OpenAI claims proofs in math, computer science and physics, adds outside expert review

OpenAI announced three results it calls major, in mathematics, computer science and physics, less than a month after releasing hundreds of math manuscripts. The difference this time, according to The Verge, is that outside experts it calls shepherds are guiding the computer science and physics results, while for the math problem advisers told OpenAI to release the raw AI output for researchers to work through.

The math result concerns local smoothing for the Euclidean wave equation. OpenAI says its model proved Sogge's local smoothing conjecture in every spatial dimension at least two, using an auxiliary partial differential equation. It says this also yields the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates across the interior of the conjectured range. The model output is being released directly.

In computer science, OpenAI says the paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The 3-SAT case would refute the Exponential Time Hypothesis, proposed in 1999 and widely believed. Impagliazzo and Paturi, who were among its originators, and MIT's Ryan Williams will examine the proof. At their request, the write-up and Lean proof were posted to GitHub.

The physics result has not been released in full. OpenAI describes it as a mathematically rigorous existence proof of certain interacting quantum field theories with gauge fields and fermions in four dimensions, including Quantum Chromodynamics and a unified completion of the Standard Model. David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov to shepherd the work.

If the claims hold, they would be significant: the ETH underpins much of the field's reasoning about which problems are hard, and a rigorous construction of QCD-type theories touches a long-standing problem in mathematical physics. None of the results has yet been independently verified, and the coverage describes them as OpenAI's claims.

The release process is itself contested. OpenAI's own AGMAI panel of math advisers said a day earlier that it recommends AI companies not adopt the practice of designating certain people to receive output first, citing unequal access, borrowed reputation and biased selection. It suggested release on scholarly repositories with Lean-formalized proofs, information on problem selection, and funding for those working to understand the results. OpenAI acknowledges its shepherd approach may have its own issues.

OpenAI also published an open letter asking the community how to set norms: what should govern early access and conflict-of-interest disclosure, how credit should reflect both discovery and the work of checking and explaining, and how to support students and researchers as methods change.

The key near-term question is whether the working groups confirm the ETH refutation and the physics proof, and how quickly the full physics materials are made public.