Vladimir Voevodsky

Vladimir Alexandrovich Voevodsky was a Russian American mathematician, born on 4 June 1966 and died on 30 September 2017, whose work in developing a homotopy theory for algebraic varieties and formulating motivic cohomology led to the award of a Fields Medal in 2002. He was expelled from Moscow State University without a diploma but received his Ph.D. at Harvard University in 1992, advised by David Kazhdan. With Fabien Morel he introduced a homotopy theory for schemes, and he used motivic cohomology to prove Milnor's conjecture relating the Milnor K-theory of a field to its étale cohomology. In 2009 he announced a proof of the full Bloch-Kato conjectures and constructed the univalent model of Martin-Löf type theory, which led to the univalent foundations of mathematics and homotopy type theory. From 2002 he was a professor at the Institute for Advanced Study in Princeton.