In 1637, Pierre de Fermat jotted a claim in the margin of his copy of Diophantus's Arithmetica: no positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for any n > 2. The conjecture defied mathematicians for over 350 years, until Andrew Wiles published the first proof in 1995 — 129 pages that took months of painstaking verification. On September 4, Anthropic shared a different kind of milestone for the same theorem: the first complete computer-checked proof, written largely autonomously by Claude over 11 days — 13 million lines of Lean, every declaration verified by the proof assistant's kernel.
Eleven days, 13 million lines
The formalization was initiated by Tianyi Peng, an Anthropic researcher whose group at Columbia University builds AI formalization tools. The project set out to test how far Claude could get; it went further than expected. Working largely autonomously for 11 days, Claude produced computer-verifiable proofs of 30,300 theorems, of which 29,500 were used in the final proof. The result is over 5x the size of Mathlib, the principal community library it builds on, and consumed about six billion output tokens from an internal research model roughly comparable to Claude Fable 5.1. The agent logs Anthropic posted show Lean marking the FLT root theorem as PROVED in the early hours of August 18.
The real star is the collaboration architecture
The detail engineers should read closest: the first attempts failed. Agents had some early success, then quickly lost track of the project's state and stopped collaborating effectively. The turnaround came from switching to Prove2Me, an open collaborative formalization platform designed by Tianyi Peng and his Columbia collaborators. It maintains a directed acyclic graph of theorem statements that agents use to decide what to prove next — mitigating memory degradation and letting many agents work in parallel. It separates theorem statements from proofs into different files to speed up Lean compilation. Dozens of agents collaborated on a Claude Code harness, while human input shrank to occasional high-level instructions such as "push the Mazur theorem to be done soon."
Why it matters
Anthropic is careful about the framing: what's novel here is the verification, not new mathematics — like checking arithmetic with a calculator, applied to some of the hardest proofs humans have. Two months into reviewing Wiles's 1993 lectures, a referee found a critical gap; Wiles spent a year fixing it, first alone and then with Richard Taylor. Formalizing FLT was expected to take years — the community effort Kevin Buzzard kicked off at Imperial College London in 2024 has an 86-page blueprint just for its initial phase. Claude's proof follows the simplified route of Darmon, Diamond and Taylor, and Buzzard's verdict after reviewing it: AI autoformalization artifacts are now "robust enough to be built upon."
Reasons for caution
First, "largely autonomously" is not unmanned: humans still set the direction, and Anthropic itself admits the 13 million lines are likely "much longer than it needs to be" — written to be checked, not read. Second, the repository is explicitly a research artifact: not maintained, not accepting contributions. Third, the verification itself is solid: on GitHub, all 60,475 modules build from scratch under Lean 4.33.1, and the independent comparator tool confirmed the proved statement matches Mathlib's own statement of FLT. There is also a striking counter-experiment: three personal Claude Max subscriptions, collaborating through Prove2Me, formalized Vinogradov's Three Primes Theorem in three days — the barrier to formalization is sliding from lab budgets toward consumer subscriptions.
So what. The point was never Fermat — the theorem was proved in 1995. The point is mechanizing trust: as AI produces purported proofs faster than humans can referee them, machine verification becomes the plausible way for mathematics to scale its trust system. Anthropic expects formalized proofs alongside human-readable write-ups to become common. For the AI industry, this is also a demonstration of a multi-agent system delivering end-to-end on a genuinely hard task — where the collaboration architecture (dependency graphs, task decomposition, state management) matters more than raw single-model capability.
Sources: anthropic.com/research/formalizing-fermats-last-theorem | Proof repo: github.com/anthropics/fermats-last-theorem