Solving olympiad geometry without human demonstrations

The Nature paper accompanying the AlphaGeometry blog describes the technical details of training a geometry-solving system entirely on synthetically generated problems — no human-labeled proofs were used in training. The system generates its own training data by constructing random geometric diagrams, deriving all provable statements about them using a deduction engine, and training the language model to predict the auxiliary constructions needed. This synthetic data approach — generating unlimited training data without human annotation — is a direct parallel to AlphaGo Zero's self-play: both avoid human knowledge as a ceiling on performance. The paper also introduces a benchmark of 30 classical IMO problems specifically for evaluating geometry reasoning AI, with full formal proofs for verification. The benchmark has since become the standard evaluation for mathematical AI systems. Hassabis describes the paper as the proof that the synthetic-data + formal-verifier architecture generalizes beyond games and biology to formal mathematics — a domain where correctness can be rigorously verified, enabling the AI to function as a mathematical collaborator that can be fully trusted within its domain of competence.