OpenAI Says Its AI Produced Three Big Proofs and Asks Outside Experts to Check Them

OpenAI says its internal AI models produced proofs for three open problems, and it has asked outside experts to check them. None of the claims is settled yet, so everything here is “OpenAI says”.

The first claim is in computer science: that the Exponential Time Hypothesis is false. That hypothesis is a widely trusted assumption about how hard it is to solve SAT, the problem of finding values that make a logical formula true. Hundreds of papers build on it. If the proof holds, those papers would lose a prop, though their results would not automatically be wrong. The second is in mathematics: the local smoothing conjecture, proposed in 1991 and proven before only in two dimensions, now claimed in all dimensions. OpenAI says this also settles two related conjectures, Kakeya and Stein’s restriction. The third is in physics: that certain quantum field theories exist mathematically in four dimensions, covering Yang-Mills theory, quantum chromodynamics and a simple grand unified theory. The Yang-Mills part touches a Millennium Prize Problem, but OpenAI says it solved only the existence part, not the “mass gap” part, so the prize is not won.

Review is being handled differently for each. For computer science, Ryan Williams and colleagues at UC San Diego are unpaid, have signed no secrecy agreements, and stress that taking part is not an endorsement. For physics, a group led by Nobel laureate David Gross is reviewing and plans its own write-up. For the math proof, there is no dedicated group; OpenAI published the proof text and a Lean version for the community to examine.

What’s behind it: Lean is a proof assistant, software that checks every logical step mechanically. It is powerful, but it only confirms that the proof matches the statement as typed into Lean. Experts still have to confirm the statement means what we think it means. OpenAI calls its manuscripts “raw research data” and pledged $5 million to the Simons Foundation for workshops on AI results. It also admits that choosing the first reviewers shapes who gets early access, and says it is not yet clear which review method works best.

A practical caveat from Williams: even if the first result stands, real-world SAT problems are usually far easier than the worst case the hypothesis describes, so everyday software may see little change.

What this means for you: nothing changes in your tools this week. The story to watch is the process: how the science community checks, and credits, work done by AI. If a headline later says “AI solved a Millennium Problem”, remember that for now the claim is partial and unverified.

Sources

• The Decoder: OpenAI asks outside experts to check proofs