The Mathematician Who Explained Sudden Catastrophes

René Thom changed modern topology through his work on cobordism, characteristic classes and transversality. Born in Montbéliard in 1923, he studied at the École Normale Supérieure and completed his doctorate under Henri Cartan in 1951. His achievements earned the 1958 Fields Medal. At IHES he later created catastrophe theory, proposing that abrupt transitions could arise from smooth underlying changes. This documentary follows his journey from rigorous topology toward biology, form and philosophy.

Thom's topology supplied enduring tools for classifying manifolds, but catastrophe theory made him famous far beyond mathematics. It offered a striking vocabulary for systems that remain stable until a small change triggers a sudden jump, from buckling structures to biological development. Though some applications became controversial, the ambition remains extraordinary: to create mathematics capable of describing form itself. This documentary explores both the rigorous achievements and the philosophical gamble.