OpenAI and Anthropic both claim their AI broke the Exponential Time Hypothesis. Here’s what that would mean

TechCrunch reports that OpenAI says one of its models found a sub-exponential algorithm for the class of puzzles covered by the Exponential Time Hypothesis, which would refute it. Hours later Anthropic released its own refutation. ETH has been a load-bearing assumption in computer science since 1999. It holds that certain hard logic problems cannot be cracked much faster than brute-force search as they grow. Many results over the past decade rest on it.

OpenAI’s own post, which we covered in Working with academic communities to build scientific understanding, also claimed existence results tied to a Millennium Prize problem. If these hold up, they are historic, and the verification burden is proportionate.

If ETH falls, papers that assumed it need a second look, and long-held intuitions about what is computationally hard get shakier. ETH also served as supporting evidence for the common belief that P does not equal NP, the famous question of whether every problem whose answer can be checked quickly can also be solved quickly. A refutation would not settle P versus NP, but it removes one of the props people leaned on. Williams says it should nudge, not flip, anyone’s bet, and he doubts OpenAI’s algorithm is the best possible.

There is a security angle as well, since modern cryptography relies on some problems staying slow to solve. OpenAI told the researchers it checked and is reasonably confident no cryptographic systems are broken. That is reassuring and should be independently confirmed by cryptographers, especially regarding key sizes.

Williams described the proof as partly routine and partly genuinely strange, with a few sections he called alien-looking. That is the signature of something worth taking seriously: not a chatbot trick but new knowledge, the kind of useful AI that justifies the field’s ambitions.

A claim is still not a consensus. Anthropic mathematician Levent Alpöge suggested OpenAI leaned on existing work, and then Anthropic posted its own refutation within hours. When rival labs race to plant flags on the same summit, credit fights and competitive pressure shape how results are presented. Peer review exists so that speed doesn’t substitute for verification.

Earlier in October, Williams called one of OpenAI’s proof releases a denial-of-service attack on mathematicians, because it dropped results faster than anyone could check them. This time computer scientists formed a working group, asked for public proofs and pushed OpenAI to fund a conference. Impagliazzo and Paturi, who first stated ETH, are helping interpret it. That is a healthy division of labor: labs bring the compute, the field keeps custody of the truth. Frustration with labs controlling who sees results first is widespread (researchers are getting tired of OpenAI gatekeeping).

There is a quieter cost to name. If the problems graduate students cut their teeth on become easy pickings for models, how does the next generation of theorists learn? Williams flagged training future scientists as a real concern. Scale that up and the research culture could consume results it cannot produce or check itself. The labs should invest in that human capacity as heavily as they invest in announcements. More in our research coverage.