OpenAI on October 26 made some of the boldest research claims any AI company has put its name to. In a post on its website, the company said its internal models had produced three results that specialists have pursued for decades: a disproof of the Exponential Time Hypothesis (ETH) in theoretical computer science, a proof of Christopher Sogge's local smoothing conjecture in every dimension, and a rigorous existence proof for four-dimensional quantum field theories that include quantum chromodynamics (QCD). At the same time, it changed how such output reaches scientists, recruiting senior researchers to lead outside groups that will examine and explain the work.
The computer science claim has the widest reach. ETH, put forward by Russell Impagliazzo, Ramamohan Paturi and Francis Zane, holds that satisfiability problems such as 3-SAT cannot be solved in subexponential time. Researchers have leaned on it for hundreds of conditional hardness results in graph theory, computational biology, databases and computational geometry. OpenAI's manuscript, dated October 25 in its public openai/math repository, describes a deterministic algorithm that counts every satisfying assignment of a fixed-width CNF formula in subexponential time while using only polynomial memory. Run on 3-SAT, that would break the hypothesis. OpenAI says the model reached the disproof on October 16 and that a Lean formalization followed a day later.
Checking it falls to Impagliazzo and Paturi, both at UC San Diego, together with MIT's Ryan Williams, who has previously refuted stronger variants of the conjecture. In an open letter quoted by The Next Web, the three stressed that taking part does not mean they vouch for the result, which they said needs careful scrutiny by others. Williams said the group signed no confidentiality agreements and is not being paid. At the group's request, OpenAI agreed to publish all raw data behind the claim and to pay for a conference on what it means for the field. OpenAI itself cautions that turning the result into faster practical algorithms would take substantial further research.
In mathematics, the claim concerns how waves concentrate. Sogge's 1991 conjecture says that extreme focusing can only last briefly. Larry Guth, Hong Wang and Ruixiang Zhang settled the two-dimensional case in 2019, and in 2025 Wang and Joshua Zahl settled the three-dimensional Kakeya problem, work for which Wang later received a Fields Medal, The Verge noted. OpenAI says its proof covers every dimension, rests on a new auxiliary partial differential equation and therefore also resolves the Kakeya and Stein restriction conjectures everywhere. The repository summary quoted by The Verge words this more narrowly, citing Stein's spherical restriction estimates across the interior of the conjectured range. This result was released openly without a shepherd group, following the approach OpenAI used for its October 6 drop of 722 mathematics papers.
The physics result is the least accessible. OpenAI says its models produced a rigorous construction of interacting four-dimensional theories with gauge fields and fermions, including QCD and the simplest grand unified extension of the Standard Model, building on Tadeusz Balaban's constructive approach. A sub-result proves that pure Yang-Mills theory exists, which is one part of a Clay Mathematics Institute Millennium Prize problem. Nobel laureate David Gross heads the shepherding group, whose members also include Nikita Nekrasov, Igor Klebanov, Arthur Jaffe and Michael Douglas. Those physicists decided to keep the AI-generated material private for now and to prepare their own write-up. OpenAI dates the proofs to September 9 and 18 and says the Yang-Mills formalization was completed on October 16.
OpenAI framed the collaborations around four commitments: openness about their existence, no academic credit claimed by the company, recognition for the groups' own explanations, and independence for participants. It also pointed to an earlier $5 million gift to the Simons Foundation for workshops on AI-produced results. The company conceded that choosing initial shepherds shapes who gets involved first. The Verge reported that AGMAI, a panel of mathematics advisers OpenAI convened, had recommended a day earlier that labs avoid giving selected people first access, pointing to uneven access, borrowed credibility and skewed selection.
None of the three results had been independently confirmed when OpenAI announced them, and the physics material cannot yet be inspected by anyone outside the shepherd group. If the ETH refutation survives review, a large body of conditional lower bounds in computer science would lose its footing.