“Elegance is not well-defined in mathematics, but when somebody comes with a beautiful proof, everybody recognizes it; this is like music!”
Associate Professor of Mathematics Pierre Tarrès says he works well while he walks. One of his favorite places to walk is on the Bund and toward the Fairmont Peace Hotel, where he can be surrounded by its rich history, architecture, and views of Shanghai. Tarrès joined the NYU Shanghai faculty as a Visiting Professor in 2016. Moved by the community of students here, students who he says never hesitate to ask questions and possess a “wonderful willingness to learn,” he decided to stay for good, earning tenure in 2018. Tarrès was previously Associate Professor at Oxford and taught at Ecole Normale Supérieure. He says teaching is a craft: “the art of conveying difficult notions as clearly as possible.”
Recently, Professor Tarrès returned to the Fairmont Peace Hotel for the following interview with The Gazette.
Was there a significant moment that made you decide you wanted to become a mathematician?
My father is a (now retired) mathematician, which should have helped, but in my childhood and early teenage years, I was more interested in music. My interest in math was triggered at age 14, by a teacher in my junior year of high school. I was in a boarding school, where I started to discover the beauty of these questions by spending full weekends on them!
Mathematics is a language that many people feel is boring to learn at first. You have to master that language before you can see the artistic side of it. Once you have made that effort, it is very creative, and of course also useful in many fields: physics, biology, economics, data science.
Have you developed any habits towards your research and study of math?
I try to think of the mathematical problems I care about as soon as I wake up. This is not always immediate because of other duties, but I safeguard it as much as possible, since the early morning is one precious moment of creativity. In general, there are many questions I would like to understand better, so I spend some time on them as soon as possible. It does not mean I find a solution. Most of the time, I find I have to refine my approach, or use another one.
One of my specificities, compared to other mathematicians, is that I don’t write very much. I don’t write a lot of papers or do many computations before I solve a problem. I spend a lot of time thinking about the best strategy to tackle a problem, and when I am convinced that I’ve found it, I begin making corresponding computations. Sometimes it does not work, and I need to spend more time thinking before continuing with other computations. I can spend hours and even days immersed in thinking about problems; it challenges the banalities of daily life.
Something John von Neumann said that completely resonated with me: “If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.”
Tell us about winning the Philip Leverhulme Prizes back in 2006 and the Prix des Annales de l'IHP in 2009. How did that recognition affect the trajectory of your career?
Those awards meant my research gained international recognition, and they were certainly very good news. But, the recognition that struck me the most came mainly from the positions to which I was hired, such as the French National Center for Scientific Research (CNRS), the University of Oxford, or the tenure appointment here, which is decided by the Courant Institute in New York—probably the most prestigious school of mathematics in the world. I will always remember the day that I learned I was hired for the CNRS, and the inspiring email Wendelin Werner (who was in the committee) sent me on that occasion, with some advice on my future career. In particular he wrote that I should allow myself some time (not too much though!) to decide which problems I found interesting before trying to solve them. That choice is always subtle and subjective.
You've made significant achievements in Stochastic Analysis and self-interacting random processes, particularly reinforced random walks. Can you explain what this means to those of us who stopped studying math in high school?
The relationship between self-interaction and learning is fascinating. If you play a game and reinforce the strategies that have more payoff, you have a good chance to play it optimally in the long run—if you don’t reinforce too fast. But if you play with other people, things start to get more complex. This is also applicable to biology, statistical physics, dynamical systems, ad some of my work aims at developing those interactions. I feel I won’t have enough of a lifetime to understand it.
What do you hope students will take away from your classes?
I’m known among my students to ask difficult questions.The one thing I would like them to take away is the challenge that some problems will not be solvable in under 20 minutes. They could spend a few hours, or even a few days to try to solve a problem or understand a difficult notion, and then finally come up with a solution.The capacity to answer difficult questions is a unique skill and will be useful to them for any life they have later on.
Are there any upcoming research collaborations you are looking forward to?
One of my goals is to pursue work with my colleauges, in particular Christophe Sabot, in further developing the link we have started to unveil between self-interacting random walks and statistical physics. Another aim is to understand better the connection between self-interaction and learning, particularly in the multiparticle context.
This interview has been edited for clarity and length.
See this story in the NYU Shanghai magazine here.