Five months at IAS, two-hundred-fifty pages, and a Fields Medal
Cédric Villani, Member in the School of Mathematics in the spring of 2009 and currently Professor at Université Lyon I and Director of the Institut Henri Poincaré, has called his stay at the Institute one of his most productive periods, during which more than 250 pages were written. In his Member report to then-Director Peter Goddard at the end of his stay, Villani wrote of his collaboration with Clément Mouhot from Paris, “Writing up the paper on Landau damping was one of the most intense experiences of my professional life: for three months in a row, we kept unlocking seemingly untractable obstacles on a weekly basis. Our 180-page-long paper solves a fifty-year-old open problem.” A year after his IAS visit, Villani was awarded the 2010 Fields Medal, in part for the work that he did at the Institute on his proof of nonlinear Landau damping. Following are excerpts from Birth of a Theorem, translated by Malcom DeBevoise (Farrar, Straus and Giroux, 2015), originally published in 2012 as Théorème Vivant (Éditions Grasset & Fasquelle), which describe his fervent, halting, and very human experience in trying to obtain the proof.
Princeton, January 1, 2009
Finally, the Institute for Advanced Study—the IAS, as everyone calls it—comes into view. A little like a castle rising up in the middle of a forest. We had to go around a large golf course in order to find it. . . .
It is here that Einstein spent the last twenty years of his life. True, by the time he came to America he was no longer the dashing young man who had revolutionized physics in 1905. Nevertheless, his influence on this place was deep and long-lasting, more so even than that of John von Neumann, Kurt Gödel, Hermann Weyl, Robert Oppenheimer, Ernst Kantorowicz, or John Nash—great thinkers all, whose very names send a shiver down the spine.