AitopkitOpenAI announced on October 26, 2026 that its internal AI models have produced three new scientific results — in mathematics, computer science and physics — and this time it has handed verification to outside academics rather than publishing alone. The boldest claim: a proof that refutes the Exponential Time Hypothesis (ETH), a conjecture from 2001 that underpins hundreds of papers on what computers cannot solve efficiently.
According to OpenAI, the ETH refutation — a deterministic algorithm counting satisfying assignments of fixed-width formulas in subexponential time — was formally verified in Lean, and will now be checked by a group led by the hypothesis’s own proposers, Russell Impagliazzo and Ramamohan Paturi, with MIT professor Ryan Williams. The mathematics result proves the local smoothing conjecture in all dimensions, which OpenAI says also resolves the Kakeya conjecture and Stein’s restriction conjecture. The physics result is a rigorous existence proof for four-dimensional quantum field theories including quantum chromodynamics — including pure Yang-Mills theory, part of a Millennium Prize problem — to be checked by a group led by Nobel laureate David Gross.
The verification setup is itself the news. After criticism earlier in October for dropping hundreds of mathematical claims at once, OpenAI says the external “shepherd” groups set their own terms: no non-disclosure agreements, no payment, and the right to say no. The ETH proposers have already publicly drawn that line, stressing that participation is not endorsement and that a result of this size needs careful independent checking.
Readers should treat all three results as claimed, not settled. Formal verification in Lean is a strong signal for the ETH proof, but the wider mathematical and physics communities have not yet endorsed the results, and the history of claimed breakthroughs says caution is warranted. If even one survives scrutiny, it changes how science gets done — a model proposing proofs that humans then verify. If they do not, the episode still matters: it shows the new bottleneck in AI science is not generating claims, but earning trust for them.