Mathematics is the Poetry of Science

0: Foreword, Elisa Brune

1: Mathematics, Science, and Poetry

2: Constraints and Creativity

3: Inspiration

4: Making Connections

5: A Portable Universe

6: The Form of Words

7: Visionaries

8: Poincaré and the Omnibus

9: Ping-Pong

10: Ode to Imperfection

11: Appendix: Henri Poincaré on Mathematical Discovery

CÉDRIC VILLANI, a Fields Medalist in 2010, is mathematician, director of the Henri Poincaré Institute (IHP) and professor at the University of Lyon. After entering the École Normale Supérieure of Paris, he was glad to find a place of inter-disciplinary scholarship and to discover the intense cultural life of Paris. When writing his thesis, he summarized the influences of Pierre-Louis Lions, Yann Brenier, Eric Carlen, Michel Ledoux; he later found his chosen field in the fusion between analysis, probability and geometry. He worked in analysis when at heart, he was initially an algebraist; his choice of a thesis on the theory of Boltzmann’s equation, when he hardly had the temperament of a physicist; his first collaborations with Italian and German scientists, exploiting ideas put forward during travels or conferences; he shifted towards optimal transport after a series of coincidences and a beautiful talk given by Craig Evans in Paris; then his shift towards geometry at an impromptu meeting with John Lott in Berkeley; and finally his research on Landau damping. Most of his work have been done in collaboration with French, Italian, German, Austrian, Spanish, Swedish, American scientists. His main collaborators were Laurent Desvillettes, Clément Mouhot, Felix Otto, John Lott. 

He is convinced that teaching is inseparable from research, he has always worked as a university lecturer, and has never applied for a full-time research position. He invested considerable effort in writing reference books and course notes—on optimal transport, measure theory, and kinetic equations. He was formerly the president of the students’ association he belonged to, he is now director of the Henri Poincaré Institute, which each year welcomes hundreds of invited scientists from all fields of mathematics and theoretical physics, and from all continents. Outside of mathematics, he spent an equal amount of effort in communicating with society as a whole: forums, radio and television programs, public talks, etc. His first book for a general public, Living Theorem, was published in 2012 (in a literary collection), wherein he described the daily life of a mathematician in the style of a logbook mixing various forms and influences. He is also the president of an association that combines art and technology aimed at the integration of disabled youth, the administrator of a philanthropic initiative in the fieldof education, the president of a scientific council of a research institute located in Senegal, and the vice-president of an association promoting a federal Europe in the public debate.