Source: https://www.anthropic.com/research/formalizing-fermats-last-theorem Published: Sep 4, 2026 Fetched: 2026-09-06
Source text (verbatim extract)
We are sharing the first complete computer-checked proof of Fermat's Last Theorem. Claude worked largely autonomously over 11 days to write the proof in the Lean programming language. Below, we describe how the formalization was done and share some thoughts about what this work could mean for research mathematics.
Around 1637, Pierre de Fermat jotted down a claim in the margin of his copy of Diophantus's Arithmetica that would become one of the most famous mathematical conjectures of all time: no positive integers a, b, c satisfy aⁿ + bⁿ = cⁿ for any n > 2. Fermat's Last Theorem (FLT), as the conjecture became known, turned out to be incredibly difficult to prove. The first proof, from Sir Andrew Wiles in 1995, ran to 129 pages and required months of painstaking work to verify.
Recently, Tianyi Peng, an Anthropic researcher whose group at Columbia University builds tools for AI formalization, set out to test whether Claude could make progress on formalizing FLT. The result went further than he expected. In 11 days, working largely autonomously, Claude produced the first end-to-end, computer-checked proof of FLT. Along the way, it wrote 13 million lines of Lean and proved 29,500 intermediate theorems.
We shared the resulting proof with Kevin Buzzard, who said:
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. Along the way we see autoformalization of algebra, harmonic analysis, geometry and number theory, and we learn that AI autoformalization artefacts are now robust enough to be built upon; the proof is multi-layered.
Claude completed the proof in 11 days, producing computer-verifiable proofs of 30,300 theorems along the way (using 29,500 in the final proof). Dozens of Claude agents collaborated to define concepts, prove intermediate theorems, and use those theorems to prove ever harder statements. At 13 million lines of Lean code, Claude's proof is over 5x the size of Mathlib, the principal community library of mathematical proofs this theorem builds on.
A number of Claude's initial attempts failed: while agents had some early success, they quickly lost track of the project's state and stopped collaborating effectively. Their failed efforts contributed ~7% of the non-boilerplate lines in the final proof.
The effort succeeded when we switched to using Prove2Me, an open collaborative platform for formalizing mathematics designed by Tianyi Peng and his collaborators at Columbia University. Prove2Me helped by:
- Maintaining a directed acyclic graph (DAG) of theorem statements that agents used to decide what proofs they should attempt next. This was particularly helpful for mitigating memory degradation and allowing multiple agents to work in parallel.
- Speeding up Lean compilation and minimizing resource consumption by separating theorem statements and proofs into different files, with the links between them maintained independently.
- Enabling search and reuse by maintaining a natural-language description of each theorem statement, resulting in a simpler proof path.
With Prove2Me and a Claude Code-based multi-agent harness, a team of agents completed the proof in a little under two weeks, consuming about six billion output tokens from a general-purpose internal research model roughly comparable to Claude Fable 5.1. The finished proof was checked by Lean; it uses just Lean's three standard axioms, and a comparator confirmed that the theorem's statement matches Mathlib's own statement of FLT.
Mathematical input from humans was limited to occasional high-level instructions from Tianyi: "Jacobian as a scheme sounds high priority," "push [the] Mazur [theorem] to be done soon."
Writing Lean also seems to help Claude prove novel results. Many of our recent Claude-authored results have been formalized in parallel with their proofs, and Claude appears to use these partial proofs to independently check its hypotheses much like it writes numerical simulations to check that it's on the right track.
Formalizing FLT was a token-intensive project, but it is also the largest Lean proof ever constructed. Anthropic researchers did a small experiment using three personal Claude Max plans to formalize applications of the Hardy-Littlewood Circle Method. Collaborating entirely through Prove2Me, the agents jointly completed a formalization of Vinogradov's Three Primes Theorem in just three days. We think with the right scaffold, collaborative formalization of major results with consumer AI subscriptions is achievable.
Related paper cited: Chen, S., Marwaha, K., Lu, X., Yuen, H., & Peng, T. (2026). Prove2Me: An open collaborative platform for scaling math formalization. arXiv. https://doi.org/10.48550/arXiv.2608.28433
The full proof is available on GitHub along with a written walk-through of the proof.