Did Claude actually prove Fermat's Last Theorem?

Not in the sense of discovering a new proof. The theorem was first proved by Andrew Wiles in 1995. Claude completed the first full formalization of that proof — translating it into roughly 13 million lines of Lean code that a computer can verify line by line, with no human shortcuts.

What does it mean to formalize a proof in Lean?

Lean is a proof assistant that checks mathematical arguments algorithmically. A formalized proof spells out every logical step, so the computer can confirm each inference follows from the axioms — turning 'this looks right to expert readers' into machine-verified certainty.

How did Claude finish in 11 days when mathematicians planned for years?

Anthropic ran dozens of collaborating Claude agents on Prove2Me, an open platform that tracks which theorems are proved and which are still needed. Roughly six billion output tokens later, Lean checked the completed proof. Human input was limited to occasional high-level guidance.

Where can I see the proof?

Anthropic published the full Lean proof and a written walkthrough on GitHub at github.com/anthropics/fermats-last-theorem, alongside its research write-up.

Claude Formalized the Proof of Fermat's Last Theorem in Lean — What It Means

Anthropic says Claude worked largely autonomously for 11 days to produce the first complete computer-checked proof of Fermat's Last Theorem, written in Lean. Here is what Claude actually did, how the multi-agent effort worked, and why formalization matters.

Anthropic announced on September 4, 2026 that Claude, working largely autonomously over 11 days, produced the first complete computer-checked proof of Fermat’s Last Theorem — written in the Lean programming language. This is not a new human-style proof of the theorem; Andrew Wiles’s 1994 proof remains the mathematical breakthrough. What Claude delivered is something different: the first end-to-end translation of that proof into a form a computer can verify step by step, with no step left to human judgment.

What Claude actually did

In 11 days Claude wrote roughly 13 million lines of Lean, proved about 30,300 intermediate theorems along the way, and used around 29,500 of them in the final proof — a body of code more than five times the size of Mathlib, the main community library of formalized mathematics, according to Anthropic’s research post. The finished proof was checked by Lean and uses only Lean’s three standard axioms, and a comparator confirmed that the theorem statement Claude proved matches Mathlib’s own statement of Fermat’s Last Theorem.

The project follows a simplified version of Wiles’s proof based on the exposition by Darmon, Diamond, and Taylor. Human mathematical input was deliberately small: Anthropic researcher Tianyi Peng, who designed the effort, mostly gave high-level instructions such as which theorems to prioritize. Kevin Buzzard of Imperial College London, who leads a separate multi-year community project to formalize Fermat’s Last Theorem, reviewed the result and called it an “extraordinary autoformalization achievement.”

How a multi-agent team stayed on track

Claude did not succeed on the first try. Anthropic says early agents made progress but quickly lost track of the project’s state and stopped collaborating effectively; those failed attempts contributed only about 7% of the non-boilerplate lines in the final proof. The turning point was switching to Prove2Me, an open collaborative platform designed by Peng and collaborators at Columbia University. Prove2Me maintains a directed acyclic graph of theorem statements so agents can see what is proved and what to attempt next, separates theorem statements from proofs to speed up compilation, and keeps natural-language descriptions so agents can find and reuse results.

The full run consumed about six billion output tokens from a general-purpose internal research model roughly comparable to Claude Fable 5.1. Anthropic also ran a small follow-up experiment in which three personal Claude Max plans, collaborating entirely through Prove2Me, formalized Vinogradov’s Three Primes Theorem in three days.

Why this matters beyond one theorem

The significance is less about Fermat and more about verification. Human review of long proofs can take years — Wiles’s own proof took months of checking and initially contained a gap. If AI can formalize large modern proofs quickly, referees gain a tool to check LLM-produced mathematics rigorously, and errors in the existing mathematical corpus become easier to root out. Buzzard told Anthropic that if automatic formalization of Fermat’s Last Theorem is possible now, the field has taken a big step toward automatic formalization of the modern mathematical literature.

What this means for desktop AI users

Long-running, multi-agent work like this is a preview of what autonomous AI can do when it has a stable task structure, clear state, and a way to verify its own progress. The same principle applies on a smaller scale to everyday agent tasks: an agent is only as trustworthy as the boundaries and checkpoints around it. A desktop client such as MOOGH gives you that structure locally — files, approvals, and history stay on your machine while the model does the heavy lifting.

Want to see agentic work with clear boundaries on your own PC? Download MOOGH for Windows and put a capable model to work on your files.

Anthropic's Claude Completed the First Machine-Checked Formalization of Fermat's Last Theorem in 11 Days

What Claude actually did

How a multi-agent team stayed on track

Why this matters beyond one theorem

What this means for desktop AI users

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