The 2002 Fields Medal was awarded to Vladimir Voevodsky for his contributions to the development of homotopy theory for algebraic varieties and the formulation of motivic cohomology. His work bridged algebraic geometry and topology, providing new analytical frameworks that allowed for the resolution of long-standing conjectures within the mathematical community.
Early Education and Path to Harvard
Born in 1966 in Moscow, Voevodsky attended Lomonosov Moscow State University, specifically the Faculty of Mechanics and Mathematics. He was expelled from this institution without a diploma due to persistent absenteeism and academic failure. Despite this lack of a formal undergraduate degree, he produced independent mathematical research that led to his admission to Harvard University. Recommended by David Kazhdan, he completed his Ph.D. there in 1992.
Twenty questions, eight minutes on the clock, and a percentile measured against everyone who has taken it. No sign-up.
Take the IQ test →Contributions to Algebraic Geometry
Voevodsky focused his research on the intersection of algebraic geometry and topology. In collaboration with Fabien Morel, he introduced a homotopy theory for schemes. His development of motivic cohomology provided the necessary tools to prove the Milnor conjecture, which links the Milnor K-theory of a field to its étale cohomology. In 2009, he announced a proof of the full Bloch–Kato conjectures at an anniversary conference at the Institut des Hautes Études Scientifiques.
Type Theory and Mathematical Foundations
Beginning in 2002, Voevodsky held a professorship at the Institute for Advanced Study in Princeton, New Jersey. During this period, he shifted his focus toward the foundations of mathematics. In 2009, he constructed a univalent model of Martin-Löf type theory using simplicial sets. This initiative aimed to advance computer-aided proof verification, leading to his work on the UniMath library using the Coq proof assistant.
Final Years and Legacy
In recognition of his impact on the field, the University of Gothenburg awarded Voevodsky an honorary doctorate in April 2016. He passed away on 30 September 2017 at his home in Princeton, aged 51, following an aneurysm. His remains were interred at Khimki Cemetery. He was survived by two daughters, Diana Yasmine Voevodsky and Natalia Dalia Shalaby.
Fast facts
- Born: 1966, Moscow
- Died: 2017, Princeton
- Fields Medal: 2002
- Citizenship: United States, Soviet Union
- Ph.D.: Harvard University, 1992
- Primary employer: Institute for Advanced Study
- Honorary doctorate: University of Gothenburg, 2016
Questions readers ask
What is the significance of the Milnor conjecture?
It relates the Milnor K-theory of a field to its étale cohomology, a problem that Voevodsky solved using his newly developed tools in motivic cohomology.
What are univalent foundations?
It is a framework for the foundations of mathematics that Voevodsky developed, involving the construction of a univalent model of Martin-Löf type theory in simplicial sets.
Achievements
- Fields medal — 2002
- Held posts at Institute for Advanced Study
- Fields: algebraic geometry, topology and Galois theory