anthropic.com web signal

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

By Published Updated
5 sources tracking this story
Anthropic Generative AI ai-research

TL;DR

  • Claude ran several dozen parallel agents generating 6 billion tokens; the 11-day figure is wall-clock time, not the output of a single sustained agent.
  • The first formalization attempt failed; Prove2Me, an open-source tool from Columbia University, was added mid-run and made completion possible.
  • Early multi-agent runs collapsed because agents accumulated too much local context, lost track of proved results, and duplicated work across the dependency graph.

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 24h after publish

  1. SiliconANGLE Read →

    Places the achievement in direct competition with OpenAI's Astra solving Erdos problems; notes mathematicians expected formalization to take several years.

    Mathematicians expected the process of formalizing Wiles' proof to take several years...completed the task in 11 days
  2. Data Studios Read →

    Focuses on systems architecture: the orchestration layer of shared dependency graphs and distributed compilation was as important as raw model capability.

    Claude did not discover Fermat's Last Theorem or replace Andrew Wiles's 1995 mathematical breakthrough.
  3. GetAIBook Read →

    Argues formalization is the least forgeable AI evaluation task because the Lean compiler accepts or rejects with no middle ground, making benchmark inflation impossible.

    A Lean proof does not accept plausible-sounding arguments; the compiler either verifies or rejects it.
  4. AIToolly Read →

    Traces the historical arc from Fermat's 1637 marginal note through Wiles's 1995 proof, framing this as a shift to machine-checked proof standards across mathematics.

    Claude completed the end-to-end, computer-checked proof in 11 days, producing 13 million lines of Lean code and proving 29,500 intermediate theorems.

Shared on Bluesky by 5 AI experts

Originally reported by anthropic.com

Read the original article →

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