Univalent Foundations: New Foundations of Mathematics

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. Voevodsky explains how new ideas that make this goal attainable arise from the meeting of two streams of development—one in constructive mathematics and the theory and practice of programming languages, and the other in pure mathematics.