Cédric Villani

Young Leader, Fields Medal-winning mathematician talks about new book, math education in France and worldwide

Cedric Villani2012 Cédric Villani, French mathematician and recipient of the 2010 Fields Medal for his work on differential equations, joined the French-American Foundation upon a recent trip to New York to promote his book Birth of a Theorem (Théorème Vivant), recently last week in English. In addition to sharing insights on his tale of how his prize-winning theorem came to be, Villani shared his insights on math and science education in France, the United States, and worldwide and about his time as a Young Leader.

French mathematician Cédric Villani is Director of the Institut Henri Poincaré and 2010 recipient of the Fields Medal. His book, Birth of a Theorem: A Mathematical Adventure (Farrar, Straus and Giroux, 2015), was originally published as Théorème vivant (Grasset, 2012) in France.

Villani was born in 1973 in France and studied mathematics at the École Normale Supérieure in Paris, from 1992 to 1996 and spent four more years as assistant professor there.

In 1998, Villani defended his PhD on the mathematical theory of the Boltzmann equation, building on strong influences from his advisor Pierre-Louis Lions (Paris, France) and fellow mathematicians Yann Brenier (Nice, France), Eric Carlen (Rutgers, USA) and Michel Ledoux (Toulouse, France).

From 2000 to 2010, Villani was professor at the École Normale Supérieure de Lyon, and now at the Université de Lyon. He has occupied visiting professor positions in Atlanta, Berkeley and Princeton. Since 2009, Villani has served as director of the Institut Henri Poincaré in Paris; this 80-year old national institute, dedicated to welcoming visiting researchers, is at the heart of french mathematics.

Villani has received several national and international prizes for my research, in particular the Fields Medal, awarded at the 2010 International Congress of Mathematicians in Hyderabad (India), by the President of India. Since receiving the prestigious award, Villani has served as a spokesperson for the french mathematical community in media and political circles.

Villani's main research interests are in kinetic theory (Boltzmann and Vlasov equations and their variants), and optimal transport and its applications, a field in which he has written the two reference books: Topics in Optimal Transportation (2003); Optimal Transport, old and new (2008). More generally, Villani is fond of subjects which combine several (if not all) of the following themes: evolution partial differential equations, fluid mechanics, statistical mechanics, probability theory, smooth and nonsmooth “metric” Riemannian geometry, and functional inequalities with geometric content.

Villani belongs to the editorial boards of Inventiones Mathematicae, the Journal of Functional Analysis (JFA), the Journal of Mathematical Physics (JMP) and the *Journal of Statistical Physics (JSP). He also serves as an administrator for several associations, in particular the pro-European Think-Tank EuropaNova. He is President of the Scientific Board of the panafrican institute AIMS-Senegal.

Read full bioHide bio

How did your most recent book, Birth of a Theorem (Théorème Vivant) come about? What did you want tell in this book, which goes beyond the mathematical aspect of your work but about your experience as a mathematician?

You compare math to a desert. In the grander spectrum of studies that we go through, math and science are often separated from the humanities and other subjects, where interdisciplinary approaches are more encouraged. Your book tells the story of a mathematical process, undoubtedly involving interplay between your work and others', as well as the historical look at mathematicians long deceased whose work has impacted yours. How do you apply storytelling to this field which is usually associated with numbers, facts, and theories?

In addition to publishing Birth of a Theorem, you were recently involved with the documentary Comment J’ai Detesté les Maths (How I Came to Hate Math). It seems that you are making an effort to make math and science more accessible. Do you feel that there is a general tendency for people to be afraid of or intimidated by math and science? Why is that, and what can we do to change that?

You mentioned earlier that mathematicians are among the most needed professionals in the global professional workforce. How is science and math education addressing this in France and the United States? How would you compare the two nations?

Usually this conversation focuses on the emergence in Asia, where we often talk about a much stronger investment in and general devotion to the sciences? How do France and the United States fare in the changing globalized realm of education?

What was it like being a Young Leader? How has being part of this network impacted your life professionally and/or personally?

Anything else?