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# The first machine-checked proof of Fermat's Last Theorem took 11 days: 13 million lines, 30,000 theorems
- URL: https://globalfeed.ai/en/the-first-machine-checked-proof-of-fermats-last-theorem-took-11-days-13-million-lines-30-000-theorems/
- Published: 2026-09-04T19:41:41.000Z
- Updated: 2026-09-04T19:41:50.000Z
- Description: Anthropic says Claude formalized Fermat's Last Theorem end to end in Lean. It is the largest Lean proof ever written, and along the way it proved more than 29,000 other theorems in areas of mathematics that had never been formalized.
- Author: GlobalFeed Editor
- Tags: Anthropic, Claude, Lean, mathematics, Fermat, formalization, x-AnthropicAI, x-claudeai, x-XenaProject, dil-en, elle, video, x-gitti

Anthropic has announced that its model Claude produced the first end to end, computer checked proof of **Fermat's Last Theorem** in the **Lean** language, in a [research post dated 4 September](https://www.anthropic.com/research/formalizing-fermats-last-theorem?ref=globalfeed.ai). The proof follows a simplified version of the proof Andrew Wiles published in 1995.

The theorem was posed in the 17th century and was first proved only **more than 350 years later**, by Wiles in 1995\. Formalization is a separate job: turning mathematical reasoning into a form that proof assistants such as Lean can check line by line.

## The numbers

- **13 million lines** of Lean
- **30,300 theorems** proved, of which **29,500** were used in the final proof
- **11 days**
- Roughly **six billion output tokens**

The model used is described by Anthropic as "a general-purpose internal research model roughly comparable to Claude Fable 5.1". The full proof is [open on GitHub](https://github.com/anthropics/fermats-last-theorem?ref=globalfeed.ai).

## The human part

The project was initiated by **Tianyi Peng**, an Anthropic researcher whose group at Columbia University builds tools for AI formalization. According to Anthropic, "mathematical input from humans was limited to occasional high-level instructions from Tianyi".

The completed proof was reviewed by **Kevin Buzzard** at Imperial College London, whose community had been working on formalizing this theorem since 2024\. The work also drew on **Prove2Me**, an open collaborative platform for formalizing mathematics designed by Peng and his collaborators at Columbia.

Anthropic stresses that the work is built on "three centuries of mathematicians' work and the efforts of hundreds of contributors to Lean and Mathlib".

## The caveat the company states itself

Anthropic writes one limit plainly: Claude's proof is **over 5x the size of Mathlib** and "likely much longer than it needs to be". What came out is not the most elegant proof; it is a complete, working proof that a machine can verify.

## Why it matters

Checking whether a large mathematical proof is correct can take years. Formalization hands that burden to the computer: once a proof is translated into Lean, its correctness can be machine verified. Anthropic presents this as a step toward reducing "the burden of mathematical refereeing in an era when more proofs are being produced than ever before".

The more than 29,000 theorems proved along the way are a separate gain, since they sit in areas of mathematics that had never been formalized before and now form ground for future formalization work.