OpenAI has announced three major scientific discoveries generated by its artificial intelligence systems, spanning mathematics, computer science, and theoretical physics. In a departure from its previous release strategies, the organization adopted differing publication and evaluation approaches for each breakthrough, involving external academic experts to lead the interpretation of the results.
The mathematical result centers on harmonic analysis, specifically addressing the local smoothing conjecture originally proposed by Christopher Sogge in 1991 to describe wave behavior during focusing. Because the conjecture is foundational, it implies both the Kakeya conjecture and the Stein restriction conjecture. While previous researchers had proved limited dimensions in recent years, the OpenAI model produced a proof for the local smoothing conjecture across arbitrary dimensions, thereby resolving the Kakeya and Stein restriction conjectures in all dimensions. The new proof relies on a novel auxiliary partial differential equation. The model output was obtained on October 18, 2026, and its formal verification in Lean was completed the following day.
In computer science, the system reportedly falsified the exponential time hypothesis, a long-standing conjecture regarding the computational complexity of Boolean formula satisfiability that is closely linked to the P versus NP problem. OpenAI stated that its system proved the hypothesis does not hold, with verification completed in Lean. The paper presents a deterministic algorithm capable of precisely counting satisfying assignments for fixed-width conjunctive normal form formulas in sub-exponential time while utilizing only polynomial space, with the 3-SAT case refuting the hypothesis. This work was examined and interpreted by an independent group led by Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams. Impagliazzo and Paturi were co-originators of the hypothesis alongside Francis Zane. At the group’s request, the related materials were immediately made public, and OpenAI committed financial support for a conference to discuss the implications for the field. The natural language proof was generated on October 16 and formalized on October 17.
The physics results provide rigorous existence proofs for certain interacting quantum field theories incorporating gauge fields and fermions in four dimensions, including quantum chromodynamics and a unified complete version of the Standard Model. This work builds upon the constructive quantum field theory methods of E. Seiler and I. Ya. Aref’eva or closely related constructive frameworks, specifically incorporating approaches established by D. Balaban. As a sub-problem, the work includes the existence proof for pure Yang-Mills theory, which falls under the Millennium Prize Problems designated by the Clay Mathematics Institute. This research was led by 2004 Nobel laureate David Gross, alongside Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. Jaffe co-formulated the Yang-Mills Millennium problem with Edward Witten and helped found the Clay Mathematics Institute, while Douglas has studied the problem for two decades. The working group established a dedicated contact email for the project and decided against immediately publishing the raw AI output, opting instead to write their own paper following the completion of Lean formalization on October 16, after initial generation occurred on September 9 for Yang-Mills existence and September 18 for QCD.
To govern these collaborations, OpenAI established four core principles: transparency, requiring no non-disclosure agreements and allowing free discussion and sharing of intermediate products; non-seeking of academic credit for internal models; acknowledgment of contributions, ensuring working groups receive credit for their understanding and authored texts while properly citing prior research; and independence, confirming that participants serve on a voluntary, uncompensated basis without acting as representatives for OpenAI.
Despite these measures, the collaborative model has encountered criticism. OpenAI acknowledged that selecting initial expert groups creates information asymmetry and introduces preferential access. A more direct critique emerged from the organization’s own AGMAI mathematics advisory panel, which recommended that artificial intelligence companies avoid granting specific groups preferential access to outputs, citing concerns over unequal access, the borrowing of external reputations, and selection bias. To support broader research, OpenAI highlighted a previously announced five-million-dollar contribution to the Simons Foundation, managed and distributed independently to fund workshops, conferences, and specialized programs helping researchers interpret and build upon AI-generated findings.
