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.

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.