OpenAI announces three AI results
On 26 October 2026 OpenAI announced three results that it says its models produced: a proof of Sogge's local smoothing conjecture in every dimension, which also settles the Kakeya conjecture; a refutation of the Exponential Time Hypothesis (ETH); and a mathematically rigorous existence proof for quantum chromodynamics and a grand unified completion of the Standard Model, including pure Yang-Mills theory. OpenAI published the manuscripts of the first two with their Lean formalizations and asked outside experts to lead groups that verify and explain them; the physics materials are withheld.
Why it matters
These are OpenAI's claims about its own models, made before any outside verification: the post says the groups led by Impagliazzo, Paturi and Williams (complexity) and by David Gross (physics) are only beginning to understand the results, and for the ETH it says the Lean check has been done and asks the community to help examine the claim. What is new is the release process: the results go to named outside shepherds under three different strategies, with no non-disclosure agreements and no academic credit sought, and OpenAI will fund a conference on the ETH. If the refutation of the ETH holds it would overturn an assumption used in hundreds of papers, as the post itself says; no outside party had confirmed it on 28 October.
Dates. The post is dated 26 October 2026. The GitHub repository openai/math received the manuscripts (folders with "October-25-2026" in their names) and the Lean proofs in a single commit at 20:35 UTC on 26 October. Internal dates from the post: the AI output on local smoothing on 18 October, Lean the next day; the natural-language refutation of the ETH on 16 October, Lean on 17 October; the proof of Yang-Mills existence on 9 September, of QCD on 18 September, the Lean formalization of Yang-Mills finished on 16 October. The date line of the ETH manuscript reads "17 October 2026, revised 25 October 2026". What the manuscripts say. The ETH manuscript, with the author line "OPENAI", gives in its abstract a deterministic algorithm that exactly counts the satisfying assignments of an arbitrary k-CNF in subexponential time and polynomial space and says this refutes the ETH. The local smoothing manuscript ("OpenAI October 25, 2026") claims a proof of Sogge's local smoothing conjecture for the Euclidean wave equation in every spatial dimension at least two, and of the Kakeya and Nikodym maximal conjectures. There is no physics manuscript: the group chose to hold the materials back and write its own account. The groups. For the ETH: Russell Impagliazzo and Ramamohan Paturi (UC San Diego) and Ryan Williams (MIT); OpenAI agreed to make all raw data public and to fund a conference. For physics: David Gross with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. Principles: transparency, no academic credit sought, recognition for the groups, independence, voluntary and unpaid participation. What the record does not claim. None of the three results has been confirmed by outside experts; the Lean files and manuscripts were not checked here, and whether the Lean statements match the theorems claimed is for specialists. A search for outside reaction on 28 October found none.