“‘AI achieves silver-medal standard solving International Mathematical Olympiad problems’” by gjm

This is a link post.Google DeepMind reports on a system for solving mathematical problems that allegedly is able to give complete solutions to four of the six problems on the 2024 IMO, putting it near the top of the silver-medal category.Well, actually, two systems for solving mathematical problems: AlphaProof, which is more general-purpose, and AlphaGeometry, which is specifically for geometry problems. (This is AlphaGeometry 2; they reported earlier this year on a previous version of AlphaGeometry.)AlphaProof works in the "obvious" way: an LLM generates candidate next steps which are checked using a formal proof-checking system, in this case Lean. One not-so-obvious thing, though: "The training loop was also applied during the contest, reinforcing proofs of self-generated variations of the contest problems until a full solution could be found."[EDITED to add:] Or maybe it doesn't work in the "obvious" way. As cubefox points out in the comments [...] --- First published: July 25th, 2024 Source: https://www.lesswrong.com/posts/TyCdgpCfX7sfiobsH/ai-achieves-silver-medal-standard-solving-international --- Narrated by TYPE III AUDIO.