OpenAI’s biggest claim yet gets guarded welcome after Erdős, Navier-Stokes and a sign error

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The scientists that OpenAI has appointed to verify its latest claim that one of its internal models has successfully refuted the Exponential Time Hypothesis have declined to endorse the claim, pointing to past drama around the AI lab’s math announcements, which they say tend to be exaggerated.The Exponential Time Hypothesis, which the Altman-led lab claims to have cracked, is a measure of the difficulty of solving the Boolean satisfiability, a problem tied to the P versus NP question and a conjecture that underpins hundreds of computer science papers.MIT’s Ryan Williams and Russell Impagliazzo and Ramamohan Paturi from UC San Diego will lead the group responsible for independently verifying the results on the hypothesis originally proposed by Impagliazzo and Paturi, along with Francis Zane.The math community has not accepted OpenAI’s ETH claimThe three researchers leading the group checking the claim wrote in an open letter to their field that their “involvement should not be taken as certification of the claim,” before adding that “a result of this significance requires careful, independent scrutiny.”Writing on his X account, Williams said that the group did not sign a nondisclosure agreement (NDA) and would not be paid for the “open and independent examination” work that he and his colleagues were asked to do after “an internal model at OpenAI has produced a claimed refutation of ETH.”Williams added that OpenAI agreed to their request to publish all the raw data behind the result. The AI lab also agreed to fund a conference on its implications.Why the field is not supporting OpenAI’s claim without proofThree times OpenAI announced math breakthroughs. Each time, mathematicians checking the work found a gap between what was claimed and what held up.Previous OpenAI claims in the field of mathematics have not gone according to plan. An independent team of researchers is independently examining OpenAI’s claim even after the lab verified the disproof the internal models found on October 16 in Lean by the next day. The write-up and the Lean proof are posted to GitHub.Lean is a language that checks proofs by machine. However, even that method has been refuted 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 named OpenAI’s Navier-Stokes work as a case study.The mathematician who maintains the Erdős problems site, Thomas Bloom answered OpenAI VP Kevin Weil’s October 2025 claim that GPT-5 had solved 10 previously unsolved Erdős problems “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 had to make three withdrawals within a day of mass releasing 722 preprints on 372 math problems on October 6 due to a sign error that invalidated one argument and two dependent papers. The AI 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 AI lab said its model settled the Navier-Stokes problem.OpenAI denied that claim.Two more results, three release strategiesETH was one of three claims OpenAI made in the same announcement.In mathematics, OpenAI says its models proved the local smoothing conjecture, which Christopher Sogge posed in 1991, in every dimension, which would also settle the Kakeya and Stein restriction conjectures. The lab released the write-up and a Lean proof.In physics, it 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.Don’t just read crypto news. Understand it. Subscribe to our newsletter. It's free.