Artificial Intelligence
Anthropic says Claude formalises Fermat's Last Theorem proof
Anthropic said Claude completed a Lean formalisation of Fermat’s Last Theorem in 11 days, and said the proof was checked by Lean after earlier attempts failed and the workflow changed.
- Anthropic said Claude completed a formalisation of Fermat’s Last Theorem in Lean in 11 days.
- The company said the system worked largely autonomously, with only occasional high-level instructions from Tianyi Peng.
- Anthropic said the finished proof contained 13 million lines of Lean and 29,500 intermediate theorems, and that Lean checked it.
- The article said the effort succeeded after Anthropic switched to Prove2Me and a Claude Code-based multi-agent harness.
Anthropic said Claude had completed a Lean formalisation of Fermat’s Last Theorem in 11 days, with little direct human input. The company said it was sharing what it called a computer-checked proof and said the result had been checked by Lean.
The article traced the theorem to Pierre de Fermat’s 1637 note and said Sir Andrew Wiles published the first correct proof in 1995 after a verification gap was found in 1993. It said Jan Bergstra later proposed formalising Wiles’s proof, and that Kevin Buzzard started a community effort in 2024 to complete the work in Lean.
Anthropic said Tianyi Peng set out to test whether Claude could formalise the theorem, and that early attempts failed when agents lost track of the project. The company said the effort then succeeded after it moved to Prove2Me and a Claude Code-based multi-agent harness.
Anthropic said the finished proof had 13 million lines of Lean code and 29,500 intermediate theorems, and that it used Lean’s three standard axioms. It said it shared the proof with Buzzard, who said the result showed autoformalisation could be built on, and the company said the proof and walk-through were available on GitHub.
Named in this story
People
- Tianyi Peng
- set out the test and gave Claude high-level instructions
- Kevin Buzzard
- reviewed the proof and led a community formalisation effort
- Pierre de Fermat
- wrote the original statement in 1637
- Sir Andrew Wiles
- published the first correct proof in 1995
- Jan Bergstra
- proposed formalising Wiles’s proof
Companies
- Anthropic
- said Claude produced the proof and published the account
Organisations
- Imperial College London
- hosted the community FLT formalisation effort
- Columbia University
- was where Peng’s group built AI formalisation tools
Products and systems
- Claude
- carried out the Lean formalisation largely autonomously
- Lean
- checked the proof mechanically
- Prove2Me
- provided the collaborative platform used to finish the work
- Claude Code
- formed part of the multi-agent harness
- Mathlib
- supplied the theorem statement and supporting library
How the source tells it
The source read like a celebratory company announcement, using technical detail to support claims of novelty, scale and future value in mathematical verification.
- vendor boosterism The piece repeatedly framed the result as a landmark achievement and repeated the company’s own claims without outside challenge.
- triumph Celebratory status updates and victory-style language were used to present the run as a successful conquest.
- novelty The story leaned on first-ever and largest-ever claims to cast the work as a unique advance.
- reassurance Future benefits for checking mathematics and reducing refereeing were asserted as likely outcomes.