Vladimir Voevodsky – one of the most influential mathematicians of the last decades – deceased yesterday at the age of only 51 years.
He became famous more than twenty years ago for his work on the A1 homotopy theory, with which he transferred the methods of the algebraic topology to algebraic geometry over any base field. Tangible results of this approach were e.g. the proof of the Milnor Conjecture and the Bloch-Kato conjecture.
In the last few years he had dealt mainly with the formalization of mathematical proof. Here, too, he wanted to make use of methods derived from topology. Homotopy type theory, in which types of objects are represented by homotopy types of topological spaces, seems to be more suitable for the creation of computer-verifiable proofs than the classical set theory; the univalence axiom which he proposed in 2009 was the 2012-13 topic of a special year at the Institute for Advanced Study Princeton, from which the book Homotopy Type Theory: Univalent Foundations of Mathematics arose. He gave a general audience lecture about this at the Heidelberg Laureate Forum last year:
The picture is from the Oberwolfach Photo Collection: https://opc.mfo.de/detail?photo_id=13818
Added: For an obituary see https://www.ias.edu/news/2017/vladimir-voevodsky-obituary.