OpenAI releases three major science proofs and asks academics to verify them

OpenAI has released three new mathematical and scientific results, marking a shift in how the company shares AI-generated discoveries with the academic world. The latest batch includes work in physics, computer science, and mathematics. Unlike previous releases, OpenAI appointed specific external experts to oversee the verification process for the physics and computer science findings. For the mathematics result, the company stated it advised the AI to release the raw output directly so independent researchers could develop their own explanations.

The computer science release claims to disprove the Exponential Time Hypothesis, a long-standing belief in the field. The accompanying paper describes a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. Specifically, the work addresses the case of 3-SAT, which refutes the hypothesis if the proof holds. A working group of computer scientists is currently examining the material to verify its validity and prepare a public explanation.

Russell Impagliazzo and Ramamohan Paturi from UC San Diego lead this verification effort. Both researchers were part of the original group that proposed the Exponential Time Hypothesis in 1999. They are joined by Ryan Williams, a professor at MIT. At the group's request, OpenAI made the AI output write-up and the Lean proof available on GitHub immediately. This allows the wider community to inspect the materials while the designated experts conduct their review.

In physics, OpenAI describes a mathematically rigorous existence proof for certain interacting quantum field theories in four dimensions. The theories include gauge fields and fermions, specifically citing Quantum Chromodynamics and a unified completion of the Standard Model of particle physics. The company has not yet released the full details of this work. Instead, David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov to shepherd the work through verification.

The mathematics discovery addresses the local smoothing conjecture in every dimension. The proof uses an auxiliary partial differential equation to establish Sogge’s local smoothing for waves in spatial dimensions of at least two. This result also resolves the Kakeya maximal and dimension conjectures and Stein’s spherical restriction estimates within the interior of the conjectured range. OpenAI released the model output directly, following the same method used in its October 6 release of hundreds of manuscripts.

This approach follows a recommendation from the AGMAI panel of math advisers, which OpenAI assembled recently. On October 25, the panel stated that AI companies should not adopt practices that designate certain people to receive output first. The panel cited unequal access, borrowed reputation, and biased selection as potential issues with that method. They recommended that AI labs instead release output on scholarly repositories with Lean-formalized proofs, details on problem selection, and funding for researchers working to understand the results.

OpenAI published an open letter to the scientific community to solicit input on how to examine these claims. The letter asks for discussion on three specific areas. These include expectations for early access to AI-generated results, disclosure of conflicts of interest, and the use of unpublished material for subsequent research. The company also seeks guidance on how credit should be allocated for both new discoveries and the work of checking, fixing, simplifying, and explaining them.

The letter further asks how the community can support students and researchers as methods change while preserving the judgment needed to question results. OpenAI noted that the mathematics proof resolves the Kakeya conjecture and Stein’s restriction conjecture in all dimensions. Just a few months ago, NYU professor Hong Wang received the Fields Medal from the International Mathematical Union for resolving the Kakeya conjecture in three dimensions.