OpenAI Says Its AI Disproved the Exponential Time Hypothesis, a Rule Behind Hundreds of Papers

On October 26, 2026, OpenAI announced that an internal model had produced a disproof of the Exponential Time Hypothesis (ETH), a long-standing conjecture in computational complexity, along with two other claimed results in math and physics.

What ETH is

The Exponential Time Hypothesis is a conjecture about Boolean formula satisfiability, a problem closely tied to P vs. NP. Roughly, it says problems like 3-SAT can’t be solved in subexponential time. OpenAI says ETH has been widely believed and has been used in hundreds of papers to derive hardness results in graph theory, computational biology, databases, computational geometry and more.

According to the AI write-up summary, the paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. The 3-SAT case is what refutes ETH.

How it was checked

OpenAI says its AI found the natural-language disproof on October 16, 2026, and the result was formalized in Lean, a machine proof checker, on October 17. OpenAI has published both the write-up and the Lean proof on GitHub.

An independent group led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego, two of ETH’s original proposers along with Francis Zane, and Ryan Williams of MIT will organize an open examination. In an open letter, they wrote that their involvement “should not be taken as certification of the claim.” Williams said the group signed no NDAs and will not be paid. At the group’s request, OpenAI agreed to release all raw data and to fund a conference on the work.

If the result holds, OpenAI says it reopens questions about how much faster many tasks could become, though practical algorithms would still take significant further research.

Two more claims

• Math: OpenAI says its models proved Sogge’s local smoothing conjecture in every dimension, which would also resolve the Kakeya and Stein restriction conjectures in all dimensions. The AI output and a Lean proof are public.
• Physics: OpenAI claims a rigorous existence proof for certain four-dimensional quantum field theories, including quantum chromodynamics and pure Yang-Mills theory. A group led by Nobel laureate David Gross will shepherd it, and those materials have not been released yet.

OpenAI says it does not seek academic credit for the discoveries. None of the three results has been independently verified yet.