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OpenAI and Anthropic each say an internal AI model disproved the Exponential Time Hypothesis

Two of the people who proposed the hypothesis in 1999 are now leading the check on it.

By Think Facility · November 7, 2026 · OpenAI AI research Save

On October 26, 2026, OpenAI added a paper called The Exponential Time Hypothesis is False to its public math repository on GitHub. Anthropic put up a paper of its own, credited to Claude, in its formal-math repository, and it claims the same thing.

Both companies say an internal AI model found it. No human has confirmed it. OpenAI says the proof will be examined by a group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams, and two of those three (Impagliazzo and Paturi) proposed the hypothesis in the first place, back in 1999.

Anthropic's account of how its version was found came from Levent Alpoge, at midnight Eastern going into October 27.

What the hypothesis says

The Exponential Time Hypothesis, or ETH, is about 3-SAT. It holds that every correct algorithm for 3-SAT needs time that grows exponentially with the number of variables.

It's been used a lot. In parameterized complexity, ETH is what tells you many known algorithms are about as fast as they can get, so if it falls, those guarantees fall with it.

Claim

the Exponential Time Hypothesis is false

Published

October 26, 2026, on GitHub

Hypothesis proposed

by Impagliazzo and Paturi in 1999

Formal proof

Lean formalizations from both labs

Peer-reviewed

not as of November 2026

It doesn't touch P versus NP. ETH implies P ≠ NP, but knocking ETH down doesn't give you P = NP, so even if the claim holds, the field's best-known open problem stays open.

What each lab released

OpenAI's entry describes a deterministic algorithm that exactly counts the satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The 3-SAT case is what refutes ETH. OpenAI says it made the materials public right away because the review group asked it to.

It's one of 721 manuscripts in that repository, all from an unnamed internal model. OpenAI posed the model about 4,000 problems; on average a result took three hours of ChatGPT Pro thinking compute. OpenAI calls the lot raw research data. On credit, it says it defers to mathematicians.

Anthropic's paper is titled A 2^o(n) Time Algorithm for 3-SAT. Its README says AI models wrote the Lean proof too, and it ends with something I hadn't seen a lab do before: a one-paragraph sketch of the idea, with the note that Claude Opus 5.5 at high effort can rederive the refutation from that paragraph alone.

What it means outside computer science

Some coverage has tied the result to encryption and chip design. Neither lab's page does. Anthropic's README says the opposite, in so many words, and I'd take that at face value: nothing here makes a real formula faster to solve this year.

What could change sooner is how mathematics gets checked, and who does the checking. OpenAI's history page is candid about the risk. On October 7, 2026, it withdrew three manuscripts because a sign error broke the argument under them. Fourteen more got proof repairs.

Lean helps with that. It doesn't close the gap, though. Anthropic's README says no machine checks that the short statement file says what the paper says, so the file is kept short enough for a person to read and compare.

What happens next

Impagliazzo, Paturi and Williams have published a message to the theoretical computer science community asking for input. As of November 2026 the claim hasn't been peer-reviewed.

The last entry on OpenAI's history page is dated October 29, and it's a fix to a different paper.