OpenAI says its AI model has disproved the Exponential Time Hypothesis

Hundreds of computer science papers rest on a conjecture that an internal OpenAI model now claims to have refuted, the company said on Monday. OpenAI announced two more results the same day, one in mathematics and one in physics.

In a blog post, OpenAI said the Exponential Time Hypothesis (ETH) has been “widely believed to be true”. The conjecture 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 are hard to solve quickly.

According to OpenAI, its model found the disproof on 16 October. The company checked it in Lean, a language that verifies proofs by machine, the next day. It has published the model’s write-up and the Lean proof on GitHub.

The scientists who proposed ETH will examine it

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.

An internal model at OpenAI has produced a claimed refutation of ETH! Russell Impagliazzo, Mohan Paturi, and I have been asked to help organize an open and independent examination of this claim. 1/4

Ryan Williams @rrwilliams.bsky.social (@rrwilliams) October 26, 2026

In an open letter to their field, the three researchers said their role is not an endorsement.

“Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny,” Impagliazzo, Paturi and Williams wrote.

Williams said on X that the group signed no non-disclosure agreements and will not be paid. The group asked OpenAI to release all its raw data on the ETH result and to fund a conference for the research community. OpenAI agreed to both, according to Williams and OpenAI.

A maths proof and a physics proof

In mathematics, OpenAI says its models proved the local smoothing conjecture, which Christopher Sogge proposed 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 the Kakeya conjecture in three dimensions in 2025. OpenAI released the model’s write-up and a Lean proof, as it did with the 722 maths papers it published on 6 October.

In physics, OpenAI says its models produced a rigorous proof that certain quantum field theories exist in four dimensions. These include quantum chromodynamics, which describes the strong force between quarks and gluons. The work includes a proof that pure Yang-Mills theory exists, which is part of one of the Clay Mathematics Institute’s Millennium Prize problems. OpenAI said in September it would not claim the prize for its Navier-Stokes proof.

Nobel laureate David Gross will lead the physics group, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. That group chose not to release the AI-produced material for now and will write up the work itself.

Who gets the credit

OpenAI says it does not seek academic credit for the discoveries. It says the researchers in each group should get the recognition for the explanations they write. It has also given $5m to the Simons Foundation for workshops and conferences on AI-produced results.

The three computer scientists ask in their letter how credit should work when AI finds results first. They warn that recognition may go to those who publish first or have the most powerful tools, while checking and explaining the work gets less credit. Mathematicians raised similar concerns in the Leiden declaration in June.

“If the claim is correct, it will change an important part of theoretical computer science,” the three researchers wrote.