OpenAI says its AI disproved the Exponential Time Hypothesis

What is the Exponential Time Hypothesis?

The Exponential Time Hypothesis (ETH) is a long-held conjecture about how hard it is to solve Boolean formula satisfiability, a famous kind of logic puzzle that is deeply related to the P vs NP problem, according to OpenAI.

OpenAI says ETH has been widely believed to be true and has been used in hundreds of papers to show that problems in graph theory, computational biology, databases and computational geometry are hard to solve.

What did OpenAI announce?

On 26 October 2026, OpenAI announced three new discoveries in mathematics, computer science and physics. One of them is a result that, in its words, proves the ETH is false.

OpenAI says its AI found a natural language disproof on 16 October 2026, and that the result was then verified in Lean, a proof-checking language, on 17 October. It has published the written proof and the Lean proof on its public GitHub repository.

OpenAI says the refutation reopens questions about how much faster these tasks could become, and may help guide the search for better algorithms.

Has anyone checked the claim?

Not independently yet. OpenAI says the work will be verified and shepherded by a group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego, and Ryan Williams of MIT. Impagliazzo and Paturi are, with Francis Zane, the original proposers of ETH.

In an open letter they wrote that their involvement should not be taken as certification of the claim, according to TechCrunch. OpenAI says it agreed to their requests to make all raw data public and to fund a conference on what the result means for the field.

OpenAI also says the group members take part independently, unpaid and without non-disclosure agreements.

If the claim is correct, it will change an important part of theoretical computer science.

Russell Impagliazzo, Ramamohan Paturi and Ryan Williams, in their open letter, as quoted by TechCrunch

What were the other two results?

In mathematics, OpenAI says its models produced a proof of the local smoothing conjecture in every dimension, which it says also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions.

In physics, OpenAI says its models produced a mathematically rigorous existence proof for certain quantum field theories, including quantum chromodynamics. A group led by David Gross decided to hold off on releasing the AI-produced material and to write it up themselves.

Why does it matter?

If the disproof holds up, an AI system has overturned an idea that many researchers relied on for decades, and papers that assumed ETH may need a second look.

It also raises questions about how scientists should check, credit and release results that AI systems produce. OpenAI says it does not seek academic credit for the discoveries.

What's next?

Outside experts will examine the proof in the open, and OpenAI has committed to funding a conference on the result. Until that review is done, the claim is OpenAI's, not an established fact.