty during all the commotion, excitement that's going on.

And he did better than that. He had two committees-- a faculty advisory group and a student advisory group. FAG and SAG we called it at the time. And we met frequently and were made aware of what the issues-- there were always a crisis coming up all the time. So that was something special. And when it was over with, we had a party at our house for Howard. And since then, we've become very good friends.

That's one example of something that happened. Paul Gray-- I don't think people realize how much Paul and Priscilla did for MIT in terms of supporting the search for women to come here, making it a more amenable place for everybody. In my case, I got involved in trying to get African Americans here, again, through Paul's push and our chair at the time, Ken Hoffman.

So on several occasions-- for example, I think I gave a talk at Georgia Tech and used the occasion to visit a technical school for African Americans, an engineering school. And I went there and talked to the dean of science and the members of the faculty. It's very funny, if you want a story. I've given this talk at Georgia Tech. And I had this appointment, but we played tennis first afterward. And so I ended up at the campus with my tennis racquet, luckily, because those were difficult moments between places, between African Americans and Caucasians.

And I walked on the campus, and the first look of students was a glare at me. But then they saw my tennis racket and smiled. So that was my entree. And I went to talk to the math department. The dean was there. He was very antagonistic, because he thought, somehow, MIT was trying to take away some of his power. And that was unpleasant, the discussion we had, going nowhere. He was just protecting his power.

He left, and then the faculty relaxed, and we had a very nice chat. They were very pleased to have someone of my stature come down and talk to them. Another occasion, which did work well, was I went to Howard University. And I had talked to our chair, Ken Hoffman, who urged me to go. Our trouble with getting African Americans is they don't want their best students to come to MIT. They want to keep them.

And I suggested that maybe we could have them come during their junior year and then go back for their senior year and report on their experiences at MIT. And that would be constructive. And so I went, and it worked out. We had two women come up. I only kept track for a while with one of them. And she had a terrific experience and played around, became head of a company or a leader in some administrative capacity down in the South. I've lost track of it.

But sort of always knowing that Paul and Priscilla were behind many of these things. And now we're just good friends as a result of that. Chuck Vest and I became good friends, as well, because he comes from Michigan. And that's where I went, to the University of Michigan. So I talked to him a lot.

He invited me to-- he asked me-- I've forgotten who is going to be the new inauguration or new president at the University of Michigan. But he asked me to represent MIT at that inauguration. I was pleased to do that. Nice to get back to home base, so to speak. And I've told you, Jerry Wiesner and I, I've known him from way back. I'd always consult with him, and he was always so positive and constructive about everything.

INTERVIEWER: Did you ever have an interest in administration?

SINGER: No. No, not at all. I've been lucky to avoid it, except for the big chair of this committee in Washington, and I had a very good staff who took care of everything. Of course, I was on the search committee for Susan Hockfield. And we had a-- just when she came and talked to us, I felt we were close friends the moment she talked about what her ideas were for MIT. have I left anybody out in that period of time?

INTERVIEWER: I don't think so.

SINGER: I don't think so, yeah.

INTERVIEWER: Who was president when you arrived? Was that Howard Johnson?

SINGER: No, it was before that. Someone I didn't know then.

INTERVIEWER: Okay. Let me ask a little about the School of Science.

SINGER: Yes.

INTERVIEWER: I'm wondering if you have any thoughts about what its strengths are or its role at MIT? Your impressions of the school itself.

SINGER: Well, I've known a couple of deans. They've been terrific. Mark's a terrific dean. I don't really have any comments. And I make a lot of contact with the physics department, because of my math physics seminar. They have a very strong faculty. And their postdocs are very good now. They weren't for a while, but they are very good now.

And I've seen some of the people grow and are really an integral part of the faculty. So those are the only two departments I know. I don't know biology, really, at all.

INTERVIEWER: What makes a good graduate student or a postdoc?

SINGER: Well, for me, it's, again, the interface between fields and the eagerness to understand what's going on between fields. And I have people out there who are in that category now in physics.

INTERVIEWER: How about the strengths of the mathematics department?

SINGER: Well, it came in first in the popularity ratings this year, and it did five years ago. And I think rightly so. And this means not tied first, but first. And that shows that we're recognized for its strength. One of the things that's happened in our department is attention to the undergraduates and preparing them for these various competitions, which they more or less win or are close to winning. And that created an understanding with high school students that MIT was the place to go.

And so we've been very lucky that we get finalists in various competitions for high school coming to MIT. So the MIT undergraduate program right now, although I'm not part of it at all, they have to take into account that they have brilliant kids coming in who are ready for anything when they arrive and are well advanced beyond anything that we've really seen. We may see it in one or two students in the past, but now it's common for those undergraduates.

And our grad students who come, they're just excited about coming here because there's so much going on. So we've benefited by that combination of exciting undergrads, grad students now. Much better program of students we have now than we had, say, 10 years ago. My criteria was where do they go after they get their PhD. Where do they end up? Didn't look too good before. Now it's looking much better.

INTERVIEWER: Since you have the perspective of being here for a long time, can we talk a little bit about the changes that you've seen? How about in the culture? Has that changed in the time that you've been here?

SINGER: I don't really know what culture means in this context. The only thing I've noticed is that students have much more say in what's happening at MIT than they used to. I think that's all for the better. And they also have a different attitude. When I first came to MIT, it was very strict, and they did what they were told. They'd better do it or else, that kind of a "tech is hell" was not there, but the reflections of it, the relics of it were there.

Now, that's not true at all. Students have a lot to say about what's going on. They have much more flexibility. That's part of the generosity I'm talking about, flexible to do what they want. We've learned that a student may come in with an idea that they're going to major in field x, and they end up doing something entirely different and have different aims and interests by the time of their second year. And having learned that, it's been built into the program.

So we're much more flexible and much more generous than we used to be. Europe, for example, is something that was not there a long time ago. And that's another example of generosity, of taking people who are kids, really, and spending some time with them. And I don't do that, but a lot of my colleagues do. And I think it's a very important program. It does a lot for the student. And in fact, students have become so good, it also does a lot for the faculty member, especially in laboratories.

INTERVIEWER: Why do you think it's so much better for students to have a greater say in what's going on at MIT?

SINGER: I think they're pretty astute. And so when they see things that are wrong, they now can speak up about it in a way that they hadn't before. So, for example, going back to when I taught, I was TA, students in my class would invite me to some event-- lunch, dinner, something like that. And they would talk freely about the difference between MIT and Harvard in a way that didn't happen years ago.

So they're astute. They're constructive. So their insights are important.

INTERVIEWER: How about changes that you've seen in the faculty?

SINGER: I don't see much difference, actually. What I see that's different is the climate in which they're in. But I don't see them any different. I think they are as focused in a combination of research and teaching as we were earlier on. I don't see much difference.

The one real big difference is certainly the women in the math faculty are very gung-ho about making sure that women are well represented in the field. And they have lectures by women on mathematics. They're also probably more socially oriented than we were years ago, but in a different way. So the changes there are simple enough. We were very socially bound in the sense that we would have a party after every colloquium, and wives would come to that party. And we got to know everybody quite well.

Now, of course, that's changed a great deal, because women work much more independently, where there are no such parties. There are too many colloquia anyway, so we couldn't keep that up. And so that's been separated, and the sociability occurs in different ways.

INTERVIEWER: Has the increase in women in your department, has it changed the department in ways?

SINGER: I think it has.

INTERVIEWER: In what ways? Can you speak to that at all?

SINGER: Well, though I haven't spoken to any students, I'm sure that women students feel much more comfortable, because they have women they can come and talk to, which was difficult a long time ago. I think there's more sociability in the department than there was before-- more parties, more celebrations, more contacts in the department as opposed to parties had somebody's house, as there were years ago.

INTERVIEWER: Have you seen MIT change academically over the years in any significant way?

SINGER: Greater interconnection between fields. Biotech, for example, is something that's very important that's fairly new and I don't know much about. I think the interaction between departments is increasing rapidly. It's one thing I tried to promote in this seminar I had.

INTERVIEWER: It does seem to be a trend academically.

SINGER: Yes.

INTERVIEWER: Any institutional turning points that you've seen or that you want to speak to?

SINGER: I wouldn't know anything about that. As I told you, I've avoided all that. It's not my bag.

INTERVIEWER: What things have we not talked about that you think are important to say? Can be anything about your own research, about MIT, about your hopes for MIT in the future.

SINGER: I think we've covered everything that I can imagine. I'd just like to say that I've been very fortunate in the support I've gotten from MIT and growing up here at MIT and having the freedom and opportunity to do the things I want int mathematics. And fortunate that I feel confident that I can continue doing it.

INTERVIEWER: So what will you be working on after June?

SINGER: My tennis game, for one. But I mentioned that I think something can be said about black holes that involve a new form of geometry, noncommutative geometry. Again, there are some connections between topology analysis and geometry that haven't been pursued by others that I think I can have something interesting to say.

The main thing is I can afford to gamble, you know? Why not? And I will gamble, and I'll enjoy doing that.

INTERVIEWER: That's what you're supposed to do when you retire.

SINGER: I see. Okay.

INTERVIEWER: Thank you so much.

SINGER: Thank you. It's my pleasure.

INTERVIEWER: It's been a pleasure to talk to you.