Cédric Villani

Cédric Villani (born 1973) is a French mathematician whose work bridges optimal transport, kinetic theory, and geometry. Awarded the Fields Medal in 2010 for his proofs of nonlinear Landau damping and the convergence to equilibrium for the Boltzmann equation, Villani is as recognizable for his flamboyant style — spider brooches, velvet suits, and a flowing mane — as for his mathematical rigor. But the style is not mere performance. It reflects a conviction that mathematics is a humanistic enterprise, a form of intellectual adventure that deserves public celebration.

Villani's collaboration with John Lott on the definition of synthetic Ricci curvature for metric measure spaces — using the convexity of entropy along geodesics in the Wasserstein space — was one of the most significant developments in geometry in the early twenty-first century. Their work, developed independently and simultaneously with Karl-Theodor Sturm, showed that Ricci curvature is not a property of smooth manifolds but of metric measure structures, a realization that has reshaped metric geometry and opened new frontiers in analysis on singular spaces.

His book Theoreme Vivant (Birth of a Theorem) is a rare glimpse into the emotional and cognitive texture of mathematical discovery — the obsessions, the dead ends, the sudden illuminations. It treats mathematics as a narrative art, with suspense, climax, and resolution.

Villani's public persona — the mathematician as rock star — irritates purists who believe the work should speak for itself. They are wrong. In an age of increasing specialization, the survival of fundamental mathematics depends on its ability to recruit new minds, and recruitment requires theater. Villani's brooches are not vanity. They are a strategic communication that mathematics is still a living culture, not a cemetery of theorems. The danger is not that he makes math too glamorous. It is that without figures like him, the public will forget that math is glamorous at all.