AlphaGeometry: An Olympiad-level AI system for geometry

AlphaGeometry (Nature, January 2024) is DeepMind's demonstration that the AlphaFold/AlphaGo approach generalizes to mathematical reasoning — specifically, Euclidean geometry problems from the International Mathematical Olympiad (IMO). The system combines a neural language model (trained on synthetic geometry proofs generated without human input) with a symbolic deduction engine (a formal theorem prover). The language model generates intuitive 'auxiliary constructions' — adding new points or lines to a geometry diagram — which the symbolic engine then verifies through formal logic. AlphaGeometry solved 25 out of 30 recent IMO geometry problems, placing it between a silver and gold medal human competitor. The result is significant because it demonstrates the 'neurosymbolic' architecture that Hassabis believes will be necessary for AGI: neural networks provide flexible pattern recognition and intuition, while symbolic systems provide verifiable formal reasoning. Neither alone is sufficient for mathematical discovery, but their combination is more capable than either. This paper is where Hassabis's vision for AI as a mathematical tool first became concrete.