On September 4, 2026, Anthropic revealed that a fully computer-checked proof of Fermat's Last Theorem has been completed. Claude did most of the work, over roughly 11 days. The output came to 13 million lines of Lean code, and the final proof draws on 29,500 intermediate theorems. No new mathematics was created here, but the work of checking a proof just moved at a speed nobody had seen before.
A 350-year proof, and the verification wall behind it
Fermat scribbled his claim in the margin of a book around 1637. For any exponent greater than 2, no positive integers a, b, c satisfy a to the n plus b to the n equals c to the n. Anyone can read the statement, yet no proof surfaced for more than 350 years. In 1908 a prize of 100,000 German gold marks was announced, and 621 incorrect proofs arrived in the first year alone.The prize would be worth roughly 1 to 2 million USD today (about 160 million to 310 million yen). Converted at 1 USD = 156 JPY.
The matter was settled in 1995 by Andrew Wiles in a 129-page paper. That proof was not accepted on sight either. The first version, presented in lectures in 1993, was found to contain a critical gap during review, and Wiles spent a year closing it with his former student Richard Taylor. Several mathematicians spent months working through those 129 pages before anyone could say with confidence that the argument held.
This is where formalization enters. You rewrite a proof in a language a machine can read and let the computer hunt for logical holes. Proofs written for humans skip countless steps as obvious, while the Lean proof assistant demands every one of them. For Fermat's Last Theorem, a community project launched in 2024 by Kevin Buzzard at Imperial College London has been under way, and the blueprint describing just the opening phase runs to 86 pages. The job was expected to take years.
Eleven days, 13 million lines
The push came from Tianyi Peng, an Anthropic researcher whose group at Columbia University builds tools for formalization. He set out to see how far Claude could get on the problem, and the answer went past what he expected.
The numbers give a sense of scale. Eleven days produced 13 million lines of Lean. Along the way 30,300 theorems were proved, of which 29,500 ended up in the final proof. Mathlib, the community's central library of formalized mathematics and the foundation this work builds on, is less than a fifth of that size. Anthropic itself notes the proof is likely far longer than it needs to be.
The path follows not Wiles's original argument but a simplified exposition by Henri Darmon, Fred Diamond and Richard Taylor. Human input was limited to occasional high-level nudges such as prioritizing the Jacobian as a scheme. The finished proof relies on nothing beyond Lean's three standard axioms, and a dedicated comparator confirmed that the statement being proved matches Mathlib's own statement of the theorem.
This did not come out of nowhere. The work adapts pieces from Buzzard's project and from flt-regular, which handles the regular-prime case, and Lean and Mathlib themselves are the product of hundreds of mathematicians. After reading the proof, Buzzard highlighted that AI autoformalization artifacts are now robust enough for others to build on.
The first attempts failed
Progress was not smooth. Early runs saw agents make some headway and then lose track of where the project stood, at which point their collaboration broke down. Roughly 7 percent of the non-boilerplate lines in the final proof came out of those failed efforts.
Things turned once the team switched to Prove2Me, a collaborative formalization platform designed by Peng and his collaborators. Three things mattered. It maintained the dependencies among theorem statements as a directed acyclic graph, so agents could decide what to attempt next. It split statements and proofs into separate files, which kept compilation light. And it attached a natural-language description to each theorem, making already-proved results searchable and reusable.
Underneath sat a multi-agent harness built on Claude Code, consuming about 6 billion output tokens. The model was a general-purpose internal research model, roughly comparable in capability to Claude Fable 5.1.
What this changes for working mathematicians
Once formalization finishes in a realistic amount of time, the weight of peer review shifts. Years of human effort spent confirming whether a new result holds can be partly handed to a machine. With AI-generated mathematics piling up, that verification cost is becoming impossible to ignore.
Nor does the method appear reserved for flagship projects. In a smaller experiment, Anthropic researchers used just three consumer Claude Max subscriptions, coordinated through Prove2Me, and formalized Vinogradov's three primes theorem in three days. Given the right scaffolding, formalizing major theorems on ordinary subscriptions looks within reach.
There is a side effect for Claude as well. Recent Claude-authored results have been formalized in parallel with their proofs, and Claude appears to use those partial formalizations to check its own hypotheses, much as it writes numerical simulations to confirm it is heading in a sensible direction.
The completed proof is available on GitHub, along with a written walk-through of how it fits together.
Summary
Eleven days, 13 million lines, 29,500 intermediate theorems. For the first time, Fermat's Last Theorem has a proof a machine can verify end to end. The value lies not in new mathematics but in verification. The job of confirming that a proof is correct is moving from human hands to machines, and the resulting artifacts are now solid enough to serve as foundations for the next proof. That is the real shift here.
