Claude proves Fermat's Last Theorem – generating 13 million lines of Lean code
Anthropic has announced that its AI model, Claude, has created the first machine-verified proof of Fermat's Last Theorem using 13 million lines of Lean code.
What happened?
On 4 September 2026, Anthropic announced that its AI model, Claude, has completed a fully machine-verified formalisation of Fermat's Last Theorem. Claude worked largely autonomously for 11 days, generating approximately 13 million lines of code in the proof assistant Lean 4. This is the first complete machine-verified proof of the historic theorem.
Key facts
| Offentliggjort datum | 4 september 2026 |
|---|---|
| Tidsåtgång | 11 dagar |
| Kodvolym | 13 miljoner rader Lean 4-kod |
| Utvecklare | Anthropic |
”Checking that a major mathematical proof is correct can take years. Formalization—converting the mathematical reasoning into a form computer proof assistants like Lean can verify—guarantees mathematical correctness.”
Why it matters
Verifying large mathematical proofs manually often takes several years. By converting mathematical reasoning into code in verification systems such as Lean 4, computers can automatically check for correctness. Claude demonstrates that AI models can now perform advanced logical formalisation and code generation over several consecutive days with minimal human guidance.
Who is affected?
The result is primarily of interest to mathematics researchers, AI developers, and experts in formal verification. It paves the way for AI to be used in automating the verification of extremely complex mathematical proofs that would otherwise take human experts years to validate.
Impact on the EU
The work and the code for the machine-verified proof have been published globally by Anthropic and are available to researchers and developers within the EU without restrictions.
What else you should know
The code base amounts to approximately 13 million lines of Lean 4 code. Anthropic has published the research findings and the code openly so that other mathematics researchers and developers can review and build upon the proof.
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