Proof assistants

…combined with theorem provers and proof assistants have recently reached gold-medal level at the International Mathematical Olympiad and contributed to research-level results, including the resolution of many Erdős problems and a 2026 counterexample to Erdős's unit distance conjecture. A central theme is integrating proof assistants with LLMs: proof assistants check every logical step of

Kevin Buzzard explains how proof assistants check mathematical arguments against axioms and logical rules. The discussion covers the interactive process of formalizing a proof, the collaborative communities around these tools, and the project to formalize Fermat’s Last Theorem. It also examines how proof assistants might work with AI to strengthen mathematical practice.