Anthropic stated that Claude has completed the first full formal proof of Fermat's Last Theorem. This is not a rediscovery of the theorem, but rather a transcription of the existing proof into logical code that a computer can verify line by line. The company said the project took 11 days and ultimately generated approximately 13 million lines of content.
The significance of formal proof lies in expressing mathematical arguments in a language that machines can verify. Traditional paper proofs often require extensive peer review over long periods, and if a flaw is found in any step, correcting it can take months or even years. Andrew Wiles, a British mathematician, completed the proof of Fermat's Last Theorem in 1995, but converting this entire proof into a fully machine-checkable version has long been regarded as an intensive engineering endeavor.
Achieve long-term project goals in 11 days
Since 2024, mathematician Kevin Buzzard from Imperial College London has been leading a project with the same goal: translating Wiles’s proof into the Lean proof assistant. As originally planned, this effort requires long-term collaboration, with funding secured through 2029.
Anthropic stated that Claude completed this task ahead of schedule compared to similar objectives. After review, Buzzard confirmed that this proof holds without relying on additional assumptions, verifying it solely based on the most fundamental axiomatic system of mathematics.
Completed in parallel by multiple agents
According to Anthropic, a research team led by Tianyi Peng at Columbia University enabled multiple Claude agents to work in parallel, each responsible for writing definitions and proving smaller conclusions, which were then gradually assembled into larger proof structures. Human intervention was minimal, primarily limited to providing阶段性 priority orders.
Early progress was not smooth. Anthropic reported that some agents were initially unable to share completed work and would duplicate efforts. Later, the team used a tool called Prove2Me to provide all agents with a unified task list and file organization system, while retaining natural language notes to help them reuse each other’s results.
- More than 30,000 supporting theorems
- Total consumption has reached billions of tokens.
- Final proof of approximately 13 million lines
Focus on verifiability rather than new theorems.
The focus of this achievement is not on discovering new mathematical theorems, but on transforming existing major proofs into versions that can be gradually verified by computers. As the number of mathematical papers and AI-generated content increases, the cost of manually checking each proof is rising, making formalization tools increasingly important.
Anthropic also stated that the proof is more than five times larger than Mathlib, the commonly used shared library in the mathematics community. The full document has been uploaded to GitHub, allowing researchers to continue reviewing its structure and correctness line by line.