OpenAI Says Its AI Disproved the Exponential Time Hypothesis, but Independent Review Is Only Starting

OpenAI said on 27 October 2026 that its AI system produced a proof that the Exponential Time Hypothesis (ETH), a 1999 conjecture about the hardest problems in computer science, is false, and that the argument was checked in the Lean proof assistant. The company released the claim alongside two more, in mathematics and physics, and none of the three has yet been confirmed by outside experts, according to Tech Insider's summary of OpenAI's announcement.

The announcement matters less for any single theorem than for how the evidence is offered: a machine-checked result, an unpaid review by the hypothesis's own authors, and a promised data release. How that review plays out will shape how much weight researchers give AI-generated proofs.

What did OpenAI claim?

The headline result is a paper titled "The Exponential Time Hypothesis is false." According to KuCoin's report, the 67-page paper is dated 17 October and was revised on 25 October. It describes a deterministic algorithm that counts the satisfying assignments of 3-SAT formulas in subexponential time. Counting is harder than merely deciding whether a satisfying assignment exists, so the same result covers the decision problem.

OpenAI says its system found the disproof on 16 October and that it was formalized in Lean the next day, per the same report. The paper and the formalization are on GitHub. Tech Insider describes the algorithm as deterministic with polynomial space, and quotes OpenAI's own phrasing: "Surprisingly, our system has recently proved that the ETH is false."

ETH was proposed by Russell Impagliazzo, Ramamohan Paturi and Zane. It holds that 3-SAT, the problem of satisfying formulas built from three-variable clauses, cannot be solved much faster than by testing every combination of variables. OpenAI says hundreds of papers rely on ETH to argue that other problems are computationally hard, in areas such as graph theory, computational biology, databases and geometry, according to KuCoin. A refutation would therefore weaken a large body of conditional results at once.

Two more claims in the same release

Tech Insider reports that OpenAI made two further claims on the same day. In mathematics, a paper titled "Local smoothing for the Euclidean wave equation" claims Sogge's local smoothing conjecture in every spatial dimension of at least two. OpenAI says this also yields the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates, though Tech Insider notes the technical wording limits those to the "interior of the conjectured range", which is narrower than OpenAI's broader summary.

In physics, OpenAI says its models produced a natural-language existence proof for interacting four-dimensional quantum field theories with gauge fields and fermions, including quantum chromodynamics. Per Tech Insider's reading of OpenAI's page, the Yang–Mills existence proof was produced on 9 September and the QCD proof on 18 September. Fox News' live coverage says a physics group led by Nobel laureate David Gross is reviewing that work and that its release has been delayed. Tech Insider adds that the physics materials have not been released in full, so outsiders cannot audit the argument end to end.

Who is checking the work?

For the ETH result, Impagliazzo, Paturi and MIT's Ryan Williams are leading an independent examination, KuCoin reports. In an open letter they wrote that participation "should not be interpreted as certification," and called for rigorous independent review and an explanation that other researchers can reconstruct and challenge, according to the same report.

OpenAI says participants are unpaid and signed no non-disclosure agreements, that it has agreed to release all raw data, and that it will fund a conference on the result. KuCoin also reports that OpenAI contributed $5 million to the Simons Foundation to support workshops and programs that help researchers scrutinize AI-produced results.

For physics, Tech Insider says the Gross-led group includes Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, and that participation does not imply endorsement. It names no reviewers for the mathematics or computer-science results.

What are the limits of the claim?

Several caveats appear across the coverage. The paper does not show that every problem in NP has a subexponential-time solution, and P versus NP remains unresolved, per KuCoin. OpenAI itself cautions that turning the theoretical progress into practical gains would need substantial further research, and Tech Insider says the ETH result has no direct practical speedup implications.

A Lean check confirms that a formal statement follows from its formal assumptions. Tech Insider notes that a match between that statement and the informal claim still needs expert confirmation. The review panels were also chosen by OpenAI, and the article says questions remain about how independent they are and how disagreements would be published.

Independent academic confirmation is not clearly established for any of the three results as of 27 October, according to Tech Insider. Only the ETH result has a cited machine-checked step; the mathematics and physics results do not.

What do the sources disagree on?

Dates differ slightly between outlets. Some give the disproof as found on 16 October and others describe publication around 17 October; one account places the announcement on 26 October. KuCoin's summary also reports that Anthropic published a paper titled "A 2^o(n) Time Algorithm for 3-SAT" on 26 October, saying an internal research version of Claude found it, and that Anthropic's repository makes no practical formula-solving claim. The other sources reviewed for this article do not mention that paper, so it should be treated as unconfirmed until Anthropic's own publication is checked.

KuCoin also notes that OpenAI earlier published 722 math manuscripts on GitHub, only 162 of which included a computer-checked main result.

What happens next?

The near-term test is whether the examination led by the hypothesis's own authors reaches a public verdict, and whether OpenAI's promised data release lets others reproduce it. If the algorithm holds up, it would be among the most consequential results in complexity theory in decades, and it would hand AI labs a concrete benchmark for what machine-found mathematics can do. If it fails, the episode will still have set a template: formal verification, named reviewers with stated limits, and open data.

The physics claims face the slower path. With the materials not fully released and no group verdict published, they remain assertions rather than results. Readers should weigh all three claims accordingly: the ETH paper is the one that can be checked soonest, and the one whose outcome will say the most about the reliability of AI-produced proofs.