Claude Formalized Fermat's Last Theorem in Lean After 11 Days of Autonomous Work

Anthropic announced on September 4 that Claude, working largely autonomously for 11 days, produced a complete machine-checked Lean formalization of Fermat’s Last Theorem, per Anthropic’s research post and SiliconANGLE’s coverage. Along the way it generated computer-verified proofs of 30,300 intermediate theorems, using 29,500 of them in the final proof, amounting to roughly 13 million lines of coherent Lean code by mathematician Daniel Litt’s count. A human collaborative project has been working toward the same goal for years.

Why This Is Different From a Benchmark Score

Formalization is the least forgiving task in AI evaluation. A Lean proof does not accept plausible-sounding arguments; the compiler either verifies the mathematics or rejects it, which makes this the rare AI achievement that cannot be inflated by benchmark contamination or generous grading. The verification is the result. It also explains the working pattern: an 11-day autonomous run implies sustained subgoal planning, error recovery across millions of lines, and the judgment to build reusable intermediate lemmas (the 30,300 verified theorems function as a library), which is a fuller demonstration of agentic engineering than any single-shot benchmark.

What It Means for Formal Mathematics and Beyond

The immediate implication lands on the formalization community, which has spent years human-months formalizing major results and now has both a completed FLT artifact and, more importantly, 30,300 verified building blocks future formalizations can import. Mathematician reaction over the weekend ranged from astonishment to scrutiny of how much human-authored structure Claude inherited from the existing Lean library, and that scrutiny is healthy: the claim is not that Claude invented new mathematics, but that it executed a formalization workload previously considered a multi-year human project.

The broader signal connects directly to Astra solving open math problems with Lean 4 proofs last month: formal verification is emerging as the field’s preferred ground truth for AI reasoning claims, precisely because everything else can be gamed. Expect the next generation of model announcements to include machine-checked artifacts rather than benchmark tables, and for formalization capacity to become a competitive metric labs report on purpose.