Proposing and solving olympiad geometry with guided tree search (www.nature.com)

Researchers have introduced TongGeometry, an innovative neuro-symbolic AI system designed to both propose and solve geometry problems at the level of prestigious mathematics olympiads. This system uses guided tree search techniques to navigate the complex landscape of geometric reasoning while effectively integrating large language models to enhance its problem-solving capabilities. Notably, TongGeometry has compiled an extensive repository of 6.7 billion geometry problems, exhibiting impressive performance: it successfully solved all problems in the International Mathematical Olympiad’s IMO-AG-30 benchmark and contributed three problems that were selected for actual regional math competitions. The significance of TongGeometry lies in its dual capability as both a discoverer and solver of mathematical problems, which has vast potential for applications in mathematical education and research. Its underlying architecture employs a Markovian framework to systematically generate and evaluate geometric states and actions, leveraging auxiliary constructions to enhance reasoning. By efficiently exploring this structured problem space with consumer-grade computational resources, TongGeometry not only surpasses traditional AI systems in performance but also reshapes the understanding of automated mathematical discovery, making high-level geometric reasoning more accessible to scholars and enthusiasts alike.