# AlphaGeometry AlphaGeometry is the [[Google DeepMind]] system for solving Olympiad-level Euclidean geometry problems. Published in *Nature* in January 2024, it pairs a language model (to suggest useful auxiliary constructions) with a classical symbolic deduction engine (to verify and extend chains of deductions). The **AlphaGeometry 2** successor was part of the joint system (with [[AlphaProof]]) that reached IMO 2024 silver-medal level. ## How it works - **Neuro-symbolic architecture**: LM proposes candidate auxiliary constructions (the creative step humans find hard), symbolic engine executes the rigorous deduction - **Synthetic training data**: trained from ~100 million synthetic geometry theorems and proofs generated by the symbolic engine itself, sidestepping the scarcity of human-labelled geometry data - **Problem-class focus**: classical Euclidean geometry at the IMO level, where hand-crafted axioms make the deduction side tractable ## Performance - AlphaGeometry (original): solved 25 of 30 IMO-style geometry problems in a held-out benchmark, approaching the average human gold medalist - AlphaGeometry 2: stronger than AG1 on the same benchmark; the IMO 2024 geometry problem (P4) was solved in 19 seconds ## Why it matters - Proof-of-concept that synthetic data + neuro-symbolic hybrids can reach Olympiad performance in narrow mathematical domains - Complements [[AlphaProof]] on the IMO 2024 demo: AlphaGeometry handles geometry, AlphaProof handles algebra / number theory via Lean - Part of the broader "AI-for-math" thrust that DeepMind has pushed alongside [[AlphaFold]] and AI-for-science more generally ## References - Nature paper (2024): https://www.nature.com/articles/s41586-023-06747-5 - DeepMind blog: https://deepmind.google/discover/blog/alphageometry-an-olympiad-level-ai-system-for-geometry/ - IMO 2024 silver-medal demo: https://deepmind.google/discover/blog/ai-solves-imo-problems-at-silver-medal-level/ ## Related - [[Google DeepMind]] - [[AlphaProof]] - [[AlphaZero]] - [[Artificial Intelligence (AI)]]