My four grandparents were born very poor into large peasant families. Against all odds they managed to give my parents access to higher education. My father became a mathematics professor and it was he who sparked my interest in science.
I was born with congenital defective retinas and lost one eye at age five. When I was fifteen, I suffered from several consecutive retinal detachments in the remaining eye, causing me to miss school for half a year. Fearing that I would shortly become blind, I focused my energy on studying. I learned that this focus and hard work could make me competent in mathematics and physics. I did not attend an elite university, but the local university in Lyon close to where my parents lived. My university years were very happy and I built a solid foundation in mathematics.
My great luck is that the National Centre of Scientific Research offered me, in 1974, a research position, even though I had not yet done any research. This was uncommon, and the last year that such positions were offered. I have treasured this position all my life as it allowed me to work without any constraint on the topics of my liking.
I started doing research in the Functional Analysis group of Professor Choquet in Paris, where I completed my PhD. Professor Choquet’s mathematics were supremely elegant and seemed effortless. Unfortunately, this is not the style I was born for, but several of my later contributions would not have been possible if I had not been inspired by his vision of mathematics. My interests shifted over the years but I belonged to this group for my entire career. Paris is a fantastic place to be a mathematician. Many mathematical stars work there and there are so many prominent visitors. I benefitted immensely from interaction with these visitors, and with my colleagues, at the numerous conferences I attended, but overall, I had few collaborators.
Thanks to mathematics, I met a wonderful woman who highly valued academic achievement. She has supported my work in every conceivable way, as well as bringing me so much personal happiness.
I developed an early interest in measure theory. While in the seventies this theory was well past its prime, it helped me learn to look at things in an abstract way, which served me well later in my career. It also triggered my interest in Banach Spaces, although it was clear that I could not have the same impact as the leaders in the field. The arrival of Gilles Pisier in our group, in 1983, was a turning point for me. Gilles shared his private notes on Probability in Banach Spaces, an area that I could then learn and where I eventually became successful. He also directed me to the problem of characterizing the continuity of Gaussian processes, on which X Fernique had made determining advances, and which I was able to solve in 1985. This started my work on upper and lower bounds of stochastic processes. Pisier’s influence changed the very nature of my work, which became far more quantitative.
I was also greatly influenced by Vitali Milman, who was most energetically expounding the concept of concentration of measure. I did not understand the depth of this concept at first, but it directed me to the discovery of several “concentration inequalities’’ that have since proved useful. The most important of these required taking a convex hull, and certainly this was easier to discover having been a student of Gustave Choquet.
I started mathematics with the modest goal of making a living out of it and began by working on small problems in somewhat exotic areas. My interests later shifted towards more central areas of mathematics, but I always worked on the problems I enjoyed the most, following my own preference. The path of discovery in mathematics can be very tortuous. The discovery of new classes of concentration inequalities stemmed from considering a problem of seemingly secondary interest. Many times, what I had learned by writing a paper of trifling importance proved a key step in a far more substantial theorem.
Rather late in life, I attacked a well-established problem in theoretical physics. The physicists were studying purely mathematical objects (called spin glasses) using methods which do not belong to mathematics. It was an all-consuming eight-year effort to prove that mathematics could bring a far more solid solution to this problem.
In later years, I have tried to write textbooks to communicate the experience of a lifetime in probability theory and have not shied away from reworking them over and over.
The Shaw Foundation recognition is an honour I could never have dreamed of. It will allow me to set up a far more modest mathematical prize recognizing the achievements of young researchers in the areas to which I have devoted my life.
25 September 2019 Hong Kong
