The Extraordinary Theorems of John Nash - with Cédric Villani

Bright. Nash hated every part of the movie. But interestingly, his wife, Alicia, found it charming to be played on screen by Hollywood beauty Jennifer Connelly. Now it was still a problem for mathematicians, you know, that Nash's genius had been recognized in economics, but not for his really beautiful mathematical work related to geometry and analysis. And little by little this public recognition came. 2009 was a big splash, when Nash's ideas led Camillo De Lellis and Laszlo Szekelyhidi, brilliant young mathematicians from Italy and Hungary, respectively, to construct some impossible solutions to Euler's equation: crazy solutions. Imagine a fluid that would initially be at rest, then start shaking like crazy, and then be at rest again, with no force acting on it.

Something that made us rethink the definition of what a solution to a fluid equation is. In 2012, I described my emotional encounter with Nash in "The Birth of a Theorem." This was like an autobiographical book, or at least it talked about what it's like to prove a theorem. All the ups and downs, difficulties, mistakes, trips, meeting people... you name it. And a chapter is dedicated to my meeting with Nash in Princeton, at the T. And I was, you know, he meant a lot to me. I was so, how can I put it, impressed that I didn't even dare to talk to him at the first meeting.

And in 2015, Nash was finally awarded the Abel Prize. The Abel Prize is, along with the Fields Medal, undoubtedly the most prestigious award. The Abel Prize is certainly more difficult to obtain than the Fields Medal. The Abel Prize is younger... it started about 15 years ago. The Abel Prize is usually awarded to old living legends in their 70s who made contributions that everyone knows and surprises. And I was part of the Abel Prize committee, in those days. It was also very emotional for me, being on that committee the person scientifically closest to Nash, you know, the one in charge of defending Nash's work.

I will not say more about the discussions, because, of course, it is secret. But the discussions we had about this were very interesting. On May 19, 2015, in Oslo, the Abel Prize was jointly awarded to John Nash and Louis Nirenberg (you know, these guys have a long history together) for surprising and similar contributions to the theory of nonlinear partial differential equations and its Applications to geometric analysis. Very emotional moment. You also have to imagine the ceremony: the king of Norway was there, Nash gave a speech, etc. There was a public speech by Nash, in which Nash recalled some of his earliest work, some other work that he discussed with Einstein, related to general relativity.

I had the honor of being its president. In fact, this was our fourth meeting. And for the entire community, everyone thought, Nash finally received this reward. And it was quite due. That was the mood... after this award, at least... you'll be able to relax... recognition, money, whatever. Not so. On May 23, 2015, upon returning from the ceremony, on the way to Princeton, he died, along with his wife, in a taxi accident. We later caught up with Nirenberg again, trying to make sense of it, whatever it was. Nirenberg Nash once did something like anyone else. Alien. He always gives these proofs that no one can understand at first.

He himself was incapable of explaining them; He always saw things that people think are impossible. He wins the Nobel Prize for his doctoral work, after being driven mad by an illness from which he is never supposed to recover. And, in the end, he dies like no one else. Anyway, this is tragic. But the good thing about this, of course, are the methods. And many mathematicians feel that Nash is part of his family, in the sense that he contributed so many ideas and techniques. If I think about my own work, I can clearly see the relationships to Nash's work.

The problems of the statistical mechanics of taste, the taste for entropy, the key role of regularity, which I discovered with my collaborators on similar problems. We, for example, in the problem that was one of my (our) most notable papers, on the behavior of plasmas, discovered how critical the role of regularity was, in a way that had not been understood before by physicists or mathematicians and this. And, like Nash, I admire and enjoy his talent in this sharp, massive attack on a given simple problem, in a sense, with simple, well-calibrated tools, always trying to discover new connections.

This idea, that idea, let's put it together, and so on. And so, in a way, Nash's legacy lives on. And I will conclude with this. Putting, showing, just this bibliography, recommending to you, by the way, the book Beautiful Mind by Nasar-- well, especially chapters 20, 30, 31, in which you will find the behind-the-scenes stories of mathematical achievements- - which, for us, is even much more important than the mental in history. Nash wrote four important articles, you know? That's nothing compared to a big list of articles. But, of these four articles, three would probably, in retrospect, have deserved the Fields Medal.

On my website, on my blog, dated December 26, 2015, you will also find, in French, a short article--or not so brief-- in memoriam John Nash, entitled "Breve rencontre"-- "Brief Encounter ". ". And with this I will conclude this speech. Thank you.