OpenAI and Anthropic announced on the same day that each used its own AI model to disprove the Exponential Time Hypothesis, a longstanding premise in computational theory, and both results were verified using the proof verifier Lean. The announcements came on October 26 from OpenAI and a day later from Anthropic, according to a briefing published on November 2. The review of the proofs is still ongoing, and until external validation concludes, nothing is definitive, the briefing cautioned. The claims are therefore reported here as announcements under review, not as settled results.
The Exponential Time Hypothesis holds that the 3-SAT logical problem cannot be solved quickly. In plain terms, 3-SAT asks whether a set of logical conditions, each involving three variables, can all be satisfied at once. The hypothesis, formulated in the late 1990s by Russell Impagliazzo and Ramamohan Paturi, has served as a premise for hundreds of studies. If the new proofs are confirmed, the premises of those studies would need to be revisited.
What the Exponential Time Hypothesis claims say
On October 16, both models solved the problem with the identical bound expression, 2 raised to the power of n divided by the square root of log n, formalising the results using Lean. Anthropic’s paper is titled “A 2^o(n) Time Algorithm for 3-SAT”. Lean is a proof verifier that checks each step of a mathematical argument against formal rules, so a proof that passes Lean has cleared a mechanical check. That check is not the same as acceptance by the research community, which is why external verification matters.
Impagliazzo and Paturi, who originally formulated the Exponential Time Hypothesis, along with Ryan Williams of the Massachusetts Institute of Technology, are leading the external verification. Their involvement is notable because the originators of a hypothesis are well placed to judge whether a claimed disproof answers the statement as originally made. The briefing does not say when that review will finish, and it does not report a verdict from the reviewers.
Why two Exponential Time Hypothesis results arrived together
The fact that two companies announced the same finding on the same day demands rigorous verification rather than celebration, according to commentary in the briefing by attorney Kim Kyung-jin. Two independent systems reaching an identical bound expression on the same problem could reflect genuine progress in AI assisted mathematics. It could also reflect shared training material, shared problem framing, or a subtle error repeated in both efforts. External reviewers will need to test those possibilities, and the briefing gives no basis for choosing between them yet.
AI assisted mathematics has advanced in recent years as models have grown better at searching for proofs and checking steps. A model can propose many candidate arguments quickly, while a verifier such as Lean can reject those with gaps. That combination changes how fast a proof can be produced, but it does not remove the need for human reviewers to judge whether the formal statement matches the intended mathematical claim.
What confirmation of the Exponential Time Hypothesis claims would change
If confirmed, the results would upend the premises of hundreds of studies relying on the Exponential Time Hypothesis. Researchers who assumed 3-SAT could not be solved within the stated time bound would need to re-examine conclusions built on that assumption. Some results might survive under weaker assumptions, while others might need new proofs. The briefing does not list which studies would be affected, and this article does not guess at that list.
If the proofs fail review, the hypothesis would stand, and the episode would still show how AI systems are now producing claims in complex mathematical theory at a pace that review processes must absorb. Either outcome leaves a clear next step: publication of the reviewers’ findings. Until Impagliazzo, Paturi, and Williams complete their work, the correct description of the Exponential Time Hypothesis claims is that OpenAI and Anthropic have announced proofs, formalised them in Lean, and submitted them to external verification that has not yet concluded.