The Mathematician Who Rebuilt the Foundations of Proof

Vladimir Voevodsky revolutionized algebraic geometry by developing motivic cohomology and A1-homotopy theory, linking algebraic varieties with methods from topology. His work led to proofs of the Milnor and Bloch–Kato conjectures and earned the 2002 Fields Medal. Later, concerned that highly complex proofs were becoming difficult to verify, he developed univalent foundations and promoted computer-checked mathematics. This documentary follows his path from Moscow and Harvard to the Institute for Advanced Study.

Voevodsky's career contains two rare mathematical revolutions. First, he built new tools that transformed algebraic geometry and number theory. Then he questioned how mathematics itself should be written and verified, helping create foundations suited to proof assistants. His work connects Grothendieck's geometric vision with the future of computer-checked reasoning. This documentary shows why deep abstraction can solve old conjectures while also changing the methods by which future mathematicians establish certainty.