Poincaré conjecture fully formalized in Lean: 4.7M lines, AI wrote 2.7M in two weeks
新智元 · wechat · 2026-09-28
A four-person team led by UCSD professor Ben Chow (Yau Shing-Tung's student) has fully formalized the Hamilton–Perelman proof of the Poincaré conjecture in Lean: 4.7M lines of code, all passing the Lean kernel with zero sorries, of which 2.7M lines were produced in a two-week sprint with help from ChatGPT Astra and Claude Fable.
Only 660K lines trace back to Perelman's three papers (one-sixth of the dependency chain); the rest fills in mathematics Perelman left implicit — 1.09M lines of analysis and 770K of differential geometry, with the canonical neighborhood theorem alone consuming 2.72M lines. The team ran an AI-orchestrating-AI pipeline: a Claude "lead" agent held the mathematical line and reviewed work, a dispatcher agent split and assigned tasks, ephemeral agents wrote proofs, and Claude once decomposed a topology chapter into parallel task lines handed to OpenAI's Codex — with humans deciding what to prove and verifying that the Lean statements matched the mathematics. The authors see this as a preview of future mathematical research: human effort shifting from writing proofs to judging what should be proved and auditing AI output.
Related event: Poincaré Conjecture Fully Formalized in 4.7M Lines of Lean(3 posts)→
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