Key Notes
- Anthropic says Claude produced the first complete, computer-checked Lean formalization of Fermat's Last Theorem (originally proved by Andrew Wiles in 1995) in 11 days, largely autonomously, using dozens of agents that wrote 13 million lines of Lean code and proved 29,500 of 30,300 attempted intermediate theorems.
- This is formalization (mechanically verifying an existing proof), not new mathematics — it changes nothing about the mathematical result itself, as Kevin Buzzard, the Imperial College London mathematician leading a parallel 5-year formalization effort since 2024, stressed alongside his praise for the achievement.
- The project built directly on existing community infrastructure Anthropic didn't create — Buzzard's own FLT blueprint, the Mathlib library, and Prove2Me (a tool built by Anthropic researcher Tianyi Peng's Columbia group) — and used about 6 billion output tokens from a Fable-5.1-class model. .
Anthropic said it has produced the first complete, computer-checked formalization of Fermat’s Last Theorem, with dozens of Claude agents writing the proof into the Lean programming language over 11 days, working largely autonomously. The agents wrote roughly 13 million lines of Lean code and proved 29,500 intermediate theorems, out of 30,300 attempted, drawing on about 6 billion output tokens from a general-purpose internal research model Anthropic describes as roughly comparable to Claude Fable 5.1.
It is essential to be precise about what this represents. Fermat’s Last Theorem, the claim that no positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for any whole number n greater than 2, was first proved by British mathematician Andrew Wiles in 1995, a 129-page proof that took months of expert effort to verify. What Claude did was not prove a new theorem but formalize Wiles’s existing proof, following a later exposition by Henri Darmon, Fred Diamond and Richard Taylor, converting the human-readable mathematical argument into a form a computer can check step by step, with no gap left unstated. Formalization and original discovery are different accomplishments, and this is squarely the former.
Anthropic shared the resulting proof with Kevin Buzzard, the Imperial College London mathematician who has led a parallel, EPSRC-funded community effort to formalize the same theorem since 2024, a project on a five-year grant timeline. Buzzard called it “an extraordinary autoformalization achievement” that “proves Fermat’s Last Theorem with no assumptions other than the axioms of mathematics,” and said the result signals a genuine step toward automatically formalizing much of the modern mathematical literature.
He independently compiled Anthropic’s code himself and ran Lean’s standard checking tool over it to confirm it holds. But Buzzard’s fuller reaction, reflected in a blog post he titled “Anthropic has beaten me to it,” was more measured than the celebratory framing that dominated most coverage: on the underlying mathematics, he was clear the result “changes nothing,” since the theorem was already proven and accepted.
The achievement also rests heavily on prior work that Anthropic did not create. The formalization built on Buzzard’s own FLT blueprint project, Mathlib, the community’s foundational library of formalized mathematics, and Prove2Me, an open collaborative platform built by Anthropic researcher Tianyi Peng and collaborators at Columbia University specifically to help AI agents coordinate large-scale formalization work.
Anthropic’s own account describes early multi-agent attempts failing outright, with agents losing track of the project’s state and duplicating effort, roughly 7% of the final proof’s non-boilerplate lines came from these failed early attempts, until the team adopted Prove2Me’s shared dependency graph, which let agents track what had already been proven and work in parallel without stepping on each other.
What Verification, Not Discovery, Actually Buys
The genuine significance here is narrower and more practical than “AI proved a famous unsolved problem,” and it lies in speed and scale of verification rather than new insight. Checking a complex human-written proof for hidden errors traditionally takes specialist mathematicians months or years, precisely the ordeal Wiles’s own proof went through in 1993 when reviewers found a critical gap he spent a year repairing.
A fast, reliable formalization pipeline could compress that verification burden dramatically for future results, both human-authored and AI-generated, functioning less like a mathematical discovery and more like a very thorough calculator run over an already-completed argument. Buzzard’s own caveat is worth including directly: Lean itself has had soundness bugs discovered in it in the past, meaning a sufficiently capable or misdirected system could in principle exploit a flaw in the checker itself, a risk Buzzard says he specifically tested for by having an agent flag every line of the repository that touched Lean’s core logic.
As AI systems increasingly produce candidate mathematical results at a pace human reviewers cannot match, tools that speed up rigorous, mechanized checking may matter more for the field’s near-term integrity than any single formalized proof, however famous the underlying theorem.
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