OpenAI published mathematical and computer science materials and outlined a physics result, with outside experts helping assess two of the claims.
OpenAI announced three results in mathematics, computer science and physics on October 26, 2026, and described new arrangements for outside experts to examine some of the work. The claims are not all at the same stage of public review: the company released materials for the mathematics and computer science results, while the physics work has not been fully published.
In mathematics, OpenAI says its model produced a proof of local smoothing for the Euclidean wave equation in every spatial dimension of at least two. The company says the result also establishes related conclusions involving the Kakeya conjecture and Stein’s spherical restriction estimates. It released the model’s output for researchers to analyze, rather than providing an expert-written explanation alongside it.
For computer science, OpenAI says a paper presents a deterministic, subexponential-time algorithm for exactly counting satisfying assignments of fixed-width CNF formulas. The 3-SAT case, if correct, would refute the Exponential Time Hypothesis, a longstanding conjecture in complexity theory. OpenAI released a write-up and Lean proof; computer scientists Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will lead an independent effort to examine and explain the argument.
The physics claim concerns a mathematically rigorous existence proof for certain interacting quantum field theories in four dimensions, including theories with gauge fields and fermions. OpenAI says David Gross will lead a group that includes Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov in examining that work. The full physics materials were not yet public when The Verge reported the announcement.
The release approach also raises questions about access and attribution. An OpenAI advisory panel of mathematics researchers had recently cautioned against giving selected experts early access, citing risks including unequal access and perceived endorsement. OpenAI’s accompanying open letter asks the research community to discuss how AI-generated results should be checked, explained and credited.