Mathematical Reasoning

Mathematical reasoning asks how AI systems can solve multi-step problems, apply mathematical concepts, construct proofs, and help discover new results. Common approaches include supervised learning and reinforcement learning with verifiable rewards, alongside self-distillation, search, and structured methods that use code, symbolic solvers, or formal proof assistants such as Lean. Work spans arithmetic and competition problems, geometry, statistics, multimodal tasks, and research-level proofs, with benchmarks increasingly testing robustness, multilingual ability, and intermediate reasoning rather than answers alone. Models have improved on many standard tasks, but remain brittle under equivalent problem changes and difficult proof or construction demands; reliable verification, useful exploration, and meaningful measures of reasoning quality remain open challenges.