Anthropic Claude Agents Formalize Fermat Proof in Lean in 11 Days

{"The project used a multi-agent workflow in which Claude instances decomposed the 1995 proof into intermediate lemmas, generated Lean code, and iteratively repaired type-checking errors. The team started from the existing Lean mathlib library and focused on the elliptic-curve and modular-form sections that had not yet been formalized. Total human oversight was limited to high-level goal setting and final review of the generated repository.","This result extends earlier AI-assisted formalizations such as the 2021 Liquid Tensor Experiment and the 2024 Google DeepMind FunSearch work on cap sets. Unlike those projects, the present effort tackled an entire landmark theorem rather than an isolated conjecture. The speed suggests that current frontier models can now handle the combinatorial complexity of long proof scripts when scaffolded by agentic loops and retrieval over existing formal libraries.","Key limitations remain: the formalization still required a human mathematician to confirm semantic fidelity to Wiles's argument, and several steps were completed via brute-force search rather than genuine insight. Scaling to open research problems will require benchmarks that measure novel lemma invention, not merely translation of known proofs.","Next milestones include releasing the Lean repository for community audit and testing whether the same pipeline can formalize portions of the Langlands program within months rather than decades."}