Vladimir Voevodsky proves the Milnor conjecture on algebraic K-theory and Galois cohomology, announcing it in a 1996 preprint and presenting it at the 1997 Bourbaki Seminar; the final, fully revised version would be published in 2003. The proof decisively employs the theory of motives and motivic cohomology, a theoretical framework Voevodsky himself develops in parallel and which profoundly generalizes the tools of classical algebraic geometry. Voevodsky received the Fields Medal in 2002.