OpenAI says its model refuted the Exponential Time Hypothesis. The check is still open

OpenAI said on October 26, 2026 that one of its internal models has refuted the Exponential Time Hypothesis, a roughly 30-year-old conjecture about how hard it is to solve logical formulas. If the claim holds, OpenAI's ETH result is among the largest AI contributions to theoretical computer science so far. It has not been confirmed, and the people best placed to check it say so in the first line of their own statement.

What OpenAI claims

According to The Next Web's report of the announcement, OpenAI says its model produced the disproof on October 16, and the company checked it in Lean, a proof assistant that verifies arguments step by step, the next day. The natural-language write-up and the Lean proof were put on OpenAI's public GitHub repository. OpenAI describes the hypothesis as "widely believed to be true."

The announcement had three parts. Beside the ETH result, OpenAI says its models proved the local smoothing conjecture in every dimension, which would also settle the Kakeya and Stein restriction conjectures. In physics, it says its models proved that certain four-dimensional quantum field theories exist, including quantum chromodynamics, with a proof that pure Yang-Mills theory exists. We focus on the ETH claim because it is the one with an open independent check already organized.

What ETH is, and why people care

The Exponential Time Hypothesis concerns SAT, the problem of deciding whether some assignment of true and false values makes a logical formula true. OfficeChai's explainer says ETH holds that brute-force search is close to the best possible for SAT, so the time needed grows exponentially with the number of variables. Russell Impagliazzo, Ramamohan Paturi and Francis Zane proposed it in the late 1990s.

Its importance is as a foundation. Hundreds of papers use ETH as a working assumption to prove conditional hardness: if this problem were easy, SAT would be easier than ETH allows, so it must be hard. Those results span graph theory, computational biology, databases and computational geometry.

If ETH is false, the field has to work out which of those hardness results still stand on other grounds. OfficeChai is explicit about the limits: SAT does not become easy automatically, and P versus NP remains open. OpenAI itself says turning the theoretical result into practical, faster algorithms "will take substantial further work."

Who is checking, and on what terms

OpenAI asked three outside computer scientists to organize an open examination: Impagliazzo and Paturi of UC San Diego, who co-proposed ETH, and Ryan Williams of MIT, who has worked on refuting strong versions of it. Williams posted on X: "An internal model at OpenAI has produced a claimed refutation of ETH!"

The three then published an open letter to the theory community. Two of its sentences set the terms. The first: "Our involvement should not be taken as certification of the claim." The second: "If the claim is correct, it will change an important part of theoretical computer science."

According to Williams and OpenAI, as relayed by The Next Web, the group signed no non-disclosure agreements and will not be paid. It asked OpenAI to release all raw data on the ETH result and to fund a conference for the research community, and OpenAI agreed to both. That arrangement is better than most AI science announcements get, and it is worth saying so plainly.

Why a Lean proof is not the end of the story

A Lean check confirms that each step follows from the last, given the statement as written. It does not tell you that the statement is the one the field cares about, or that the human-readable write-up matches it. That gap has already mattered once this fall. Scientific American reported on September 21 that OpenAI's Navier-Stokes proof solved a variant of that problem involving an external force, which most researchers do not study, and quoted Luis Silvestre of the University of Chicago saying "The most important problem is unsolved." Our piece on what a verified AI proof means covers the same distinction between checked and correct.

The ETH case looks structurally cleaner, because the statement of ETH is short and precisely defined, and because its authors are the reviewers. That is a reason to take the claim seriously. It is not a reason to cite it as settled.

The context around the announcement

OpenAI said it does not seek academic credit and gave $5 million to the Simons Foundation for workshops and conferences on AI-produced results. The three computer scientists raised the credit question themselves, warning that recognition may go to those who publish first or hold the most powerful tools, while checking and explaining work earns less. The Next Web notes mathematicians raised similar concerns in the Leiden declaration in June.

There is also a backlog. OpenAI's October 6 release of 722 math manuscripts drew criticism from mathematicians including Terence Tao over the volume of claims released without structured verification, per OfficeChai. A reader should weigh the ETH announcement against that record: a lab with a very high claim rate and an uneven verification rate.

Our take

Treat this as a claim under review, with unusually good reviewers. What would change our view in either direction: a published verdict from Impagliazzo, Paturi and Williams; an independent re-derivation outside OpenAI; or a flaw found in the formal statement. What would not: more announcements from OpenAI. Until the group reports, the accurate sentence is that OpenAI says its model refuted ETH, a Lean check passed, and independent examination is open.