OpenAI announced three new discoveries produced by its models — in harmonic analysis, complexity theory, and quantum field theory — and is trying a new release model: external experts act as shepherds, organizing groups to convert raw AI research output into scientific understanding. The three results get three different strategies. For the mathematics result, the AI output is released publicly and researchers are free to organize their own explanations. For the computer science result, an external group of collaborators will explain the result while the AI output is public. For the physics result, an external group will write up the work, and the group decides when materials are released.

The collaborations follow four principles: transparency (no NDAs, participants can discuss and publish), no academic credit claimed by OpenAI, recognition for the group’s write-ups and materials, and independence (voluntary, unpaid, conclusions belong to the group). OpenAI turns over materials and artifacts. The computer science group chose to make the natural language proof and Lean formalization public immediately via GitHub; the physics group chose to hold off releasing AI artifacts and write up the work themselves. OpenAI acknowledges tradeoffs: expert shepherds help unpack results and place them in context, but choosing initial shepherds shapes who participates first and creates information asymmetry.

The mathematics result is a proof of Sogge’s local smoothing conjecture in every dimension. The conjecture concerns how waves behave as they focus: the most extreme focusing is short-lived, and typical focusing at a random time is far smaller than worst-case focusing. It implies the Kakeya conjecture and Stein’s restriction conjecture. In 2019 Guth, Wang, and Zhang proved local smoothing in two spatial dimensions, and in 2025 Wang and Zahl proved Kakeya in three dimensions. The new proof also resolves Kakeya and Stein restriction in all dimensions, based on a novel auxiliary partial differential equation. The AI output was obtained on October 18, 2026 and formalized in Lean the next day; following the same strategy as the October 6, 2026 release, both the AI natural language writeup and Lean proof are in the public GitHub repository.

The computer science result refutes the Exponential Time Hypothesis (ETH), a conjecture about Boolean formula satisfiability closely related to P vs NP and widely used in hundreds of papers for conditional hardness results. The system proved ETH false, and the result was verified in Lean. The refutation reopens questions about how much faster these tasks could become, but finding better algorithms and turning theoretical advances into practical improvements will require significant further research. The group is led by Russell Impagliazzo (UC San Diego), Ramamohan Paturi (UC San Diego), and Ryan Williams (MIT). It requested public raw data and OpenAI funding for a conference; the group invites community examination. The AI disproof was found on October 16, 2026 and formalized in Lean on October 17, 2026; the writeup and Lean proof are public.

The physics result gives a mathematically rigorous existence proof of interacting quantum field theories with gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model. It builds on Balaban’s constructive quantum field theory approach and includes a proof of pure Yang–Mills existence, part of the Quantum Yang–Mills Theory Clay Mathematics Institute Millennium Prize problem. The proof pertains to the simplest grand unified theory that includes the Standard Model’s gauge fields and fermions, since the Standard Model itself cannot be extrapolated to arbitrarily short distances. QCD describes quark and gluon interactions via the strong force, while pure Yang–Mills describes only gluon self-interactions. David Gross leads a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. The natural-language proofs for Yang–Mills and QCD were produced on September 9 and September 18, 2026; formalization of Yang–Mills completed on October 16, 2026, after which release was arranged.

OpenAI also says it is committed to supporting independent research on these results, including a $5 million contribution to the Simons Foundation for workshops, conferences, and special programs to help researchers understand and build on AI-produced results. It continues to invite feedback on how to disclose results and engage with scientists.