Birth of a Theorem: A Mathematical Adventure by Cédric Villani

Author:Cédric Villani [Villani, Cédric]
Language: eng
Format: epub
Tags: Non-Fiction, Science, Biography
ISBN: 9780374710231
Google: iP-cBAAAQBAJ
Amazon: 0865477671
Barnesnoble: 0865477671
Goodreads: 23257776
Publisher: Farrar, Straus and Giroux
Published: 2012-01-01T00:00:00+00:00

Princeton

April 1, 2009

The first day of April—the day of fishes and fools!

This afternoon watched an episode of Lady Oscar with Claire and the children. Marie-Antoinette, Axel de Fersen, and Oscar de Jarjayes spinning round in a whirl of fine phrases and noble sentiments amid the lengthening shadows of the French Revolution.

And this evening, before going to sleep, we watched a YouTube video of Gribouille singing “Le Marin et la Rose.” Simply marvelous! There’s some great stuff on the Internet.

During the past week I’ve learned so much from lecturing on Landau damping.

After my first talk, once his irritation had subsided, Elliott shared some valuable insights into the conceptual difficulties of the periodic Coulomb model.

At the second talk I laid out the main physical idea of the proof. Elliott very much appreciated the mixture of mathematics and physics; he seemed not only engaged but genuinely supportive.

By the time of the third talk I’d come up with an answer to Hammett’s objection, and I was able to formulate almost optimal assumptions regarding the stability condition and perturbation length.

I’d taken a risk, presenting completely new results that were still only half-baked, but the gamble paid off: their criticisms enabled me to make much faster progress than I could have otherwise! Once again I had to put myself in a vulnerable position in order to become stronger.

And … the connection with KAM finally became clear to me!

The ability to detect hidden connections between different areas of mathematics is what has made my reputation. These connections are invaluable! It’s a bit like a game of Ping-Pong: every discovery you make on one side helps you discover something new on the other. The connections make it possible to see more of the landscape on both sides.

My first important result, with the Italian mathematician Giuseppe Toscani, came in 1997, when I was twenty-four years old: the unsuspected link between Boltzmann entropy production, the Fokker–Planck equation, and entropy production for plasmas.

The next one came eighteen months later, with my German coauthor Felix Otto: the hidden link between the logarithmic Sobolev inequality and Talagrand’s concentration inequality. Two other proofs have been proposed in the years since.… This is how I got started exploring the field of optimal transport. Thanks to our paper I was invited to give a graduate-level course at Georgia Tech, which in turn gave birth to my first book.

During my thesis defense in 1998, Yves Meyer marveled at the “miraculous” relations I had brought to light. “Twenty years ago people would have laughed at your work. No one believed in miracles then!” But I believe in miracles—and I shall uncover more of them.

In my thesis I recognized four spiritual fathers: my thesis director, Pierre-Louis Lions; my tutor, Yann Brenier; and Eric Carlen and Michel Ledoux, whose works opened up the fascinating world of inequalities to me. In addition to the joint influence of these four teachers, I incorporated other elements and created my own mathematical style, which then evolved—as it pleased chance to bring me into contact with new friends and new ideas.

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