Formalizing Fermat's Last Theorem
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Anthropic's Claude formalized Fermat's Last Theorem in Lean, producing 13 million lines of code in 11 days. This machine-checked proof confirms Wiles's 1994 result, marking a leap in AI-driven formal.
背景
Fermat's Last Theorem, proposed in 1637, states no whole numbers satisfy a^n + b^n = c^n for n>2. Andrew Wiles proved it in 1994 after seven years of work, but his 129-page proof was not machine-checkable. Formalization converts such proofs into a language computers can verify, eliminating human error. Since 2024, a community effort led by Kevin Buzzard at Imperial College has been working to formalize FLT in Lean, a project expected to take years. Anthropic's Claude accomplished this in 11 days using a multi-agent platform called Prove2Me, producing the largest Lean proof ever.
来龙去脉
- 1994Andrew Wiles proves Fermat's Last Theorem after seven years of work; the proof is later published in 1995.
- 2004 -2024Freek Wiedijk lists FLT as a formalization challenge; Kevin Buzzard's team begins a multi-year Lean formalization effort in 2024.
- Sep 4, 2026Anthropic publishes 'Formalizing Fermat's Last Theorem,' announcing Claude's complete machine-checked formalization in Lean, built on Mathlib and existing projects.
- Sep 5, 2026News outlets report the achievement; prediction markets spike to 99% for a formalized proof by 2029, and mathematicians like Buzzard praise the result.
各方怎么说
- Official
- Anthropic states Claude produced an end-to-end, machine-checked formalization of Fermat's Last Theorem in Lean, built openly on existing work.
- Expert
- Kevin Buzzard calls it 'a major step toward the automatic formalization of modern mathematical literature,' noting the proof is multi-layered.
- Caution
- Some observers note the result is a formalization of Wiles's known proof, not new mathematics, and Anthropic's process claims are not independently verified.
待核实
Anthropic's claims of 11 days, ~6B tokens, and dozens of agents are not independently verified; the formalization's correctness is machine-checked but the process details are company-reported.