AI solves IMO geometry

Geometry problems at the International Mathematical Olympiad ask students to turn a picture into a proof, and Google DeepMind says AlphaGeometry 2 now does that at gold-medalist level. (arxiv.org) In a February 2025 paper, DeepMind researchers reported that AlphaGeometry 2 solved 84 of 95 geometry problems from the Olympiads held from 2000 through 2024, an 88% solve rate. The earlier AlphaGeometry system covered 66% of that same set. (arxiv.org) The system works as a hybrid: a neural model proposes useful construction steps, and a symbolic engine checks them with formal rules, like a chess player generating moves and a referee enforcing legality. DeepMind said those additions let the system handle moving points, angle equations, ratio equations, distance equations, and some non-constructive problems that the first version missed. (arxiv.org) That geometry work sits beside AlphaProof, a separate DeepMind system for algebra and number theory that writes machine-checkable proofs instead of ordinary text. In the 2024 International Mathematical Olympiad, DeepMind said AlphaProof and AlphaGeometry 2 together solved four of six problems for 28 points, a silver-medal score under that year’s cutoff. (deepmind.google) The International Mathematical Olympiad is a six-problem contest taken over two 4.5-hour sessions by teams of six pre-university students from more than 100 countries. Medals go to roughly half of contestants, with about 8% receiving gold, which is why Olympiad results have become a benchmark for mathematical reasoning systems. (deepmind.google) DeepMind’s first AlphaGeometry result, published in January 2024, solved 25 of 30 Olympiad geometry problems in a benchmark set drawn from 2000 to 2022. DeepMind said the average human gold medalist on that set solved 25.9 problems, while the previous automated method solved 10. (deepmind.google) Outside DeepMind, mathematicians have treated the result as part of a larger shift toward formal reasoning tools that can check every logical step. Nature reported that AlphaGeometry 2 reached the level of gold-medal students on Olympiad geometry, while later commentary on AlphaProof focused on its use of proof assistants to verify arguments rather than just generate plausible ones. (nature.com 1) (nature.com 2) The limitation is that these systems still rely on formalized problem statements, not the handwritten diagrams and informal language human contestants see first. DeepMind said the 2024 Olympiad problems had to be manually translated into formal mathematical language before AlphaProof and AlphaGeometry 2 could work on them. (deepmind.google) So the result is not that a chatbot suddenly “understands” school geometry the way a student does. It is that a neurosymbolic system — one part pattern finder, one part rule checker — can now solve a large share of the hardest geometry problems in a competition built to defeat almost everyone who enters. (arxiv.org)