On last Thursday at the Heidelberg Laureate Forum, Vladimir Voevodsky gave perhaps the most revolutionary scientific talk I’ve ever heard. I doubt if it generated much buzz among the young scientists in advance, though, because it had the inscrutable title “Univalent Foundations of Mathematics,” and the abstract contained sentences like this one: “Set-theoretic approach to foundations of mathematics work well until one starts to think about categories since categories cannot be properly considered as sets with structures due to the required invariance of categorical constructions with respect to equivalences rather than isomorphisms of categories.”
Eyes glazed over yet?