Google DeepMind today published a paper in Nature introducing AlphaGeometry, an AI system that solves complex geometry problems at a level approaching a human Olympiad gold medalist. In a benchmark of 30 geometry problems from International Mathematical Olympiads between 2000 and 2022, AlphaGeometry solved 25 within the standard time limit. The previous state-of-the-art system, Wu’s method, solved only 10. The average human gold medalist solved 25.9 problems.

AlphaGeometry is a neuro-symbolic system combining a neural language model with a symbolic deduction engine. The language model predicts which new geometric constructs—such as points, lines, or circles—would be most useful to add, guiding the deduction engine toward a solution. To train the language model without human demonstrations, the team generated 100 million unique synthetic examples by creating one billion random diagrams and exhaustively deriving geometric relationships, then filtering to remove duplicates.

The system’s performance marks a milestone in AI reasoning. When applied to the full IMO, AlphaGeometry’s geometry capability alone would have passed the bronze medal threshold in 2000 and 2015. However, since only two of six IMO problems typically focus on geometry, the system only covers one-third of a competition’s problems. The team has open-sourced the code and model, hoping the synthetic data approach will open new possibilities in mathematics and science.

Reactions from the mathematical community have been notable. Former Olympiad gold medalist and math coach Evan Chen praised the output as verifiable and clean, noting it uses classical geometry rules like a student would. Fields Medalist Ngô Bảo Châu called the achievement stunning, comparing the problem-solving approach to chess. The paper fits into DeepMind’s broader push on mathematical reasoning, following FunSearch’s discoveries in open problems last year.