Anthropic Uses Claude to Formalize Proof of Fermat's Last Theorem
Anthropic has used Claude to create a 13-million-line computer-verifiable proof of Fermat's Last Theorem, completing in 11 days a task mathematicians expected to take years.
Fermat's Last Theorem, first proposed in 1637, concerns the properties of positive whole numbers. Its proof was developed by mathematician Andrew Wiles in 1995, running 129 pages and taking months to verify. Anthropic's project formalized Wiles's proof, turning it into a form that can be automatically checked by computers. Formalizing proofs eliminates the risk of human error and makes it easier for mathematicians to share and build on each other's work.
The formalized proof takes the form of code written in Lean, a specialized programming language used by mathematicians to verify hypotheses. Anthropic's version comprises 13 million lines of Lean code, the largest file of its kind ever created.
Formalization is a difficult process because proofs tend to be terse and omit explanations a computer would need. Mathematicians had expected the work to take several years. According to Anthropic, its researchers completed it in 11 days using an internal research model described as roughly comparable to Claude Fable 5.1, the immediate predecessor of GPT-6 Astra. The model needed only limited high-level human input, spawned several dozen agents that generated 6 billion tokens of output, and proved at least 29,500 intermediate theorems along the way.
Anthropic's first attempt was unsuccessful. The breakthrough came when the company gave Claude access to an open-source tool called Prove2Me, which helps AI agents decide the best next step in a lengthy workflow and lowers inference costs.
"We see autoformalization of algebra, harmonic analysis, geometry and number theory, and we learn that AI autoformalization artefacts are now robust enough to be built upon; the proof is multi-layered," said Kevin Buzzard, a mathematician whose work Claude used for the formalization.
The milestone follows an announcement a month earlier in which Anthropic used Claude to discover new information about the Riemann zeta function, the focus of the Riemann hypothesis. Rival OpenAI has also used its latest Astra model to solve several Erdos problems and narrow open questions in theoretical computer science.