OpenAI published a preprint on October 26 titled “The Exponential Time Hypothesis is False.” If it survives review, it would be one of the most important results in computational theory in two decades, and an AI model would have found it.
What Is the Exponential Time Hypothesis?
The ETH (Exponential Time Hypothesis) was formulated by Russell Impagliazzo and Ramamohan Paturi in 2001. It says that solving 3-SAT, the problem of deciding whether a logical formula with n variables has any assignment that makes it true, requires worst-case time of 2Ω(n): it grows exponentially with the number of variables, with no substantial shortcuts.
It isn't the same as P vs NP. The ETH is a stronger, more specific assumption, and hundreds of "hardness" results in graphs, databases, computational biology and parameterized algorithms use it as a starting point: "if the ETH is true, this problem can't be solved faster than X."
What the Paper Claims
The document describes a deterministic algorithm that exactly counts how many assignments satisfy a k-CNF formula, for any fixed k ≥ 2. Counting is harder than deciding: if the count is greater than zero, the formula is satisfiable.
The exponent n/(log n)1/2 is still enormous, but it grows more slowly than any c·n. That's enough to refute the hypothesis, which concerns asymptotic behavior, not practical speed.
How It Happened and Who Will Review It
An independent review will be led by Impagliazzo and Paturi (UC San Diego), the very authors of the ETH, together with Ryan Williams (MIT). In an open letter they wrote: "Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny." Williams clarified that they signed no non-disclosure agreements and are not being paid. In the same package OpenAI announced two other proofs: the local smoothing conjecture in all dimensions (which would resolve Kakeya and the Stein restriction problem) and the existence of Yang-Mills in four dimensions.
What Changes If It's Confirmed
Results that depended on the ETH would lose their foundation and have to be rewritten on weaker assumptions. Stronger versions, such as SETH, would fall with it. Cryptography in use isn't broken by this: AES, RSA and elliptic curves don't depend on the ETH, and an algorithm with this exponent has no practical use against them.
The bigger change is something else: if validated, it would be the first time an AI model on its own refutes a central conjecture of computational complexity, with a proof a machine can verify.
Sources: paper "The Exponential Time Hypothesis is False" (OpenAI, October 17, 2026, revised October 25), The Next Web and StudyFinds (October 27-28, 2026). Result not peer-reviewed.