Hundreds of scientific papers are based on conjecture that an internal OpenAI model now claims to have disproved, the company announced Monday. OpenAI announced two other results on the same day, one in mathematics and one in physics.
In a blog post, OpenAI said the exponential time hypothesis (ETH) was “widely believed to be true.” The conjecture concerns the difficulty of solving Boolean satisfiability, a problem closely related to P versus NP. Researchers have used it to show that problems in graph theory, computational biology, databases and other fields are difficult to solve quickly.
According to OpenAI, its model found the proof on October 16. The company verified it the next day in Lean, a language that verifies proofs by machine. He published the Lean model write-up and proof on GitHub.
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 verify and explain the result. Impagliazzo and Paturi first proposed ETH with Francis Zane.
An internal model at OpenAI has produced a purported refutation of ETH! Russell Impagliazzo, Mohan Paturi and I were invited to help organize an open and independent review 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 was not an endorsement.
“Our involvement should not be considered certification of the claim. A result of this importance requires careful and independent review,” Impagliazzo, Paturi and Williams wrote.
Williams said on X that the group had not signed any nondisclosure agreements and would not be paid. The group asked OpenAI to publish all of its raw ETH results data and fund a conference for the research community. OpenAI has accepted both, according to Williams and OpenAI.
A proof of mathematics and a proof of physics
In mathematics, OpenAI claims its models have proven the local smoothing conjecture proposed by Christopher Sogge in 1991, in all dimensions. This would also settle the Kakeya conjecture and the Stein restriction conjecture in all dimensions. Mathematicians had proven local smoothing in two dimensions in 2019 and the Kakeya conjecture in three dimensions in 2025. OpenAI published the model description and a Lean proof, as it did for the 722 mathematics papers published on October 6.
In physics, OpenAI claims its models have produced 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 of the existence of pure Yang-Mills theory, which is part of one of the Clay Mathematics Institute’s Millennium Prize problems. OpenAI said in September that it would not claim the prize for its Navier-Stokes proof.
Nobel laureate David Gross will lead the physics group, along with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov. This group has chosen not to publish the AI-produced material at this time and will write the work themselves.
Who gets the credit?
OpenAI says it does not seek academic credit for its findings. He says researchers in each group should be recognized for the explanations they write. He also gave $5 million to the Simons Foundation for workshops and conferences on the results produced by AI.
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 verifying and explaining the work gets less credit. Mathematicians raised similar concerns in the Leiden Declaration in June.
“If this statement is correct, it will change an important part of theoretical computer science,” write the three researchers.
Gn bussni
