Anthropic says Claude spent 11 days converting Andrew Wiles’s 1995 proof of Fermat’s Last Theorem into a form the Lean proof assistant can check step by step, producing roughly 13 million lines of Lean code and 29,500 intermediate theorems along the way. Nothing new was proved. Wiles did the mathematics three decades ago; what changed this month is that a machine, rather than a community of referees, can now confirm every logical step holds.
That distinction is the whole story. Anthropic is explicit that this is a formalization, the conversion of human-style mathematical reasoning into a language a computer can verify line by line, not a new result and not Claude discovering anything Wiles had not already shown. Kevin Buzzard of Imperial College London, who has led a multi-year community effort toward the same goal since 2024, reviewed the output and called it an autoformalization achievement built on Wiles’s original argument.
Formalization is tedious precisely because computers do not skip steps. A human proof reader accepts routine inferences on faith. Lean demands every one be spelled out and derived from its own axioms, which is why a project many mathematicians expected to take years instead ran on a blueprint document that itself stretched to 86 pages before Claude ever touched it, according to Anthropic’s account.
What makes the claim credible is not the length of the proof but the nature of the check. Lean either accepts a derivation or it rejects it; there is no partial credit and no reviewer fatigue, which is a stronger guarantee than almost any other AI benchmark on the market currently offers. That is also why this result should be read narrowly. Formal verification is one of the only domains where a model’s output can be checked completely and automatically, which makes it a natural proving ground for autonomous AI work and a poor indicator of how Claude performs in domains, such as open-ended research or business judgment, where no such checker exists.
Anthropic’s own account credits a companion tool, Prove2Me, built by the same Columbia University researcher who initiated the project, with keeping dozens of parallel Claude agents from losing track of a proof this large. The system maintained a dependency graph of which theorems needed proving next and let agents work in parallel without duplicating or contradicting each other, addressing a failure mode Anthropic says surfaced early: agents that lost the thread of the project and produced work that ended up contributing roughly 7 percent of the final proof’s lines despite ultimately being discarded.
The company is careful to separate this from its earlier work on the Riemann hypothesis, where it says Claude contributed to novel mathematical territory. Here the novelty is entirely in the checking, not the discovery. Anthropic frames the implication as a verification bottleneck problem: unrefereed proofs can sit under review for years, as Grigori Perelman’s Poincaré conjecture proof did, and a machine-checkable companion artifact could shorten that cycle for future results, human or AI-authored.
For research teams evaluating AI-assisted formal methods, the operative benchmark is not proof length or token count but whether a comparable verifier exists in your domain. Anthropic reports Claude also formalized a separate result, Vinogradov’s Three Primes Theorem, in three days using only three consumer Claude Max subscriptions, suggesting the same approach scales down as well as up. Any team weighing Claude for math-adjacent formal verification work should treat this as evidence the pipeline works when Lean or an equivalent checker sits at the end of it, and as no evidence at all for tasks where the only reviewer is a human.
Anthropic detailed the formalization effort in its own research post, “Formalizing Fermat’s Last Theorem,” published this month.
