The Mathematician Who Learned How Equations Explode

Frank Merle became a central figure in nonlinear analysis by explaining how solutions to dispersive and wave equations can concentrate, remain stable or blow up in finite time. Born in Marseille in 1962, he studied at the École Normale Supérieure and completed his doctorate in 1987. His collaborations developed classification and rigidity methods now used throughout the field. This documentary follows his work at Cergy and IHES, culminating in the 2023 Clay Research Award and 2026 Breakthrough Prize.

Nonlinear equations describe waves in fluids, plasmas, optics and relativity, but small changes can create dramatic and even singular behavior. Merle developed methods that reveal the precise profiles and mechanisms behind such blow-up, replacing chaos with mathematical structure. His work also built an international school through long collaborations and mentorship. This documentary shows how analysts study the edge of mathematical breakdown and why singularities can expose the deepest laws governing evolution.