OpenAI announced three claimed scientific breakthroughs on 26 October, with different arrangements for their publication and scrutiny. In mathematics, the company says its models proved Christopher Sogge’s local smoothing conjecture in every spatial dimension, also resolving the Kakeya and Stein’s restriction conjectures. Proposed in 1991, local smoothing concerns how waves behave when they concentrate.
In a separate computer science project, an internal model reportedly refuted the Exponential Time Hypothesis, a widely accepted conjecture underpinning hundreds of papers. The hypothesis concerns the difficulty of Boolean satisfiability problems. OpenAI says the model produced its disproof on 16 October, followed by verification in Lean, a proof-checking language, the next day.
Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will lead an independent examination. Impagliazzo and Paturi helped formulate the original hypothesis, but the reviewers emphasise that their participation does not certify the claim. Even if the refutation withstands scrutiny, it would not automatically provide faster algorithms for existing computing problems.
Separately, OpenAI claims existence proofs for interacting quantum field theories in four dimensions, including quantum chromodynamics, which describes the strong force between quarks and gluons. David Gross will lead the physics review group. Unlike the mathematics and computing materials, which are publicly available on GitHub with Lean proofs, the physics output will remain unreleased while the group develops its own account.
OpenAI says it seeks no academic credit for the discoveries, with researchers instead receiving recognition for their explanatory work. It has also contributed $5 million to the Simons Foundation to support workshops and conferences. The computing reviewers have raised broader questions about access, attribution and recognition for checking and explaining AI-generated results.
