To download the SCGP Spring 2016 newsletter – click here: http://scgp.stonybrook.edu/news/newsletters/fall-2016-newsletter

]]>If we have four objects—say A, B, C, D—there are just three ways of dividing them into pairs:

(AB)(CD) (AC)(BD) (AD)(BC).

The salient property is that 3 is less than 4. This simple fact expresses something special about the number 4. For example if we take 6 objects there are 10 ways to divide them into triples; there are 35 ways to divide 8 objects into quadruples, 126 ways to divide 10 objects into quintuples and so on. We will discuss two famous applications of this special property of 4: one going back five centuries and one underlying important concepts in contemporary differential geometry and physics.

To read the full article in PDF form click here.

Intersection of conics. Image Simon Donaldson

Jim Simons speaks at the Dedication of the Iconic Wall, standing before Maxwell’s Equations. May 8, 2015. Photo Stony Brook University

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**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

]]>**Pleasure to welcome you at the Simons Center. You were able to not only come to the Center, but to be a sole organizer of the workshop on Stochastic Partial Differential Equations. What were the workshop’s highlights?**

We naturally focused on recent developments. I tried to invite participants from different directions, who didn’t necessarily know each other before, to enable people to hear new things. A few years ago several works came out in relatively quick succession, developing different theories that now allow to deal with classes of stochastic PDEs that nobody knew how to tackle before. I developed one of these theories, and more or less at the same time Massimiliano Gubinelli and coauthors developed a different approach that solves very similar problems. These led to an explosion of new results in various directions. There are many brilliant young people who got attracted to the field, so partly the point of the workshop was to get them to meet the older crowd of the stochastic PDE community.

**Your lecture “Random Loops”, given within the Simons Center Weekly Talks framework, received many accolades among members of the Stony Brook math community. For our readers, what were its central geometric, algebraic, or analytical points?**

The central point was more on the algebraic, rather than the geometric side. There is a whole theory of renormalization developed for the last 70 years or so in order to get rid of infinities, or divergent quantities, that arise in Quantum Field Theory. These were fairly well understood at the intuitive, or physical level some time ago and, at the mathematical level, their algebraic structure was fairly well understood 15 years ago due in particular to works by Connes and Kreimer. The nice feature of the problem I presented is that one is naturally lead to two of these mathematical structures, acting in concert. One of them gets rid of the divergent quantities at very small scales, which is what one usually sees in quantum field theories – infinities showing up in the equations, and a mathematical structure acting on the problem, creating just the right cancellations for these infinities to go away. Simultaneously, part of the technique is to describe what happens at some much larger intermediate scale. When viewed from the perspective of these intermediate scales, one also sees divergences appearing at large scales. So there is another, formally very similar mathematical structure, appearing in the problem with the effect of removing these large-scale divergences. The way in which these structures appear and interplay is something people haven’t looked at before.

**Which direction is your field, stochastic PDEs, developing?**

One direction in which it is going now is to try to understand in a more systematic way how stochastic PDEs arise from classical models of statistical mechanics. What one is often interested in is to take some discrete microscopic model (spin model, particle model, etc), put some dynamic on it, and then try to understand what happens at very large scales. Typically, at very large scales, some form of the law of large numbers kicks in, leading to an effective description of the system by a PDE. In some typical situations, the system furthermore depends on a parameter like the temperature, external magnetic field, etc., such that, when one tunes this parameter there will be a critical value at which something happens, there is a change of large-scale behavior. When you then look at what happens to the large scale behavior at these critical values, one typically sees something random. So the small random fluctuations of the microscopic system build up to give a macroscopic random effect. In some cases, one can describe explicitly what happens at these large scales, how one has to rescale things in order to see a non-trivial limit. But in many cases one doesn’t know – one maybe knows it for some special situations and then one has a guess that because a given system “looks like” some other system for which one can describe the large-scale behavior, it should behave in the same way. Unfortunately, there are very few rigorous results that go beyond certain special situations. For example, the two dimensional case is very special because of its very rich symmetry group of conformal transformations. Some systems have nice integrability properties, which allow one to compute certain observables explicitly and then take limits on these explicit formulas. What is much easier, at least to some extent, is to figure out what happens with systems that have some additional parameter that one can play with, allowing to tune the behavior between one where one understands the large-scale behavior, typically via a central limit theorem yielding Gaussian behavior, and one where one doesn’t really understand the large scale behavior. When the parameter is tuned to be close to the critical value, one can observe a “crossover” regime at some intermediate scale. The behavior in this regime is typically described by classically ill-posed stochastic PDEs. One direction in which this field is going is trying to justify mathematically the story I just told you. One knows how to justify it for certain models and these are very nice results. But there isn’t yet a clean general machinery that would unify these proofs, they are still very much ad hoc.

**You have been in your area for 10 years. When and why, if ever, would you like to change the field?**

I worked on stochastic PDEs during my PhD, then moved away to do more work on finite-dimensional systems and recently moved back. I suppose it really depends on whether there are still enough interesting questions around… One just never really knows these things in advance. You work on a problem and might find an interesting question in a different area, which might drag you away from the problem that you started with in the first place. You just have to keep an open mind and be willing to explore where your explorations might take you.

**Once asked about HairerSoft, the name under which you distribute Amadeus, sound editing software, you mentioned your interest in Pink Floyd. Did their music have any influence on your becoming a mathematician?**

No, I just like Pink Floyd. (Laughs). My interest in sound came from the point of view of the physical phenomena of sound. I was in high school, and became interested in what sound is, how we perceive it, what does it mean to play a certain note or tune, how could you recognize these things, etc. That’s how my work on the Amadeus software started. In the very beginning, the plan was to write not a sound editor, but a program to which you could just feed a recording, and it would spit out the musical score. But I was 17, and that was beyond my programming abilities. (Laughs). The first step was to get the recording into the computer, so I started to write the sound editor that could do the recording and actually allow me to then mess around with sound. That’s how I started out.

To read what Tony Phillips had to say about Amadeus, go to *A True Gentleman. (Insert link to Tony’s Piece here.)*

**Do you have an answer to a question most interviewers have why the sound of one’s own voice is so terrible?**

I am not a biologist, but if you take a recording of your voice and play it back you only hear through your ears, whereas if you speak yourself you also get it directly through the bones and your body, this is why it doesn’t sound the same.

**Is it true that when you were 12 your father gave you a calculator that could execute 26-variable programs, and that triggered your interest in math? **

I don’t think it was triggered by it—I got that calculator because I asked for it, so my interest in maths was there already. But my interest in programming was certainly triggered by it.

**In the 2014 Fields Medal Simons Foundation video you demonstrate some serious scone baking skills— do you have advice for our chefs, or a recipe for our readers?**

I think your chefs are very good! At home we tend to do very simple cooking. We think that the most important thing is good ingredients, and we tend to keep their preparation very simple. My wife is Chinese, so we tend to mix things up a bit—Chinese spices with whatever vegetables we get. And relatively simple preparations, like steamed fish, or pan-fried tuna steak. We eat meat, but Xue-Mei isn’t terribly keen on it, so we eat more fish.

For Martin Hairer’s family recipe please, go to the Cafe Page of Spring 2016 SCGP News.

**You’ve referred to yourself as an “ambassador of mathematics.” In this capacity, is there a question you wish you were asked, and you are not?**

There is one thing that I would certainly like to change for mathematics, particularly in the UK, and it is to do with how the funding agencies work. There seems to be more of this tendency towards handing out big grants, singling out a few stars, handing them loads of money, and then that’s it! Many people would be very happy to get modest travel grants, I think that in the US the Simons Foundation does that, and for most mathematicians that’s fantastic —just a few thousand dollars per year to be able to go to a few conferences and to stay connected to the community. This is something that the funding agencies in the UK don’t seem to be interested in. For them, it is of course easier to administrate one large grant, rather than many disparate small pots of money. But it would certainly create a much healthier atmosphere and not divide the community into haves and have-nots. Right now, some people find it very easy to travel around to present their results and to meet new people, and some people are stuck. That’s something I would really like to see change, but unfortunately it seems to be going precisely in the wrong direction.

May 2016

]]>By Maria Shtilmark

Prof. Tokieda, who likes applying mathematics to physics, and also applying physics to mathematics, and whose interests include inventing, collecting and studying toys, grew up as a painter in Japan. Later he was educated as a classical philologist in France (in fact, English was the seventh language that he learned), before becoming a mathematician. He is known for using innocent-looking everyday objects to reveal the underlying mathematical surprises. Filled with experimental movies, table-top demos and cartoons, his talks were incredibly engaging, and sometimes even had a little magic in them.

Each edition of the series, bringing world-renowned scientists to the Simons Center, includes a technical talk, a high school lecture and a lecture for the general public. On February 9th the marathon of talks began with *Chain Reactions*, technical talk looking into phenomena in nature where the reaction seems neither equal in magnitude not opposite in direction of the action. Kicking off with a chain fountain, the talk included unknown paragraphs from Aristotle, apparently in more and more violation of Newton’s 3rd law, analysis of which suggested that these phenomena are in a sense generic, the keys being shock, singularity in the material property, and supply of “critical geometry.”

The next talk Tadashi gave that same day was titled *Science from a Sheet of Paper*. By folding, stacking, crumpling, and tearing he explored the rich variety of sciences, from geometry and magic tricks to elasticity and the traditional Japanese art of origami (ori–fold, gami–paper). But there was more in professor’s bag of tricks—during special tea, Tadashi, who knows too well that one of the most interesting places to be is around scientists when they eat, quickly performed a timely Valentine’s Day present—linked paper hearts, with a pair of rings next to them.

*Magic with a Ribbon, Paperclips, Rubber Bands*, a captivating talk given on February 10 to over two hundred high school students, confronted the perception that answering a question ‘What does it mean to calculate?’ involves numbers and formulas. Using a ribbon, paper-clips and rubber bands, he explored a sequence of magic tricks, and before they knew it, students found themselves doing sophisticated ‘calculations’ on objects, that aren’t numbers or formulas at all.

There was indeed something magical in how Tadashi’s hands, projected on the screen, showed fantastic geometry of Miura ori (a self-collapsing map being folded with only 1 degree of freedom). A true wit, with observations like “In biology cells divide by multiplying”, Tadashi filled his talks with jokes. The audience was to look differently at theories of Galois, Gauss, and Poisson, laugh about Landau preaching to his ‘disciples’ with donkey ears, Amazon River, elephants, and Leonardo Da Vinci, and learn the theory of elasticity in 45 seconds. The magic Tadashi showed is robust, you can later show it off to friends and family. So, “take a sheet of paper…” (Tadashi Tokieda)

To watch the videos, please visit the SCGP video portal.

July 2016

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Interview by Maria Shtilmark

**Was the farewell tea party a true farewell? **

It was a mock farewell, as I am staying on for three more years as a John S. Toll Professor. This Fall I will be running the Graduate Student Practicum, which involves all graduate students who are teaching for the first time. We do classroom exercises; I visit their classes and we “debrief” afterwards; another class gets taped and we review the tape together.

The main thing I am going to miss about teaching is contact with young people. Stony Brook has always had an impressive mix of undergraduates: some very well-prepared ones who barely need any guidance, and some, often the first in their families to attempt college, for whom Stony Brook is a first big step on the way to a successful life. Stony Brook students are a very good bunch and I’ve liked them all along. The graduate students are excellent, of course. Over the years I’ve been lucky to work with some very talented individuals. (M.S.- And, may we add, some very good professors!)

**Tony Phillips:** We have a great faculty, and that’s another plus. Dennis Sullivan told me once that one of the privileges of being a mathematician is being in contact with really extraordinary people, and if Dennis, who himself is quite extraordinary, thinks of it that way… We’ve worked with people like Thurston, Gromov, Milnor—and these luminaries, extraordinary human beings, were our friends!

**Jeff Cheeger (quoted by Dennis Sullivan):** “It’s somewhat hard to recreate the atmosphere of those crazy times with Jim as the ringleader. There was a new wild party every week” (at Jim’s house, or Tony’s house, or Jeff’s house) and Jeff remembers staying up until the early hours of the morning with Tony and everyone, dancing, and Tony being responsible for bringing Gromov to Stony Brook, after Tony had met him in Russia. “Tony recounted how Vladimir Rokhlin, Gromov’s advisor, had told him that Misha was the kind of person who would have been exceptional, no matter what he had chosen to do. After a moment’s thought, Tony added, “Well maybe not as a sports announcer.” (Misha Gromov speaks extremely fast and at times incomprehensively – Dennis Sullivan.)

**Tony Phillips:** We were a small department of 20–25 people, and we were young: fifteen of us were in our 20s and early 30s—you can’t recreate that! Jim Simons was the chair, tasked with building up a world-class Mathematics department.

The University was expanding, and expanding into mathematics. John Toll, the Stony Brook President, trusted Jim to make high quality hires. Jim and I arrived here in 1968; until then it had been mostly a service department, but there was a graduate program in place, and Bill Barcus and his colleagues had maintained rigorous standards. So Jim had a solid foundation to build on.

The transition from the old to the new was quite smooth, and Jim was very good at this. It was almost like an industry here, hiring mathematicians. We had dinners and parties here almost every week; it was a lot of fun. Many up-and-coming mathematicians came through, and some of them stayed. Jim ran up an incredible bill at the restaurant—he kept charging meals, but it turned out there was no account to charge them to; Ron Douglas, the next chair, for the first couple of years had to work through the accumulated local debt Jim had run up… It wasn’t lavish spending, just nice dinners at the “Elks” in Port Jefferson. (An old-fashioned American restaurant, good fish. Where the Starbucks is now). That was the adolescence of the department. Happy times, and a lot of important work got done: when Cheeger and Gromoll proved their wonderful theorem, that every positively curved complete Riemannian manifold is fibered over an embedded “soul,” we started calling them “The Soul Brothers.” It was an exciting time.

The Stony Brook department has kept this quality of **openness and lack of pretention** since those days. Many of us have worked at maintaining that spirit, and I think-I hope-it’s now in the DNA of the department. If you ask people what it’s like at Stony Brook, they’ll probably tell you it’s a very friendly department, very open, no prima donnas. I am very grateful for that.

The other thing that was very important to me was the contact between the **Mathematics and the Physics departments**, which goes way back. There is the celebrated encounter between C. N. Yang and Jim Simons, which led to the discovery that what physicists called “gauge field,” was in fact identical to something mathematicians had been studying for 40 years, under the name of “connection in a principal fibre bundle.” The insight led to an enormous development in modern physics and also, very significantly, in modern mathematics. In 1978 Jim commissioned me to write a propaganda piece for “Research,” a SUNY Central publication, about the differential geometry group at Stony Brook. He said: “Of course, you will have to talk about the Aharonov-Bohm effect.” I’d never heard of it, but I read up and realized it was an example of really non-trivial topology and geometry manifesting itself in a physics experiment. I also remembered Yang coming down to tea one afternoon, very excited, exclaiming “Fibre bundles exist!”—he was talking about a neutron-precession experiment that had just been performed. I wrote about both these experiments (with my friend Herb Bernstein) in Scientific American, and ended up working in that field for 5 or 6 years; that public-relations assignment from Jim turned out to be very valuable for me.

**Mikhail Lyubich:** Just to elaborate on how Tony brought Gromov to Stony Brook I would like to quote some very nice recollections by Tony and Gromov. So, they met in Leningrad, Tony came back with this idea to bring Gromov and wrote him his famous coded letter that read: “an involutive gromomorphism G: SU ➞ US of admissible type T transforms MG ➞ SB” This cryptic message passed the Soviet censors, however, Misha himself didn’t understand it at first… Anyway, in the end it worked!

*(Quoted from “A Few Recollections” by Mikhail Gromov and “The Gromomorphism SU➞US” by Tony Phillips. The Abel Prize 2008-2012, edited by Helge Holden and Ragni Piene. Springer 2009. **Pg. 134 and 148-149 -M.S.)*

**Tony Phillips:** When I was in Russia on the Inter-Academy exchange program in 1969, my advisor Sergei Novikov told me I had to go to Leningrad to meet this young mathematician Gromov. He arranged my trip; I gave a talk, and spoke with everybody: Yasha Eliashberg, who was a student then, V.A. Rokhlin, the great topologist and Misha’s advisor. I’d studied some Russian, but it was even feebler than it is now. I couldn’t converse, but everyone knew some other language: Eliashberg knew French, Rokhlin knew German, and Misha knew some kind of English. In the evening I was invited to Misha’s apartment, where of course there was vodka. At one point I didn’t know what language I was speaking, and that’s the only time this has ever happened to me! (They say that Russians like to get foreigners drunk just to see what they are really like).

**Blaine Lawson, Jr.:** Tony made a huge difference in my life. I met him in 1971 when I came here to visit for the spring. We were both doing foliations at that time, and we went to a conference over at Oberwohlfach. We were standing around at some point and a fellow came over to me and asked: “Where is this guy from? He speaks French perfectly but I can’t figure out the accent.” I said: “New York City.”

**John Morgan:** Upper East Side!

**Tell us about your role as Mathematics Executive Officer at the Simons Center.**

In the very beginning of the Simons Center I had that title and was on the board. I was involved in all discussions about what was the best way to have a research center, about the layout of the building, volume of public and private spaces, should there be a cafeteria or not (I was against the cafeteria, as a matter of fact—I thought it would be a distraction; of course I love it now).

It was really interesting to work with the architects as they were planning it. For example, the idea of having the ground plan slightly curved came in about halfway through the project. Initially it was going to be rectangular. We all could see right away that it made the whole building so much more interesting. I am proud we have such a fantastic place on campus. I really appreciate good architecture and every time I walk through the Center I think: This place is so beautiful! It’s so well designed and so pleasant to be in! (We are certainly with you there! – M.S.)

**Jeff Cheeger (quoted by Dennis Sullivan):** “When Tony’s tenure was being decided Milnor’s letter made the positive decision clear, which Jim paraphrased as “Quality and Taste.” These attributes served Tony well as Chairman of the Art Committee for the Simons Center.”

**Tony Phillips:** Personally, I am proud of my work with Nina Douglas and Christian White on the **Iconic Wall** (and the brochure for the wall, which was a big deal and a lot of work) and I’m proud of the **Penrose pavement**. The wall wasn’t my idea, but the pavement was. Initially I wanted it for the ground floor, but the architects suggested putting it in the outdoor area where it is now. It worked out extremely well. Carmen Menocal, one of the architects, really went with the idea and adapted it brilliantly, getting the pattern to match the shape of the courtyard and even finding a way to put the trees in conforming to the pattern—it’s perfect, I’m very, very happy with it! I’ve also been very pleased to watch the development of the Simons Center Arts Program. Recently, for example, there was a great show of work by Manfred Mohr, Pioneer of Algorithmic Art. Some of his creations were done on analog printers at Brookhaven, before there was such a thing as computer graphics. I was very grateful to get acquainted with this guy.

**Mikhail Lyubich:** We are standing in Tony’s Gallery, as half of these posters in Math Common Room were produced by Tony!

**Tony Phillips:** I made some of them, I made the Milnor poster. Here is a sketch for it, made with a primitive color copier in 1991.

**In the cultural mathematics section of the list of your works the words “labyrinths and mazes” are mentioned at least 6 times.**

My interest in labyrinths came about through serendipity. I had a friend Jean-Louis Bourgeois, Louise Bourgeois’s son. Jean-Louis styled himself a labyrinthologist. He taught me about a traditional labyrinth kids draw as a game in India, which we know as the Cretan maze. Later, visiting friends in Tucson, I noticed that a basket they had on the wall, woven by the local Indians, had the same maze pattern that Jean-Pierre had told me about. How did this thing get from Crete to Arizona? The next year at my parents’, I was going through a Sotheby’s catalog (my father was working for them then). It was a sale of Judaica. There was a picture from a medieval manuscript, a Sefer Haftorot, representing the 7 walls of Jericho as labyrinth. It was very much like the Cretan, but different! Being a mathematician, I said to myself: one can be one, but if there are two, there’s got to be a lot!

I started looking at their mathematical properties and figured out how you could generate hundreds of them. Each of these labyrinths has a depth, say N, and the question naturally arises, how many different labyrinths are there of depth N? Let’s call it that number M(N). There is no way to compute this number from N: you have to construct them all and count how many you have. But M(N) increases exponentially with N. I programmed a computer to calculate it up to M(22) = 73 424 650. The next even number would have taken me 16 times longer, etc. But it turned out that the same function had just come up in theoretical physics, counting something called rainbow diagrams; physicists used better methods to push the calculation up to M(48) = 794 337 831 754 564 188 184. This was a nice example of mathematics in the air, how it crystallizes and these amazing coincidences happen (there was a third simultaneous calculation of M(N) in a still different context, in Warren Smith’s Princeton thesis). It’s like a Möbius strip – if you see a picture of one you know it has to be late 19th century, or more recent. Nobody thought of a Möbius strip before, in some sense it didn’t exist; the idea sort of blossomed.

The main reference on labyrinths is the 1988 book by Hermann Kern. It’s encyclopedic, except that he didn’t know about the stone labyrinths on islands of the Solovki Archipelago in the White Sea. There is an obvious continuity between that ancient tradition and similar constructions in Finland and Sweden (on the other side of the peninsula), with some unexplained differences. Now that I am retired maybe I can get out there to check.

**Marie-Louise Michelsohn:** “Tony is my best friend in this department and outside of it! I met Tony in 1977 at IHES. It was a wonderful year, and Tony recruited Blaine and me, and we are very grateful. I am very grateful for all the interactions!”

**Your co-authorship with Moira Chas resulted in 3 papers, one, bearing an intriguing title Counting almost simple curves on the “pair of pants”, in preparation.**

It’s been something new for me, and hard, but a lot of fun. Moira has been studying curves on surfaces (the “pair of pants” is a nickname for the thrice-punctured sphere) and has used the computer to discover very interesting patterns in the relation between length and self-intersection number; we have been trying to figure out Why? In a way it’s easier than some kind of mathematics, where the level of abstraction can be very high. Here everything is totally concrete, but the patterns are mysterious. For example, we can prove that a certain phenomenon cuts in for sufficiently long curves, but the computer data give an exact starting point. Trying to improve our result leads to more and more complications. It’s amazingly intricate, but we’re getting there.

**Jack Milnor:** I’ve probably known Tony longer than anyone, and it’s been a great pleasure all these years. Congratulations to endurance – lasting 50 years at Stony Brook!

**In a recent interview Martin Hairer spoke about his interest in sound, and his love for Pink Floyd. In your case it is Bach and bird songs.**

Martin wrote an excellent sound-processing software package called Amadeus, which I’ve been using for the last 15 years; when I read that Martin Hairer had won the Fields Medal I thought this must be the son of the person who wrote the software, as it was so long ago—but it was the same guy; he did it when he was in high school! I use his software to edit bird song recordings. It makes beautiful sonograms and is all-around perfect for the job. It was a great pleasure to meet him at his Simons Center workshop.

I believe that the connection between math and sound hasn’t been as well explored as the visual connections. Take M.C.Escher, and all the energy that has gone into making intricate mathematical graphic designs, especially with fractals. It’s like candy – you can’t stop eating it, and yet… I recently came across a website with a “Mandelbrot zoom”—you start looking, and you watch it unfold further and further; it keeps going, and going, and going… This incredible structure is there, but what does it mean?

One place where I found “**sonification**” to be useful is in thinking about tides. Before I moved out here I hadn’t thought about them all. But living on Strong’s Neck I would drive past Little Bay every morning around the same time; some days it was full, and some days it was empty. I discovered tide tables, and started wondering how they were generated. They turn out to be the product of wonderful 19th century physics and mathematics, much of it due to Kelvin. The tides are driven by gravity, and depend on the relative position of the Sun, the Moon and the Earth, and on the rotation of the Earth, so all the forces are completely understood. But at any given port, the exact pattern depends on the local undersea topography, and the way the water there is connected to other bodies of water, in a totally mathematically un-analyzable way. Also, because the various astronomical periods involved (year, month, day, etc.) are not rationally related, the pattern never repeats exactly. But Kelvin and company figured out how to take a month’s worth of tide readings at a port, and use Fourier analysis with small integer combinations of the astronomical frequencies to predict the height of that tide at that port at any time in the future. They even built amazing machines to sum up the Fourier series and produce the data for the tide tables. (Part of the joy of being a mathematician is in coming across these amazing mathematical patterns). So, sonification: the sequence of high and low tide points can be interpreted as a 4-part musical score; each port has its own distinctive tune. For a conference in Venice I recently commissioned Levi Lorenzo, one of our Music graduate students, to score a couple of ports: Venice (marimba) and Ancona (wind quartet). He did a beautiful job.

**Dennis Sullivan:** Quality, culture, and taste! A true gentleman. Now, what’s a true gentleman? There is an essay by Cardinal Newman by which a gentleman is someone “who reduces conflict without reducing content.” True gentleman, Tony Phillips!

**Tony Phillips:** *A toast to Stony Brook! Party on!*

June 2016

For Tony Phillips’s talk on theorem selection for the Iconic Wall (minutes 12-30) please, go to scgp.stonybrook.edu/video_portal/video.php?id=1889

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