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Anthropic's Claude Formalizes Fermat's Last Theorem in Lean

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TL;DR

  • Anthropic's GitHub repository credits 106 upstream files to Imperial College London's FLT project and Mathlib, undercutting the autonomous framing in the press release.
  • Claude's first formalization attempt failed; success required adding Prove2Me, a third-party open-source tool for optimizing AI agent decisions in long workflows.
  • The 11-day wall-clock time reflects massive parallelism: several dozen agents generating 6 billion tokens, not a single sustained agent effort.

Anthropic says Claude produced the first end-to-end, computer-checked proof of Fermat's Last Theorem in the Lean programming language over 11 days, working largely autonomously. According to Anthropic's research post, the run generated 13 million lines of Lean code, proved 30,300 theorems (29,500 of them used in the final proof) and consumed roughly six billion output tokens. Lean verified the result using only its three standard axioms.

"This extraordinary autoformalization achievement, which Anthropic researchers say only took 11 days, proves Fermat's Last Theorem with no assumptions other than the axioms of mathematics," writes Kevin Buzzard, the Imperial College London mathematician who reviewed the proof. He goes further: "If the automatic formalization of FLT is possible now, then we have taken a big step towards automatic formalization of the modern mathematical literature."

The work was assembled on Prove2Me, which Anthropic describes as "an open collaborative platform for formalizing mathematics designed by Tianyi Peng and his collaborators at Columbia University." Peng is an Anthropic researcher whose Columbia group builds tools for AI formalization. Prove2Me maintains a directed acyclic graph of theorem statements and coordinates multiple Claude agents against it. The finished artifact runs roughly five times the size of Mathlib, the community library the proof builds on. A companion run formalized Vinogradov's Three Primes Theorem in three days using consumer Claude Max plans.

The proof follows a simplified version of Andrew Wiles's 1995 argument, tracing an exposition by Henri Darmon, Fred Diamond and Richard Taylor. The claim comes from Anthropic itself and one named external reviewer; no third-party replication is described. It lands amid heavy Anthropic coverage this quarter, one of 335 Anthropic items we have tracked in the last 90 days, and moved through the mathematical corners of that beat faster than most releases.

What others are reporting

Coverage cluster as of 8h after publish

  1. GitHub (Anthropic) Read →

    First-party repository reveals triple-verification methodology, Apache 2.0 license, and 106 files with explicit upstream credits to Imperial College London and Mathlib contributors.

    Research artifact. Not maintained and not accepting contributions.
  2. SiliconANGLE Read →

    Reports Anthropic's first attempt failed; the breakthrough came only after giving Claude access to Prove2Me, an open-source tool for optimizing agent decisions in long multi-step workflows.

    Anthropic's proof comprises 13 million lines of Lean code, which makes it the largest-ever file of its kind.
  3. Lean Lang Read →

    The Lean community's own framing attributes the formalization to Buzzard's project and positions FLT as the final entry on Freek Wiedijk's 100-problem challenge list, with no mention of Claude.

    The project shows how Lean can handle extremely complex mathematical assertions that span thousands of pages of informal mathematics.
  4. DEV Community Read →

    A technical fact-check that separates Claude's Riemann zeta work from the FLT formalization and argues Anthropic's press framing conflates AI-assisted drafting with autonomous formal proof.

    Claude has demonstrated progress on a mathematics-related formalization task. It does not establish that Claude independently completed the Lean formalization of FLT.
  5. Crypto Briefing Read →

    Frames the achievement as a stress-test of AI reasoning beyond standard benchmarks and contextualizes it within the theorem-proving community's long-term goal of fully auditable machine-checked proofs.

    Every logical step gets encoded in a programming language designed for mathematical reasoning, and a computer checks each one independently.

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Originally reported by anthropic.com

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Original headline: Anthropic Says Claude Autonomously Formalized Fermat's Last Theorem in Lean Over 11 Days