OpenAI said on Monday, Oct. 26, that one of its internal AI models had proved false the Exponential Time Hypothesis, a widely held belief that checking whether a list of yes-or-no conditions can all be met at once takes time that grows exponentially with the list. Computer scientists have built on that belief for decades: OpenAI says hundreds of papers used it to show that, if it is true, many problems in fields such as computational biology and databases cannot be solved quickly. OpenAI says the result reopens the question of how much faster such tasks could become, though turning that into practical gains would take significant further research.
OpenAI says its AI found the disproof on Oct. 16, and that the next day the company translated it into Lean, a programming language in which a computer can check every step of a proof. OpenAI has posted the AI's write-up and the computer-checked version on GitHub. Russell Impagliazzo and Ramamohan Paturi of UC San Diego, who first proposed the hypothesis with Francis Zane, and Ryan Williams of MIT will help organize an open examination of the claim, which they say must "establish its correctness or identify its limitations." "Our involvement should not be taken as certification of the claim," the three wrote in a letter to colleagues, adding: "If the claim is correct, it will change an important part of theoretical computer science."
The same post claims two more results. In math, OpenAI says its models proved the local smoothing conjecture, a 1991 prediction that waves cannot stay sharply focused for long, for spaces with any number of dimensions. Mathematicians had proved it in two dimensions in 2019. OpenAI says the new proof would also settle the Kakeya conjecture and a related problem, Stein's restriction conjecture, in all dimensions. Mathematicians proved the Kakeya conjecture in three dimensions in 2025. It has posted that proof publicly as well, with a computer-checked version.
In physics, OpenAI says its models produced a mathematically rigorous proof that certain theories of particle physics exist as sound mathematics. These include quantum chromodynamics, which describes how quarks and gluons interact through the strong force. Part of the work is a proof that a simpler theory, called Yang-Mills theory, exists, which OpenAI says is part of one of the Clay Mathematics Institute's Millennium Prize problems. A group led by David Gross, who shared the 2004 Nobel Prize in Physics, will examine it, and has chosen to hold back the AI's material for now and write up the work itself, so the physics proof is not public.
OpenAI says the experts take part unpaid, are not asked to sign nondisclosure agreements and are free to publish their conclusions, and that it seeks no academic credit for the results. At the computer scientists' request, it agreed to make the raw data behind the computer science result public and to pay for a conference on what it means. OpenAI also pointed to $5 million it recently pledged to the Simons Foundation for workshops and programs on results produced by AI.
It is not yet known whether the three proofs hold up, or how long the checks will take. In an Oct. 7 update, OpenAI withdrew three of its earlier AI-made math papers after a sign error broke one proof and two papers that relied on it. OpenAI has not named the model behind the new results or said whether outside researchers will be able to use it.
Correction (Oct. 28): an earlier version said the proof would settle much of a related problem. OpenAI says it would settle that problem, Stein's restriction conjecture, in all dimensions.