OpenAI Says Its Model Disproved the Exponential Time Hypothesis

OpenAI said on October 26, 2026 that one of its models had produced a claimed disproof of the Exponential Time Hypothesis (ETH), a longstanding conjecture in computational complexity theory. The company's academic-communities page states that the hypothesis is false. OpenAI said its models produced three proofs spanning mathematics, computer science and physics.

The other two areas named in OpenAI's research materials are the Kakeya conjecture and quantum chromodynamics. The academic-communities page also explains how researchers can verify the model results on all three topics, according to OpenAI.

Anthropic has since released its own refutation of the ETH, after OpenAI's announcement. Anthropic mathematician Levent Alpöge has suggested that OpenAI's solutions were based on pre-existing work. TechCrunch reported both developments on October 27.

The ETH was first published in 1999 by Russell Impagliazzo and Ramamohan Paturi, computer scientists at UC San Diego. It concerns how fast algorithms can solve hard problems. For a standard example, 3-SAT, which asks whether a set of logical conditions can all be satisfied at once, the hypothesis holds that worst-case running time must grow exponentially with the size of the input. Shortcuts that avoid this growth would be a major result.

OpenAI has asked Impagliazzo, Paturi and MIT professor Ryan Williams to help interpret its ETH solution. Williams is now organizing the computer science community's response to the refutation claim.

The discussion has a prior thread. Williams had earlier criticized OpenAI's early-October proof dump as a “DDOS attack on mathematicians.” He and collaborators have since released an open letter calling for feedback from scientists and discussion of norms around AI contributions to research.

The ETH claim is not OpenAI's first announced result in discrete mathematics. In May, the company announced that one of its models had solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry.

In my view, the more consequential question is procedural rather than the headline claim itself. A disproof of a complexity-theoretic conjecture is only as useful as the community's ability to check it, and the people now asked to interpret the ETH solution are the same people who built the field's understanding of the conjecture. How reviews are conducted, whether through conventional peer channels, open letters or direct engagement with the labs, will shape how future AI-generated results are weighed.

The broader context here is the review that follows. If the ETH claim holds up under scrutiny from the researchers who first framed the hypothesis, the result would reset a line of work that has organized algorithmic lower bounds for more than two decades. If it does not, the episode still gives the field a concrete case for how AI-assisted proofs should be documented, checked and credited.