Colloque des sciences mathématiques du Québec

25 mars 2022 de 15 h 30 à 16 h 30 (heure de Montréal/HNE) Réunion Zoom

Making mathematics computer-checkable

Colloque par Heather Macbeth (Fordham university)

In the last thirty years, computer proof verification became a mature technology, with successes including the checking of the Four-Colour Theorem, the Odd Order Theorem, and Hales' proof of the Kepler Conjecture.  Recent advances such as the "Liquid Tensor Experiment" verifying a recent theorem of Scholze have provided further momentum, as likewise have promising experiments integrating this technology with machine learning.

I will briefly describe some of these developments.  I will then try to describe, more generally, what it *feels* like to carry out research-level computer verifications of mathematics proofs: the level of expression one has access to, the ways one finds oneself interrogating and reorganizing a paper proof, the kinds of arguments which are more tedious (or less tedious!) than on paper.