OpenAI says its AI disproved the Exponential Time Hypothesis; experts to check

OpenAI said on Monday, October 26, 2026, that one of its internal AI systems has produced a proof that the Exponential Time Hypothesis, a widely used assumption in theoretical computer science, is false. The company says the proof has been checked by Lean, a computer program that verifies mathematical arguments step by step. The result has not been peer reviewed. Three leading complexity theorists, Ryan Williams, Russell Impagliazzo and Ramamohan Paturi, have been asked to organise an open, independent examination of the claim. Impagliazzo and Paturi are two of the researchers who first proposed the hypothesis more than 20 years ago. The announcement also covered two other AI-assisted results, one in pure mathematics and one in physics.

The Exponential Time Hypothesis, often shortened to ETH, is about how hard it is to solve Boolean satisfiability problems. These puzzles ask whether there is a way to set a list of true-or-false variables so that a formula built from them comes out true. OpenAI describes the problem as deeply related to P versus NP, the best-known open question in computer science. ETH states, roughly, that a version of this puzzle called 3-SAT cannot be solved in time that grows more slowly than a fixed exponential of the number of variables. Many researchers have used ETH as a working assumption to prove that other problems cannot be solved quickly. If ETH is false, a large family of those conditional results in the field known as fine-grained complexity would lose their footing.

The algorithm OpenAI describes is still very slow by everyday standards. Its running time grows faster than any polynomial, but, according to the Lean statement, more slowly than any fixed exponential, and it uses only a modest amount of memory. That narrow gap is exactly what ETH said could not exist. OpenAI itself says the result "reopens questions about how much faster these tasks could become" and that turning it into practical gains "will require significant further research". In other words, nothing changes for working software tomorrow; what changes, if the proof holds, is the map of what is believed possible.

A Lean check is strong evidence but not the last word. It confirms that the formal statement follows from the proof; experts still have to confirm that the formal statement says what the headline claims. That is why the review by the very people who framed the hypothesis matters. On the physics side, a group led by David Gross has chosen not to rely on the AI-produced material and to write up the result itself.

For India, which is building its own AI models under the IndiaAI Mission, the episode shows where frontier AI companies are now pushing: from writing code and text towards producing research results that experts must test. It also sets an example of process, with formal verification, public data and outside review, that research institutions everywhere may increasingly expect.

Short-term: Complexity theorists will scrutinise the proof and the formal statement in public. Until that review reports, the claim should be treated as OpenAI's, not as an accepted result.

Long-term: If the disproof holds, researchers will have to revisit results that assumed ETH and look for faster algorithms for related problems. It would also be one of the clearest cases yet of an AI system settling a well-known open question.

Who is affected: Theoretical computer scientists and students, researchers who rely on ETH in their own proofs, mathematicians and physicists working with AI tools, and AI labs whose claims of scientific discovery will be judged against this case.

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