Sunday Sep 6
RESEARCHAnthropic

Claude Checked Fermat's Proof In 11 Days

4SEP
THE MARGIN13M LINES

Mathematicians expected years of work. Claude wrote 13 million lines of Lean, a proof-checking language, and delivered the first computer-verified proof of Fermat's Last Theorem.

Anthropic researcher Tianyi Peng set dozens of Claude agents on the problem. They proved 30,300 intermediate theorems and burned six billion tokens. Human input was a few one-line nudges like push Mazur to be done soon.

Kevin Buzzard at Imperial College London has led the community effort since 2024. He reviewed the result and called it extraordinary. His bigger point: machine-written proofs are now solid enough to build on.

The first attempts failed. Agents lost track of the project and stopped coordinating. It worked once they moved to Prove2Me, a shared board tracking which theorem to attempt next.

full brief & sources

⚡ Why this matters

  • Verifying a big proof used to take human referees months or years. That bottleneck just got much cheaper.
  • This is the clearest public evidence yet that a swarm of agents can hold one long task together for eleven days.
  • The scaffold, not the model, was the unlock. That is the transferable lesson for anyone building agent systems.

🔍 What happened

  • Anthropic published the result on September 4 and put the full Lean proof on GitHub.
  • Claude produced 13 million lines of Lean and computer-verified proofs of 30,300 theorems, using 29,500 in the final chain.
  • The proof is over 5x the size of Mathlib, the community library it builds on.
  • It follows the Darmon, Diamond and Taylor exposition of Andrew Wiles' 1995 proof. Lean checked it using only its three standard axioms.
  • About six billion output tokens came from an internal research model roughly comparable to Claude Fable 5.1.
  • A separate test formalized Vinogradov's Three Primes Theorem in three days using three personal Claude Max plans.

💬 Smart takes

  • Kevin Buzzard, Imperial College London: "This extraordinary autoformalization achievement... proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics."
  • Buzzard, on what comes next: autoformalization will root out errors in the existing mathematical corpus and lighten the load on referees.
  • Anthropic, on the limit: what is novel here is the verification, not the mathematics. No new result was found.
  • Skeptic: the target was a proof that already existed, with an 86-page community blueprint and a partially built Lean scaffold. That is a very different job from proving something nobody has proved.

🧭 Where this goes

  1. Likelyformalized proofs start shipping alongside AI-generated math papers as standard practice within a year.
  2. LikelyProve2Me-style shared task graphs get copied into non-math agent systems. The DAG is the memory fix.
  3. Possiblea journal announces it will accept a Lean artifact in place of part of human peer review.
  4. Possiblesomeone finds a genuine error in a published theorem using this technique, and it makes news.
  5. Wild Cardan AI-generated novel theorem ships with its own machine-checked proof inside 18 months, and nobody can argue about whether it is correct.

🥄 The Spoon Take

The headline is the theorem. The lesson is the scaffold. Claude's first attempts failed because agents forgot the plan and stopped talking to each other. A shared task graph fixed it. If you are building anything multi-agent, that is the whole finding: the model was already good enough, the coordination layer was not.

🤔 Pushback

Formalizing a known proof with an existing blueprint is a search problem, not a discovery problem, and the token bill was enormous.

·Anthropic - Formalizing Fermat·GitHub - Full Lean proof·SiliconANGLE - Coverage