mathlib

Headlines · 3

1. 5d
   Team completes Lean formalization of Thurston geometrization conjecture in 4.7M lines

   A team led by Princeton scholar Ayush Khaitan, working with NVIDIA's Humanfia team, says it has completed a full Lean formalization of the Thurston geometrization conjecture. The project spans roughly 4.7 million lines of code, about 2.7 million of which were added in around two weeks on top of roughly 2 million lines of prior work by Chow, Liao and Qin, and it has been open-sourced on GitHub. The team includes Bennett Chow, a Yau Shing-Tung student and UC San Diego professor, plus formalization leads Ziyang Qin and Yuan Liao; Stanford mathematician Jared Duker Lichtman publicly called the work amazing. The report notes that the geometrization conjecture is broader than the Poincaré conjecture, which Perelman proved as a byproduct, but NVIDIA has not disclosed the details of AI's role, and much of the article's account is inference.

   36氪 人工智能 · 🔥 0
2. Oct 9
   What mathematicians should know about Lean: reliability, soundness bugs and AI

   In a guest post on Terence Tao's blog, Thomas Hales surveys formalization and the Lean theorem prover, arguing that autoformalization became a practical reality in 2026: milestones cited include Math Inc.'s autoformalization of the 24-dimensional sphere-packing problem, Meta's ATLAS textbook project, Anthropic's 13 million lines of Lean for Fermat's Last Theorem in 11 days, and OpenAI's Lean formalization alongside its Navier-Stokes announcement. He also examines Lean's 2026 "Summer of Soundness Bugs" — one bug yielded an illicit disproof of the Collatz conjecture — which were found by security researchers using frontier models, quickly patched, and followed by re-verification of mathlib. Hales stresses that Lean proofs must be kernel-checked and then human-audited for statement fidelity.

   Hacker News · AI（100+ 分） · 🔥 0
3. Oct 7
   AI-assisted Lean proof of optimal packing for 11 squares passes verification

   A GitHub repository reports that a complete optimality proof for packing 11 squares has passed Lean verification: an EvolvingPrograms verification run accepted all 7,920 local Lean modules with a final audit reporting zero admissions. The project pins Lean 4.34.1 and a fixed Mathlib revision, and gives the optimal side length as T=(6u+4)/(1+2u−u²), where u is the unique root in (9/25,37/100) of a stated degree-eight polynomial, with the construction attaining about 3.8770835900228141773. Some expensive exact numerical certificate checks use native_decide, so the final theorem trusts Lean's kernel and native compiler rather than claiming kernel-only verification.

   Hacker News · AI（100+ 分） · 🔥 0

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