Claude agents have developed a fully computer-verified proof of Fermat's Last Theorem in just 11 days, marking a significant milestone in mathematical formalization.
In a remarkable achievement, Claude agents have successfully generated the first fully computer-verified proof of Fermat's Last Theorem in a mere 11 days, as revealed by Anthropic on September 4.
Formalizing significant mathematical proofs typically spans years, but utilizing computer proof assistants like Lean can significantly accelerate this process.
Last month, Claude accomplished the first formalized proof of Fermat’s Last Theorem, one of the most famous problems in mathematics.
— Anthropic (@AnthropicAI) September 4, 2026
Fermat's Last Theorem asserts that the equation aⁿ + bⁿ = cⁿ has no positive integer solutions for a, b, and c when n exceeds two. This conjecture was first proposed by Pierre de Fermat in 1637.
This achievement builds upon an established proof by Andrew Wiles published in 1995. Claude translated Wiles' mathematical arguments into a format that the Lean proof-checking system can validate stepwise.
How the Proof Was Developed
The initiative was spearheaded by Anthropic researcher Tianyi Peng, alongside a team at Columbia University focused on advancing mathematical formalization tools. According to their technical report, human contributors set the initial theorem formulation and established priorities.
The agents worked independently to record intermediate statements, verify each other's formulations, and construct the overall proof.
Utilizing the Mathlib library and resources from Imperial College London's FLT and flt-regular projects, the final implementation consisted of 106 files, with appropriate citations. Coordination among agents was maintained through the Prove2Me platform, allowing for the division of the task into manageable parts and enabling collaborative proof contributions.
Anthropic noted that Claude proved approximately 30,300 intermediate theorems, with around 29,500 included in the final output, culminating in a total of 13 million lines of code. This proof is regarded as the largest ever created within the Lean environment.
The internal model used for this experiment is similar to Claude Fable 5.1, generating approximately 6 billion output tokens.
Result Validation
The complete code and replication instructions are publicly accessible on GitHub. Documentation confirms that the proof has been validated by Lean, as well as by an independent verifier named nanoda, ensuring that the final statement corresponds with Fermat's theorem as articulated in Mathlib.
Importantly, the proof relies solely on three standard axioms of Lean, with no unproven placeholders included. The reliability of the outcome depends on trust in the verification systems employed.
Mathematician Kevin Buzzard from Imperial College London, who is also formalizing the theorem, confirmed the successful verification of the proof on his blog. He expressed enthusiasm for the potential of automated formalization tools to enhance scientific research and highlight logical inconsistencies.
"I compiled the codebase and ran the comparator — the verification was successful," Buzzard noted.
Buzzard intends to continue his project, which will focus on formalization, improving Mathlib, and developing educational documentation on the modern proof. Claude's work was based on prior methodologies related to the theorem.
In a related note, Claude Mythos Preview previously assisted researchers in identifying cryptanalytic vulnerabilities in the post-quantum signature scheme HAWK and a reduced semi-round version of AES-128, although the latter did not apply to the complete ten-round version of the cipher.
