OpenAI Claims Its Model Disproved the Exponential Time Hypothesis

OpenAI said on Monday that an internal model has refuted the Exponential Time Hypothesis (ETH), a conjecture that hundreds of computer science papers rely on. The company announced two further results the same day, one in mathematics and one in physics.

ETH concerns how hard it is to solve Boolean satisfiability, a problem closely tied to P versus NP. Researchers have used it to show that problems in graph theory, computational biology, databases and other fields cannot be solved quickly. OpenAI says the model found the disproof on 16 October, and the company checked it in Lean, a language that verifies proofs by machine, the next day. The model's write-up and the Lean proof are on GitHub.

Original authors to examine the claim

A group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego and Ryan Williams of MIT will check and explain the result. Impagliazzo and Paturi first proposed ETH with Francis Zane. In an open letter, the three said their involvement "should not be taken as certification of the claim." Williams said the group signed no non-disclosure agreements and will not be paid. They asked OpenAI to release all raw data and to fund a conference for the research community, and both sides say OpenAI agreed.

Mathematics and physics results

In mathematics, OpenAI says its models proved the local smoothing conjecture, proposed by Christopher Sogge in 1991, in every dimension. That would also settle the Kakeya conjecture and Stein's restriction conjecture in all dimensions. Mathematicians had proved local smoothing in two dimensions in 2019 and Kakeya in three dimensions in 2025.

In physics, the company says its models produced a rigorous proof that certain quantum field theories exist in four dimensions, including quantum chromodynamics. The work includes a proof that pure Yang-Mills theory exists, part of one of the Clay Mathematics Institute's Millennium Prize problems. A group led by Nobel laureate David Gross, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, chose not to release the AI-produced material for now and will write up the work itself.

The question of credit

OpenAI says it does not seek academic credit and that researchers in each group should be recognized for their explanations. It has given $5m to the Simons Foundation for workshops and conferences on AI-produced results. The three computer scientists ask how credit should work when AI finds results first, warning that recognition may go to whoever publishes first or has the most powerful tools, while checking and explaining work earns less. "If the claim is correct, it will change an important part of theoretical computer science," they wrote.