On October 26, 2026, OpenAI’s article says its models produced new results in mathematics, computer science, and physics, in harmonic analysis, complexity theory, and quantum field theory. The company calls the manuscripts raw research data and says this release tries a different process: outside experts were asked to act as shepherds and organize groups to understand the results. Those experts, the article says, advised three treatments. For mathematics, release the model output and let other researchers organize their own explanations. For complexity, form an outside group and also make the model output public for anyone to examine and extend. For physics, form an outside group and defer to that group on whether materials are released.
[1]
The page lists four rules for the collaborations. Participants are not asked to sign nondisclosure agreements and may discuss the work, share intermediate products, and publish their own conclusions. The company says it does not seek academic credit for discoveries from its internal models, and that an invitation to steward a group does not mean that person or group made the original discovery. The group is to be credited for the understanding and materials it writes, and it is asked to credit prior work. Participation is voluntary and unpaid. Conclusions belong to the participants. They do not speak for OpenAI, and OpenAI does not speak for them. Those are rules the company wrote. The page does not attach a text the invitees signed or confirmed.
[1]On the mathematics result, the company says its models produced a proof of the local smoothing conjecture in every dimension and therefore also resolve the Kakeya conjecture and Stein’s restriction conjecture in all dimensions. It says the new proof uses a novel auxiliary partial differential equation. The company says the model output was obtained on October 18, 2026, formalized in Lean the next day, and then shown to an expert. Following that person’s recommendation, the company released a natural-language writeup and a Lean proof in a public repository. That is the company’s account of the proof and the formalization. The page does not quote the expert saying the proof holds.
[1]On the complexity result, the company says its system proved the Exponential Time Hypothesis false and that the result was then verified in Lean. The page names the shepherding group as Russell Impagliazzo and Ramamohan Paturi of the University of California, San Diego, and Ryan Williams of MIT. It identifies Impagliazzo and Paturi among the people who proposed the hypothesis, and Williams as an author of algorithms and lower bounds connected to it. The company says the natural-language disproof appeared on October 16, 2026, and the Lean formalization on October 17. The group, the page says, decided to release the natural-language proof and the Lean formalization immediately, and asked the company to commit to funding a conference on the consequences. The page says the group made those release decisions. It does not quote the three of them saying they have confirmed the disproof.
[1]The physics item is older inside the company and narrower in what is public. The company says a natural-language proof of Yang-Mills existence was produced on September 9, 2026, a proof for quantum chromodynamics on September 18, and a Lean formalization of Yang-Mills existence on October 16. The shepherding group is named as David Gross, with Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov. The page recounts their prior work, including Gross’s prize-winning research connected to asymptotic freedom and Jaffe’s role in stating the Millennium Prize problem. The page says this group decided not to release the model-produced materials yet and to write the result up themselves. Of the three results, the physics one currently has no public text to check.
[1]What the three results share is a company announcement dated October 26, plus two bodies of text the company says are now in a repository, and a physics file a collaborating group is holding back. Where the company says a Lean formalization is finished, the page does not show a review conclusion from an independent group. The named researchers appear on the company’s list. The page does not give their words. The company also says it does not yet know which of the three release methods will be more useful.
[1]