Claude AI has made history by completing the first fully computer-verified proof of Fermat's Last Theorem in just 11 days, generating 13 million lines of code.
Key Developments
- Anthropic's Claude AI has completed a groundbreaking proof of Fermat's Last Theorem, marking the longest mathematical proof in history.
- The proof was generated in just 11 days, producing 13 million lines of code verified by a computer, overshadowing a human effort at Imperial College London that has been ongoing since 2024.
- Mathematician Kevin Buzzard, leading the human project, has confirmed the validity of Claude's proof based on fundamental mathematical principles.
Anthropic's Claude AI has made history by producing the first fully computer-verified proof of Fermat's Last Theorem, a problem that has stumped mathematicians for 358 years. This accomplishment, completed in a mere 11 days, generated an unprecedented 13 million lines of code that can be independently verified by a computer.
Fermat's Last Theorem states that no three positive integers can satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. Pierre de Fermat first noted this assertion in 1637, claiming to have a proof that was too lengthy to fit in the margin of his book.
For over three centuries, mathematicians attempted to reconstruct Fermat's purported proof. The theorem was finally proven in 1995 by British mathematician Andrew Wiles, who used advanced mathematical theories unavailable in Fermat’s time.
Understanding Mathematical Proofs
A mathematical proof involves a series of logical deductions, and any flaw in this reasoning can invalidate the entire proof. Historically, verifying such proofs has been a daunting task. For instance, a 1908 prize for a valid proof of Fermat's theorem attracted 621 incorrect submissions in its first year.
Last month, Claude achieved the first formalized proof of this theorem, utilizing advanced formalization techniques that convert mathematical reasoning into a computer-verifiable format.
Verifying a major mathematical proof can take years. Formalization can help facilitate this process.
— Anthropic (@AnthropicAI) September 4, 2026
Buzzard, who leads the human project at Imperial College London, has acknowledged Claude's proof, stating it adheres to the axioms of mathematics without assumptions. However, it is important to note that Claude has not developed new mathematical concepts; it has simply created a machine-checkable version of Wiles's earlier proof.
The success of Claude can be attributed to a collaborative effort among AI agents that generated definitions, proved smaller results, and integrated them into a cohesive proof with minimal human input. Despite initial challenges in tracking progress, the introduction of a tool called Prove2Me streamlined the process, allowing for efficient organization and reducing redundancy.
Claude's proof encompasses more than 30,000 supporting theorems, processing billions of tokens and exceeding five times the size of the existing shared library for mathematical work. To put this into perspective, the proof's length is equivalent to 160 novels filled with rigorous logical reasoning.
Significance of the Achievement
This milestone is particularly relevant as the mathematical community is increasingly confronted with unverified proofs, including those generated by AI. Formal proofs generated by computers are deterministic and less prone to human error, which enhances mathematical rigor. The entire 13-million-line proof is publicly available on GitHub for scrutiny by mathematicians.
