Anthropic announced on Thursday, September 4, 2026, that Claude has produced the first complete computer-checked proof of Fermat's Last Theorem, one of the most famous results in mathematics, working largely autonomously over 11 days and writing 13 million lines of code in the Lean programming language, according to the company's official announcement.
The milestone drew immediate attention across the research community, topping Hacker News within hours of publication. A formal proof of the theorem had been expected to take a multi-year community effort; instead, a team of dozens of collaborating Claude agents completed the job in under two weeks. For more context on where AI capabilities stand today, see our latest AI developments.
What Fermat's Last Theorem Is — and Why It Resisted Proof for 350 Years
Fermat's Last Theorem states that no positive integers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ for any value of n greater than 2. Pierre de Fermat jotted the claim around 1637 in the margin of his copy of Diophantus's Arithmetica, adding his now-legendary note that he had discovered a truly marvelous proof which the margin was too narrow to contain.
For more than three centuries the conjecture outlasted every attempt to prove it. According to Anthropic's account, a prize of 100,000 German gold marks announced in 1908 drew 621 incorrect attempts in its first year alone. Sir Andrew Wiles finally presented a correct proof in 1993 — only for reviewers to expose a critical gap two months into verification. Wiles spent a year repairing the proof with his former student Richard Taylor before publishing the definitive 129-page version in May 1995, which took months of painstaking work to verify.
How Claude Built a 13-Million-Line Proof
The project was initiated by Tianyi Peng, an Anthropic researcher whose group at Columbia University builds tools for AI formalization, who set out to test whether Claude could make progress on converting Wiles's proof into machine-checkable form.
The effort succeeded only after a change of approach. Anthropic reports that the agents' initial attempts failed as they lost track of the project's state and stopped collaborating effectively. The breakthrough came with Prove2Me, an open collaborative platform for formalizing mathematics designed by Peng and collaborators at Columbia. The platform maintains a directed acyclic graph of theorem statements that agents use to decide what to prove next, speeds up Lean compilation by separating statements from proofs, and lets agents search and reuse results through natural-language descriptions of each theorem.
Running on a Claude Code-based multi-agent harness, the team of agents consumed roughly six billion output tokens from an internal research model that Anthropic describes as roughly comparable to Claude Fable 5.1. Human input was limited to occasional high-level instructions — Anthropic cites messages like "Jacobian as a scheme sounds high priority" and a request to push the Mazur theorem to be done soon. The proof completed at 02:00 UTC on August 18, when the platform's root theorem flipped to Proved.
Along the way, Claude proved 30,300 theorems, using 29,500 of them in the final proof. At 13 million lines of Lean, the result is more than five times the size of Mathlib, the principal community library of formalized mathematics. The proof follows a simplified exposition of Wiles's argument by Henri Darmon, Fred Diamond, and Richard Taylor, and adapts pieces of the Imperial College London formalization project led by Kevin Buzzard.
Why a Lean Proof Settles the Question
What makes the result decisive is the arbiter. Proof assistants like Lean verify the logic of a proof algorithmically, and Anthropic states that Claude's proof uses only Lean's three standard axioms, with a comparator confirming that the theorem's statement matches Mathlib's own formulation of the theorem. The company has also published the proof in a public repository on GitHub.
Buzzard, who reviewed the result, was unequivocal: "This extraordinary autoformalization achievement, which Anthropic researchers say only took 11 days, proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics."
Anthropic is careful to position the novelty correctly. Unlike recent AI-driven work on the Riemann hypothesis, which produced novel mathematics, nothing here is new math — the achievement is verification, checking an existing proof the way a calculator checks arithmetic. Given that Lean — not Anthropic — is the final authority on correctness, the claim does not rest on the company's own assessment of its model.
What It Means for Mathematics and AI Research
The implications cut both ways. For mathematicians, autoformalization could catch errors in the existing corpus of knowledge and dramatically lighten the refereeing burden for new results, a process that can take years. "If the automatic formalization of FLT is possible now, then we have taken a big step towards automatic formalization of the modern mathematical literature," Buzzard wrote in a follow-up blog post titled "Anthropic has beaten me to it," acknowledging that his own community-led effort, kicked off in 2024, had been overtaken.
For AI labs, the result suggests that formal tools may rein in one of the technology's most notorious weaknesses. Anthropic notes that writing Lean appears to help Claude prove novel results, with agents using partial formal proofs to independently check hypotheses much as they write numerical simulations. The company also argues the barrier to entry is collapsing: in a small experiment, three personal Claude Max plans were enough for collaborating agents to formalize Vinogradov's Three Primes Theorem in three days.
The caveats remain real. The proof required a purpose-built platform, billions of tokens, and an unusually clean success criterion — checking an answer key that already exists is easier than discovering new theorems. But as a demonstration that AI systems can now formalize mathematics at the frontier, 11 days against a 358-year problem makes the point about as vividly as possible.
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