The scientists OpenAI appointed to independently verify its latest and boldest mathematical claim—that an internal model has successfully refuted the Exponential Time Hypothesis—have declined to endorse it, citing a history of exaggerated math announcements at the Altman-led lab.

The Exponential Time Hypothesis (ETH) is a measure of the difficulty of solving Boolean satisfiability—the problem of deciding whether a logical formula can be made true. The conjecture holds that satisfiability cannot be solved substantially faster than exponential time, so a genuine refutation would mean an algorithm exists that beats that bound. The problem is tied to the P versus NP question, one of the Clay Mathematics Institute's $1 million Millennium Prize Problems, and ETH itself underpins hundreds of computer science papers. OpenAI says one of its internal models has produced a claimed refutation, which the company frames as part of its effort to build scientific understanding with academic communities.

Verifying the result falls to a group led by MIT's Ryan Williams together with Russell Impagliazzo and Ramamohan Paturi of UC San Diego. The hypothesis was originally proposed by Impagliazzo and Paturi along with Francis Zane.

Verifiers stop short of endorsement

The three researchers leading the review wrote in an open letter to their field that their "involvement should not be taken as certification of the claim," adding that "a result of this significance requires careful, independent scrutiny." The distinction matters: mathematics conventionally settles claims of this scale through open community scrutiny rather than a single lab's internal checks.

Writing on his X account, Williams said the group did not sign a nondisclosure agreement (NDA) and would not be paid for the "open and independent examination" work he and his colleagues were asked to carry out after "an internal model at OpenAI has produced a claimed refutation of ETH." He added that OpenAI agreed to the group's request to publish all the raw data behind the result, and that the lab also agreed to fund a conference on the finding's implications.

Why the field is withholding judgment

Previous OpenAI claims in mathematics have not gone according to plan, and an independent team of researchers is examining the ETH claim even after the lab verified the disproof its internal models found on October 16 in Lean by the following day. The write-up and the Lean proof are posted to GitHub.

Lean is a language that checks proofs by machine. Because software, rather than human referees, checks each logical step, machine verification is prized as a defense against human error. Even that safeguard has been challenged, however, by Cambridge's Anders Hansen and co-authors, who argued in a paper that a Lean-verified formalization can compile while failing to match the natural-language proof it is supposed to represent. They cited OpenAI's Navier-Stokes work as a case study.

The scrutiny follows an earlier controversy. Thomas Bloom, the mathematician who maintains the Erdős problems site, responded to OpenAI VP Kevin Weil's October 2025 claim that GPT-5 had solved 10 previously unsolved Erdős problems by calling it "a dramatic misrepresentation." Bloom explained that the model had simply surfaced existing papers he was personally unaware of, rather than finding new solutions to the famous conjectures posed by Paul Erdős. That episode drew public mockery from Meta's Yann LeCun and Google DeepMind's Demis Hassabis.

OpenAI also had to make three withdrawals within a day of mass-releasing 722 preprints on 372 math problems on October 6, after a sign error invalidated one argument and two dependent papers; the lab revised another 14. Cornell mathematician Alex Townsend expects even more errors to be disclosed over time.

Then came the Navier-Stokes drama in September, when mathematician Tristan Buckmaster alleged that OpenAI used a method that he and a colleague were already working with when the lab said its model had settled the Navier-Stokes problem. OpenAI denied that claim.

Three results, three release strategies

ETH was one of three claims OpenAI made in the same announcement. In mathematics, the company says its models proved the local smoothing conjecture—which Christopher Sogge posed in 1991—in every dimension, a result that would also settle the Kakeya and Stein restriction conjectures. The lab released the write-up and a Lean proof.

In physics, OpenAI says the models proved that certain quantum field theories exist in four dimensions, including a piece of a Clay Mathematics Institute Millennium Prize problem. A group led by Nobel laureate David Gross chose to withhold the AI material for now and write up the work itself.

OpenAI says it is not seeking academic credit and has given $5 million to the Simons Foundation for workshops on AI-produced results. The company acknowledges that each of its three release approaches carries tradeoffs and says it wants feedback on what works. For the ETH claim, the next markers are concrete: publication of the raw data the verifiers requested, the conference OpenAI agreed to fund, and the group's conclusions once its independent examination is complete.