The Fields Medal is considered to be the mathematical equivalent to the Nobel Prize. It is awarded every four years during the International Congress of Mathematicians. It rewards a mathematician, who is less than 40 years old at the time of the Congress, for a major advance in a significant unresolved issue. On August 19, 2010, it was awarded to Cédric Villani, notably for “his proof of the nonlinear Landau damping and of the convergence towards equilibrium for the Boltzmann equation” [MOU 10]. His work extends the conditions of Landau’s damping in a nonlinear context, that is, by taking into account the interactions of plasma on itself. Such a result has theoretical and practical repercussions, for example in classical mechanical models in astrophysics [CNR 10].
In this chapter, it is not a question of discussing the theorem as such. We will focus more modestly on understanding the process that led to its emergence. If the Fields Medal rewards only one person, does that mean it is a solitary effort? Where did the knowledge to develop his theoretical building come from? Can the key factors in this process be identified? In order to gather the insights necessary to provide an answer to this question, we will rely on two types of material produced by Cédric Villani after he obtained his Fields Medal. The first is the book he wrote in 2011, entitled