An anonymous reader writes: For nearly a decade, Voevodsky has been advocating the virtues of computer proof assistants and developing univalent foundations in order to bring the languages of mathematics and computer programming closer together. As he sees it, the move to computer formalization is necessary because some branches of mathematics have become too abstract to be reliably checked by people.
“The world of mathematics is becoming very large, the complexity of mathematics is becoming very high, and there is a danger of an accumulation of mistakes,” Voevodsky said. Proofs rely on other proofs; if one contains a flaw, all others that rely on it will share the error.
This is something Voevodsky has learned through personal experience. In 1999 he discovered an error in a paper he had written seven years earlier. Voevodsky eventually found a way to salvage the result, but in an article last summer in the IAS newsletter, he wrote that the experience scared him. He began to worry that unless he formalized his work on the computer, he wouldn’t have complete confidence that it was correct.
But taking that step required him to rethink the very basics of mathematics.