OpenAI releases three more major scientific discoveries, this time asking external experts to "lead the way"

Abstract:

Less than a month after the last time it released hundreds of papers, OpenAI announced three more "major" results in the fields of mathematics, computer science and physics on October 26, and for the first time tried to let external experts lead the understanding and release process of the results as a "shepherd".

The biggest difference from the previous approach is the differentiation of release strategies: for results in computer science and physics, OpenAI invites external experts to lead a team to interpret the results; for mathematical problems, experts recommend directly making the AI ​​output public and letting researchers organize their own interpretation work. OpenAI positioned the three manuscripts as a kind of "original research data" on its official blog and admitted that "it is not yet known which of the three methods is the most useful."

Among the three results, the mathematical results are aimed at harmonic analysis. Sogge proposed the "local smoothness conjecture" in 1991 to discuss the behavior of waves when focusing - the most extreme focusing must be short-lived, and the focusing intensity at random moments is much lower than the worst case. Since this conjecture is extremely basic, it contains both the Kakeya conjecture and the Stein limiting conjecture. In 2019, Guth, Wang, and Zhang proved the two-dimensional situation, and in 2025, Wang and Zahl proved the three-maintenance Kakeya conjecture; and OpenAI's model gave proof of the local smoothness conjecture in any dimension, thus solving the Kakeya conjecture and Stein limit conjecture in all dimensions. The new proof is based on a new auxiliary partial differential equation. The model output was obtained on October 18, 2026, and the Lean formalization was completed the next day.

In computer science, the results point to the falsification of the "Exponential Time Hypothesis" (ETH). ETH is a long-term conjecture about the computational complexity of the satisfiability of Boolean formulas. It is closely related to the P vs. NP problem. It has been used by a large number of papers in the past to derive conditionally difficult results in graph theory, computational biology, databases, computational geometry and other fields. OpenAI claims that its system proves that ETH is not true, and has completed the verification in Lean: the paper gives a deterministic algorithm that can accurately count the number of satisfying assignments of the fixed-width CNF formula in sub-exponential time, and only occupies polynomial space. The 3-SAT case constitutes a refutation of ETH. This work was examined and interpreted by an independent working group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams. Impagliazzo and Paturi were the original proposers of ETH (in collaboration with Francis Zane). At the request of the working group, the relevant materials were immediately made public; OpenAI also committed to funding a conference to discuss the implications of the results for the entire field. The counter-evidence at the natural language level was generated on October 16th and formalized on October 17th.

The physical results provide a strict existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, covering quantum chromodynamics (QCD) and a unified and complete version of the Standard Model. The work builds on Balaban's approach in constructive quantum field theory and also includes as a subproblem a proof of the existence of a pure Yang–Mills theory - the latter is part of the Clay Mathematics Institute's "Quantum Yang–Mills Theory" Millennium Prize problem. The Standard Model cannot be extrapolated to arbitrarily short distances, and this existence proof is for the simplest grand unified theory involving the Standard Model gauge fields and fermions. This work was led by David Gross, winner of the 2004 Nobel Prize in Physics, and included Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov; Jaffe co-posed the Yang–Mills Millennium Problem with Witten and co-founded the Clay Institute of Mathematics, and Douglas has been following the problem for twenty years. The working group requests that all relevant contacts be sent to

[email protected]

OpenAI has set four principles for these external collaborations: transparency, not requiring participants to sign confidentiality agreements, free discussion, sharing of intermediate products and publication of conclusions; not asking for academic honors, not seeking academic credit for discoveries generated by internal models, and inviting researchers to participate does not mean they have done anything. Produced the original findings; acknowledges contributions, the working group is credited for the understanding it has built, and the manuscripts and other materials it has written, and is responsible for properly citing the researchers, techniques, and ideas it draws on; independent, participation is voluntary and unpaid, members do not speak on behalf of OpenAI, and OpenAI does not represent them.

But the model itself is controversial. OpenAI acknowledges that choosing the initial “shepherd” will inevitably determine who participates first and creates information asymmetry, so it welcomes outside opinions on how to expand participation. More direct criticism came from the AGMAI Mathematical Advisory Group formed by OpenAI itself: Just the day before (October 25), the group clearly stated that it "recommends that AI companies should not adopt the practice of designating specific groups of people to obtain output first, citing unequal access, borrowing the reputation of others, and bias in selection."

In terms of supporting scientific research, OpenAI mentioned the previously announced investment of US$5 million to the Simons Foundation. This fund is managed and distributed by the foundation to support seminars, conferences and special programs to help researchers understand and continue to work based on the results generated by AI.