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C├ędric Villani

Fields Medal

2010

Professor Cédric Villani is a recipient of the 2010 Fields Medal for his contributions to kinetic equations, specifically in the studies of stability, and is currently a politician in the French parliament. 

In 2009, Prof Villani together with his student Clément Mouhot proved that something called Landau damping still holds in nonlinear perturbative environments. It explains, for example, why if you slightly disturb a plasma that is in equilibrium, the resulting electric field will spontaneously vanish, and the system returns to a stable state.

Solving such a problem would keep most mathematicians up all night. However, Prof Vilani discovered he could solve it in his sleep. Stumped by a gap in the hundred-page proof, he resigned himself to defeat and decided to go to bed at 4 in the morning. However, when he woke up a few hours later, he heard a voice in his head telling him the way forward: "Take the second term to the other side, Fourier transform and invert in L2." 

It is jargon that only a mathematician might understand, but Prof Villani has made his life story accessible with the publication of Théorème Vivant, a memoir of the work that led up to his Fields Medal. It conveys to the layperson what it means to be a top-level mathematician, recounting the various conversations and collaborations he had with other mathematicians, replete with stories of failure, and then eventual success. The title literally translates to "Living Theorem", and it was chosen by Prof Villani to emphasise the dynamic, living nature of mathematics. Since its publication, the French edition has sold more than 100,000 copies.

This enthusiasm to influence the public to what science can do for society has extended to his professional life.  He was director of the Institut Henri Poincaré in Paris from 2009 to 2017, where he initiated the Maison Poincaré museum (due to open in 2022), with more than 900 m² of exhibition space dedicated to mathematics and its applications. 

In 2017 he ran for public office and won, becoming an M.P. for Essonne, near Paris. He believes “if you wait for politics to solve your problems, then you will be part of the problem”. He also chairs the French Parliamentary Office for the Evaluation of Scientific and Technological Choices (OPECST), where he argues that public policy has a pressing need for “empathy and science”.