The mathematical work of Vladimir Voevodsky

The mathematical work of Vladimir Voevodsky - Dan Grayson

Dan Grayson
University of Illinois, Urbana-Champaign
September 11, 2018
Abstract: Vladimir Voevodsky was a brilliant mathematician, a Fields Medal
winner, and a faculty member at the Institute for Advanced Study, until his
sudden and unexpected death in 2017 at the age of 51. He had a special flair
for thinking creatively about ways to incorporate topology and homotopy theory
into other fields of mathematics. In this talk for a general audience, I will
sketch his seminal contributions to two broad areas, algebraic geometry and the
foundations of mathematics. A colleague commented about his work in the former
area, which deals with polynomial equations in various alternative number
systems, that if mathematics were music, then Voevodsky would be a musician who
invented his own key to play in. His work in the latter area has led to a new
alternative foundation for all of mathematics, opening up a new landscape
populated by fundamental objects unseen in the traditional foundation provided
by set theory, and in which the notion of equality is interpreted in an
unexpected way. It also hastens the day when our mathematical literature has
been verified mechanically and referees are relieved of the tedium of checking
the proofs in articles submitted for publication.