Lean is an interactive theorem prover that lets mathematicians write proofs in a form a computer can check line by line. Recent coverage includes OpenAI's AI-generated Navier-Stokes solution with a Lean formal proof; an AI-assisted optimality proof for packing 11 squares, with all 7,920 Lean modules accepted; Thomas Hales writing on Terence Tao's blog about the reliability of proof assistants such as Lean; and a Hacker News argument that Lean FRO achieved more with under 1% of OpenAI's resources.
OpenAI internal model produced 722 math manuscriptsOn Oct 6, 2026, OpenAI published 722 manuscripts from an unreleased internal model, grouped into 372 result families across geometry, algebra, number theory and more, with some touching long-open problems. Many proofs were formalized in Lean; three were withdrawn the next day for a sign error, underscoring that human verification still matters.
HN discussion: why math community dumped OpenAIA Hacker News post argues OpenAI's position in mathematics rests on budget and rhetoric rather than contribution, with trust now broken. It says Lean FRO achieved more honest, impactful foundational work with under 1% of OpenAI's resources, and criticizes billions spent to devalue workers. The author says the problem is industry conduct, not LLMs themselves.
Thomas Hales on Lean prover reliability and AIMathematician Thomas Hales guest-posted on Terence Tao's blog about the reliability of proof assistants like Lean and AI-related concerns. He cites formalization projects including the four-color theorem, Feit-Thompson theorem, Kepler conjecture, and this year's sphere packing, Navier-Stokes blowup and Fermat's Last Theorem work as driving wider awareness of formal verification.
AI-assisted proof of optimal packing for 11 squaresAn AI-assisted effort produced a complete optimality proof for packing 11 squares, with all 7,920 local Lean modules accepted and a final audit showing zero admissions, while geometry and checker soundness retain ordinary Lean proofs.
Bend: a language that blocks AI mistakes via proofsBend is a new language that embeds explicit laws (LAWS.bend) and verifiable proofs (PROOF.bend) to prevent AI-introduced bugs. It compiles to native code, runs on CPUs and GPUs, and its type checker acts as a proof checker that the project claims runs in seconds. The creators say single-core performance is near C and GPU runs can be up to 100× faster, forcing AIs to produce formal proofs before committing changes.
AI-generated Navier–Stokes solution with Lean proofOpenAI shared an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean. The release demonstrates AI application to mathematical problem solving and machine-checked proofs.
The A.I. Daily