Claude AI Wrote 13 Million Lines of Code for Fermat Proof

Anthropic used its Claude artificial intelligence system to produce a version of Fermat's Last Theorem that a computer could verify from beginning to end. The work was completed in 11 days with virtually no human oversight. The final proof consists of 13 million lines of Lean code. The company initially expected the project to take several years.

Mathematician Pierre de Fermat proposed Fermat's Last Theorem in 1637. Andrew Wiles wrote the first complete mathematical proof of the theorem in 1995. That proof was 129 pages long. During formalization, the mathematical logic in the proof is converted into code that a computer can verify. This allows the program to check separately whether each step is correct.

During the process, Claude agents—artificial intelligence programs that perform tasks on their own—proved approximately 30,300 separate theorems. Of these, 29,500 were included in the final version. People only occasionally provided general guidance for the work and did not write the code themselves. Lean, a language developed for mathematicians, made it possible to verify the entire proof by computer.

Anthropic tested the formalization several times before achieving a successful result. When standard and repetitive sections of code were excluded, the earlier attempts amounted to approximately 7% of the final proof. The resulting code is more than 5 times larger than the main community library called Mathlib. Mathematician Kevin Buzzard said the proof is based solely on mathematical axioms and can be used in future research.

An open-source program called Prove2Me also played a role in achieving the result. The tool helps artificial intelligence agents choose the next useful step during long, multistage research. It also reduces the cost of the computing resources required. Anthropic has also expanded free access, research credits and grants for mathematicians working on formalization projects.

The work was published 1 month after Anthropic announced another result related to the Riemann zeta function. That function lies at the heart of the Riemann hypothesis, considered one of mathematics' most difficult and still-unsolved problems. OpenAI is also using its Astra model to work on several classic Erdős problems. Nevertheless, the fact that the process took 11 days shows that full formalization is a major undertaking even for powerful artificial intelligence systems.