Anthropic indicates that Claude has completed the first complete 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 can be verified line by line by computers. The company stated that this work took 11 days and ultimately resulted in approximately 13 million lines of code.
The significance of formal proof lies in writing mathematical arguments in a language that machines can check. Traditional paper proofs often require lengthy reviews by peers, and if there is a flaw in any step of the process, the correction may take months or even years. Fermat's Last Theorem was proven by the British mathematician Andrew Wiles in 1995, but transforming this proof into a fully machine-verifiable form has always been considered a highly challenging task.
Achieve long-term project goals in 11 days
A mathematician from Imperial College London, Kevin Buzzard, has been promoting related projects since 2024, with the same goal of transcribing the proof of Wiles into the Lean proof assistant. According to the original plan, this work requires long-term collaboration, and funding has been arranged until 2029.
According to Anthropic, Claude completed a similar task ahead of schedule. After review, Buzzard stated that this proof can be established without relying on any additional assumptions, that is, it can be verified based solely on the most fundamental axiomatic systems of mathematics.
Completed in parallel by multiple proxies
According to Anthropic, a team led by researcher Tianyi Peng from Columbia University had multiple Claude agents working in parallel, each responsible for writing definitions and proving smaller conclusions, which were then gradually pieced together to form a larger proof structure. There was minimal human intervention; the main role of the researchers was to determine the priority order for each stage of the process.
Early progress was not smooth. Anthropic mentioned that some agents were unable to share completed work at one point, which led to duplicate efforts. Subsequently, the team used a tool named Prove2Me to provide a unified task list and file organization method for each agent, while also retaining natural language notes to help them reuse each other's results.
- More than 30,000 supporting theorems
- The total consumption reaches several billion token.
- Ultimately, it was proven to be about 13 million lines.
The focus is on verifiability rather than new theorems.
The focus of this achievement is not on discovering entirely new mathematical propositions, 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 also rises, which is why formalization tools have gained more attention.
Anthropic It is also mentioned that the scale of this proof has exceeded more than 5 times that of the commonly used shared library Mathlib in the mathematical community. The complete file has been uploaded to GitHub, and researchers can continue to review its structure and correctness line by line.
