Vladimir Voevodsky

Vladimir Voevodsky

Univalent Foundations: New Foundations of Mathematics

Vladimir Voevodsky
Institute for Advanced Study; Faculty, School of Mathematics
March 26, 2014
In Voevodsky’s experience, the work of a mathematician is 5% creative insight and 95% self-verification. Moreover, the more original the insight, the more one has to pay for it later in self-verification work. The Univalent Foundations project, started at the Institute a few years ago, aims to lower the price by giving mathematicians the ability to verify their constructions with the help of computers.

Type Systems

Vladimir Voevodsky
Institute for Advanced Study
November 28, 2012

Type Systems

Vladimir Voevodsky
Institute for Advanced Study
November 21, 2012

Type Systems and Proof Assistant

Vladimir Voevodsky
Professor, School of Mathematics, IAS
October 10, 2012

Type Systems

Vladimir Voevodsky
Professor, School of Mathematics, IAS
October 3, 2012

Overview of Univalent Foundations

Vladimir Voevodsky
Institute for Advanced Study
September 27, 2012

(Continued from September 26, 2012)

Computer Science and Homotopy Theory

Vladimir Voevodsky
Professor, School of Mathematics
April 27, 2011

Univalent Foundations of Mathematics

Vladimir Voevodsky
Institute for Advanced Study
December 10, 2010

The correspondence between homotopy types and higher categorical analogs of groupoids which was first conjectured by Alexander Grothendieck naturally leads to a view of mathematics where sets are used to parametrize collections of objects without "internal structure" while collections of objects with "internal structure" are parametrized by more general homotopy types. Univalent Foundations are based on the combination of this view with the discovery that it is possible to directly formalize reasoning about homotopy types using Martin-Lof type theories.

What if Current Foundations of Mathematics are Inconsistent?

Vladimir Voevodsky, Professor, School of Mathematics
Institute for Advanced Study
September 25, 2010

This lecture was part of the Institute for Advanced Study’s celebration of its eightieth anniversary, and took place during the events related to the Schools of Mathematics and Natural Sciences.