Interview by Maria Shtilmark
How did you become the Director of the SCGP?
I was quite happy being a math professor at Columbia. I had heard about the Simons Center, mainly as Mike Douglas was ‘on the market’ and, together with the Physics department at Columbia, we made him an offer. It looked like we were going to get him. Then at the last minute he accepted the offer from the Simons Foundation to be a permanent member of the Center. That was their first permanent member. I was disappointed, but I thought: “They are off to a good start” and didn’t really pay much more mind. Then I got a phone call from a committee working on how to set up the Simons Center and hire a Director. They knew that I had experience with various institutes, and I’d been on the board of MSRI, so they asked me to come and share my experiences and thoughts with them. So I did. I went home afterwards and I said to my wife, Ellen: “That was the strangest meeting I’ve ever been in. It was half a ‘pick-your-brain’ half a job interview”. Which, in fact, was exactly what it was. They were interviewing some people to pick their brain, and some people they were interviewing to pick their brain and also thinking they could be possible candidates to be the director. Couple of weeks went by and nothing happened, and I said to Ellen: “Well, if it was the job interview I didn’t get the job”. About a week later Jim called and said: “I want to meet you. I am willing to come half-way. You’re at Columbia, I’m over at East side, let’s meet at a restaurant, in the 80s on the West side, “Isabella’s.” He offered me the job of Director at the Simons Center. I said: “Jim, I am flattered but I am not looking for another job.” We talked about it. I went home that night and said to Ellen that I was not really interested. But I described the position to her and she said: “You’re taking this job!”
My, she was right. I accepted the job. I spent the summer of 2008 here getting to know people and getting the sense of the landscape. I went off to Stanford for a sabbatical year that had already been arranged. I came back in the summer of 2009 and started the job. We were over at the Math Tower back then. In early 2010 I hired Elyce Winters, Tim Young and Jason May. We started hiring administrative staff. The building was under construction and we were quite involved in that process. I made some changes in the internal layout: more small offices, fewer large (and shared) offices; the expansion of the café from a “coffee and snacks” operation to a full service kitchen serving hot lunches, which necessitated expanding the lunch-room area. The quality of the blackboards was an important issue to which I paid a lot of attention. And believe it or not, I spent an enormous amount of time thinking about keys, eventually deciding on the key-card system we have now.
These were the practical details. Important as they are, they pale in comparison to the decisions about permanent members and other senior scientists, which was the most important aspect of the job that I was assuming. Even during my sabbatical at Stanford I was thinking about hiring permanent members. I approached people—some to pick their brains about whom we should hire and some to convince them to consider coming to the Center. Once I got to Stony Brook, the pace of these conversations and overtures increased significantly. I knew that it would take time to get permanent members on board so to provide senior leadership for the Center, in the interim, I began by bringing senior people for visits: Gang Tian came for each of the first three years for two months. Paul Seidel and Peter Ozsvath were a year-long visitors. Nick Read, Zvi Bern, and Yakov Eliashberg were semester-long visitors. Sasha Zamolodchikov visited for three months a year for several years.
In searching for permanent members and other long-term senior visitors I was very fortunate to have the aid and support of an excellent Board of Trustees. Their extensive knowledge and acute judgment informed the many lengthy conversations and eventual decisions as we moved forward in the hiring process.
Were you always interested in math or did you oscillate between it and some other science?
I’d been a mathematician before I knew there was such a thing. Like many mathematicians, I’ve always had an interest in physics. By the time I was a sophomore in college I was doing graduate work in math, so that didn’t leave much time to do other things. I did take 2 years of physics where Feynman’s lectures were used as a textbook. I essentially just did math after that. I did have to take a psychology course one summer to meet distribution requirement and a Middle Eastern history course, which I hated. All I wanted to do was math.
You’ve been living in New York City since 1976 — has it been a blessing or a curse, and what are your favorite places?
When I got to New York City in 1976 I felt “Oh, this is home. This feels natural to me”. I toyed with the idea of staying in Paris when I was at IHES. But even though I loved Paris, I decided to move to New York. As for my favorite places in the city, I used to go to the Sculpture Garden at the Museum of Modern Art, and I used to go to the Frick. They had a place you could sit and read, and I would go there and work. In Paris I would sit in cafes, I love that combination of working and watching the humanity go by. But I’ve never been able to replicate that in
New York, it’s too noisy. Instead of cafés I use the parks: Riverside Park, Central Park and, more recently, Madison Square Park, which I like a lot.
In a documentary about Perelman, that you were part of, Mikhail Gromov mentioned that for him a joke can often trigger scientific inspiration. What sparks it for you?
I interpret Gromov to mean that change in perspective or attention and a release of tension can cause things that have been ‘percolating’ subconsciously to suddenly come together in unexpected ways. New connections are made, patterns are seen in a new light and we experience the ‘Ah ha’ moment.
Many times over my career I have awakened with the solution to a problem, a problem that I had been stuck on the night before. Somehow turning off the conscience moderator that enforces attention directly on the problem under consideration allows the mind to think more intuitively and the solution arrives from left field. I am reminded of an experience of looking at one of the pictures of thousands of closely-spaced dots. When you first look at it you see no pattern, but then after a few seconds the picture resolves and you see a three-dimensional shape emerging out of the dots. What is the mind doing during those few seconds? Certainly, whatever it is, it is not conscious. It is the subconscious searching desperately for patterns.
I was very struck by a vignette Henri Poincaré recounts in Science and Hypothesis. When he was writing about mental gymnastics or the psychology of doing mathematics, he talked about how for two weeks he worked very hard on a problem and was stuck. So he decided to take a vacation, and as he was stepping onto a bus to take a tour the solution just appeared to him. This seems to me to be a description of the same phenomenon: namely, change of attention away from the problem allows the solution to appear spontaneously from the subconscious.
The ‘Ah ha’ moment when things click is for me extremely satisfying. Wanting to have more, to have more insights of understanding, is one of the main driving forces in my intellectual life.
What makes you interested in a mathematical problem?
Several things come to mind: questions that are natural and whose answers (hopefully) reveal a crucial, important feature of the structure; a special case that seems at odds with a general understanding of the way things are; a question that is important because of its connections to other areas. Of course, all these in the end involve aesthetic considerations: natural, counter-intuitive, important.
Mathematics is filled with these types of problems, some of them quite old and quite famous. The questions that I work on are ones where I feel my approach and my mathematical knowledge give me a chance to see things in a different light and make some progress. Also, I work on problems that I feel are susceptible to resolution with my ‘style’ of mathematics.
How do you work?
I walk a lot when I think. I walk around the Stony Brook campus. For a long time I lived near Columbia University, so I would walk back to my apartment, take long walks in Riverside Park. I do need a blackboard, so after walking and thinking, I will return to the board to see if the details work out. Somebody quoted Gromov saying that when he smoked a blackboard appeared in his head and he could do math, but when he stopped smoking, the blackboard disappeared. Well, I am not Gromov. I never had a blackboard in my head. I need a real one. Another way I work is with the computer. I start preparing manuscript very early in the process and I spend 90% of the time doing what you might call working out the details at the computer. It may be that this is not the most efficient way, but that’s the way I do it.
As a mathematician, interested in poetry of W.B.Yeats, have you ever come across math in literature?
Off of the top of my head, I can think of an example of very mathematical-type passages. It is “Infinite Jest” by David Foster Wallace. There is a scene that takes place at a tennis camp. The kids make up a game about territories, countries represented by different parts of the tennis courts. Tennis balls are kiloton bombs. Kids are grouped into teams (countries) with territory to defend and bombs to launch to attack other countries. At some point, because he is angry at one of his opponents, one of the players breaks out of the game, and instead of lobbing tennis balls as bombs to destroy territory he fires a shot and hits a person on an opposing team in the head with a ball. The moderators of the game begin arguing about the difference between the actual things: people, tennis courts, tennis balls and what they represent generals, countries, bombs. Are the strikes against what is represented, say a general in charge of the war, or against the person representing the general, another kid against whom you have grudge? It is similar to an analysis a semiotician or a logician would give. Anyway, the game degenerates into mayhem and full-blown mob violence ensues. It’s hilariously funny.
There are authors who, while not directly invoking mathematics, have a style that appeals to a mathematical sensibility. James Joyce immediately comes to mind as a prime example of this.
What has been the most exciting thing you’ve ever come across in math?
Transversality. It’s very powerful. A friend of mine who’s given to aphorisms once said that transversality unlocks the secret of a manifold. That was back in the days when we were trying to understand manifolds using surgery theory.
One thing that fascinates me today is what is the source of some of these symmetries that physics is predicting in mathematics. I am not sure I will live to see mirror symmetry fully understood, but it is a tantalizing mystery. And of course, more generally along these lines, what’s the most appropriate mathematical formulation of Quantum Field Theory? The math community is slowly making progress understanding mirror symmetry, more pieces of it are falling into place. There are theorems and conjectures; you can measure the progress. You can’t measure progress towards making Quantum Field Theory more rigorous. Clearly, there is something fundamental there that we don’t understand. We don’t even understand the outlines of what it might look like.
And that’s great. When you understand everything it’s boring. When you don’t understand, life is interesting.
You were elected member of the National Academy of Sciences and fellow of the American Mathematical Society. What do these honors mean to you?
It is an honor to be in the first class of AMS Fellows. Surely, there will be many, many excellent mathematicians who are or will become AMS fellows, and I am happy to be considered one of them. As far as the National Academy, I was quite pleased to be elected. It’s one of these societies that only exist to elect other people, or not. It does do some policy studies, so hopefully it plays an important role in society, but basically it is an honorific society. I looked around the other day at the membership and thought I am not sure I belong here, but I’m happy the other members think I do.
Originally physicists and mathematicians were both called natural philosophers, with no difference between the two. In a sense, is the mission of the Simons Center bringing physics and math back to their roots in an attempt to re-converge?
One of the Center’s stated goals to bring the disciplines and their practitioners closer together by having activities that draw from both worlds. But I do not believe that we are ever going to re-combine the disciplines into one. Physicists and mathematicians have very different views on what questions are important, what one considers an acceptable or an excellent answer. So, the fundamental raisons d’être of mathematics and physics are just different, and they are never going to be brought back together. But I do believe that each discipline can benefit from understanding what the other knows, what issues it confronts, and how its practitioners think. Still, while understanding each other will not make them think and react in the same way, it will make their lives richer and more interesting.
June 2014 – June 2016