Владимир Воеводский (who published in English as Vladimir Voevodsky) was a Russian mathematician working in the Institute for Advanced Study.

Voevodsky received a Fields medal in 2002 for a proof of the Milnor conjecture. The proof crucially uses A1-homotopy theory and motivic cohomology developed by Voevodsky for this purpose. In further development of this in 2009 Voevodsky announced a proof of the Bloch-Kato conjecture.

After this work in algebraic geometry, cohomology and homotopy theory Voevodsky turned to the foundations of mathematics and worked on homotopy type theory which he described as a new “univalent foundations” for modern mathematics with its emphasis on homotopy theory and higher category theory.

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