[Todos CMAT] Vladimir Voevodsky, 1966-2017

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Jue Oct 5 18:01:50 -03 2017


Vladimir Voevodsky, 1966-2017

Vladimir Voevodsky, an exceptional mathematician with deep insight who  
received the Fields Medal in 2002 for his development of a homotopy  
theory for algebraic varieties and his formulation of motivic  
cohomology, died September 30 at the age of 51. His work proved the  
Milnor conjecture, which for decades had been the major unsolved  
problem in algebraic K-theory. Voevodsky was a professor at the  
Institute for Advanced Study. In 2009 he proved the Bloch-Kato  
conjectures and more recently was working on homotopy type theory and  
computer-assisted proof verification. Voevodsky grew up in the Soviet  
Union and came to the U.S. to do graduate work at Harvard University,  
receiving his PhD in 1992 under the direction of David Kazhdan. He  
held positions at the Institute for Advanced Study, Harvard, the Max  
Planck Institute for Mathematics, and Northwestern University, before  
becoming a professor at the Institute in 2002.

In his biography at the MacTutor History of Mathematics archive is  
this passage from Voevodsky, which gives an overview of the work for  
which he won the Fields Medal:

We start with geometry, the category of topological spaces. We invent  
something about this geometrical world using our basically visual  
intuition. The notion of pieces comes exclusively from visual  
intuition. We somehow abstract it and re-write it in terms of category  
theory which provides this connecting language. And then we apply in a  
new situation, in this case in the situation of algebraic equations  
which is purely algebraic. So what we get is some fantastic way to  
translate geometric intuition into results about algebraic objects.  
And that is from my point of view the main fun of doing mathematics.

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