OpenAI Announces Three AI Research Results, Claiming an Exponential Time Hypothesis Disproof and a Kakeya Resolution

What happened

This release uses a new disclosure approach OpenAI designed for AI-produced results: OpenAI presents the three manuscripts as raw research data and has invited outside experts to act as shepherds, organizing academic verification and explanation. The three results follow different release strategies: the math result's raw AI output is public directly; the computer science result has an external collaboration group while its AI output is also public; the physics result's AI artifacts are held back for the collaboration group to write up itself.

The production and formalization dates for the math and computer science results are public: for math, the AI output arrived on October 18 and Lean formalization finished the next day, followed by publication of the natural-language writeup and Lean proof; for computer science, the natural-language disproof of the Exponential Time Hypothesis arrived on October 16 and Lean formalization finished on October 17, with the same two materials published. For physics, the natural-language proof of Yang-Mills existence arrived on September 9 and the QCD proof on September 18, with Lean formalization of Yang-Mills existence completed on October 16; release was postponed given the length and complexity.

The verification assignments and funding are also public: the Exponential Time Hypothesis group is led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT; Impagliazzo and Paturi, with Francis Zane, originally proposed the hypothesis; OpenAI agreed to the group's requests to make all raw data public and to fund related conferences. The physics group is led by 2004 Nobel Physics laureate David Gross, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. OpenAI says the collaborations follow principles of no nondisclosure agreements, voluntary unpaid participation, conclusions independent of OpenAI, and no academic credit sought by OpenAI; separately, OpenAI has provided $5 million to the Simons Foundation to support workshops and programs for understanding AI-produced results. OpenAI previously published a batch of AI math manuscripts on October 6 under the same strategy.

Key facts

1. The three results: Math: a full-dimensional local smoothing proof; computer science: a disproof of the Exponential Time Hypothesis; physics: existence proofs for quantum chromodynamics and completions of the Standard Model, including pure Yang-Mills existence, part of a Clay Mathematics Institute Millennium Prize problem.
2. Math background: Sogge proposed the local smoothing conjecture in 1991; it implies the Kakeya conjecture and Stein's restriction conjecture; the two-dimensional case was proved in 2019 and the three-dimensional Kakeya conjecture in 2025.
3. Exponential Time Hypothesis background: The hypothesis concerns the computational complexity of Boolean formula satisfiability and relates to the P versus NP problem; according to OpenAI, hundreds of papers have used it to derive conditional hardness results across graph theory, computational biology, databases and computational geometry.
4. Publication status: The AI natural-language writeups and Lean proofs for the math and computer science results are published in OpenAI's public GitHub repository; the physics result's AI artifacts are held back while the collaboration group writes the result up itself.
5. Verification groups: Exponential Time Hypothesis group: Impagliazzo, Paturi, Williams; physics group: Gross, Douglas, Jaffe, Klebanov, Nekrasov.
6. Funding and principles: OpenAI seeks no academic credit; collaborations carry no nondisclosure agreements, participation is voluntary and unpaid, and conclusions are independent; OpenAI has provided $5 million to the Simons Foundation to support workshops and programs for understanding AI-produced results.