OpenAI says its models proved the local smoothing conjecture and disproved the Exponential Time Hypothesis

OpenAI says its models produced a proof of the local smoothing conjecture in every dimension, which it says also resolves the Kakeya and Stein restriction conjectures. It also says its system proved the Exponential Time Hypothesis false, with a Lean check, and produced existence proofs for certain four-dimensional quantum field theories, including QCD. Outside review is still under way, and no model was named.

Why it matters: If the claims hold up, these would be landmark results in mathematics and computer science, but they are the company's own claims until experts finish reviewing them.

Local smoothing proof

Generated Oct 18, formalized in Lean Oct 19 (reported)

Exponential Time Hypothesis

Claimed disproof, produced Oct 16, Lean check Oct 17 (reported)

Physics results

Not released in full; under review by a group led by David Gross

Model used

Not disclosed

We could not read OpenAI's own page (403). Reports differ on scope: one says the Kakeya and Stein results follow only in the interior of the conjectured range, and one says Lean covered only select lemmas. Russell Impagliazzo, Ramamohan Paturi and Ryan Williams are reported to lead review of the complexity result. We found no outside expert verdict yet. Filed late: we missed this when it was announced.