Key facts
- Anthropic's Claude AI has produced a computer-checked proof of Fermat's Last Theorem.
- The proof, generated in 11 days, is the longest mathematical proof ever created.
- Fermat's Last Theorem, stated in 1637, was unsolved for 358 years until Andrew Wiles's proof in 1995.
- Mathematician Kevin Buzzard verified the AI's proof using basic logical rules.
- The AI's proof is significantly longer than Andrew Wiles's original 129-page proof.
Anthropic's AI model, Claude, has successfully generated a formal, computer-checked proof for Fermat's Last Theorem, a mathematical challenge that had eluded mathematicians for 358 years. The AI completed this monumental task in just 11 days, producing a proof that spans 13 million lines, making it the longest mathematical proof ever created. This achievement significantly outpaces a human-led project at Imperial College London, which has been working on formalizing the same proof since 2024 and is far from completion.
Fermat's Last Theorem, first posited by Pierre de Fermat in 1637, states that no three positive integers a, b, and c can satisfy the equation aⁿ + bⁿ = cⁿ for any integer value of n greater than 2. Fermat claimed to have a proof but did not record it, leaving subsequent mathematicians to attempt its reconstruction for centuries.
The process of formalizing a mathematical proof involves translating complex reasoning into a language that a computer can verify step-by-step, eliminating the potential for human error or subjective interpretation. This is crucial as checking lengthy proofs can take mathematicians years. Andrew Wiles eventually provided the first valid proof in 1995, which was later corrected and published in a 129-page document. However, Wiles's proof relied on advanced mathematics not available in Fermat's time, leading many to doubt Fermat's original claim.
Kevin Buzzard, a mathematician leading the human project at Imperial College London, reviewed Claude's proof and confirmed its validity, stating it adheres strictly to the fundamental axioms of mathematics. The AI's proof is not a discovery of new mathematics but rather a machine-verifiable validation of Wiles's existing theorem. This capability is becoming increasingly important as AI can generate proofs faster than humans can check them, addressing a growing backlog of unverified mathematical work.