# New OpenAI Research Says Exponential Time Hypothesis (ETH) Is False > Source: > Published: 2026-10-27 04:28:23+00:00 OpenAI continues to come up with results that have the potential to shake the very foundations of their fields. OpenAI says one of its internal models has disproved the Exponential Time Hypothesis (ETH), a nearly 30-year-old conjecture in computational complexity theory that underpins a huge body of work on how hard certain computational problems really are. The ETH concerns Boolean formula satisfiability, a problem closely tied to the famous P vs NP question. Satisfiability asks whether there’s an assignment of true/false values to the variables in a logical formula that makes the whole formula true. The ETH holds that this problem cannot be solved meaningfully faster than brute-force search as the number of variables grows, and it has been treated as a working assumption in hundreds of papers to derive “if this problem is hard, so is this other one” results across fields as varied as graph theory, computational biology, databases, and computational geometry. OpenAI says its system produced a disproof of the ETH, and the result has since been independently verified using the Lean proof assistant, a tool that checks mathematical arguments step by step for logical errors. The company notes that refuting the ETH reopens questions about how much faster certain computational tasks could become, though it cautions that turning the theoretical result into practical, faster algorithms will take substantial further work. According to OpenAI’s account, the model produced its natural language disproof on October 16, 2026, with the Lean formalization following a day later. Both the natural-language writeup and the Lean proof have now been published to OpenAI’s public GitHub repository. ## A verification group led by the people who proposed the ETH Unlike a mathematics result OpenAI released the same day — a proof of the Kakeya conjecture in all dimensions, which the company put out for the research community to pick apart on its own — the ETH result is being handled through an organized external collaboration. OpenAI says it reached out to outside experts to act as “shepherds” for each of its three new results, and settled on different release strategies for each depending on their advice. For the ETH, that group is led by Russell Impagliazzo and Ramamohan Paturi of UC San Diego, and Ryan Williams of MIT. Impagliazzo and Paturi are, notably, two of the three researchers who originally proposed the Exponential Time Hypothesis more than two decades ago, alongside Francis Zane. Williams has previously worked on refuting strong versions of the ETH and on connecting algorithmic results to complexity lower bounds, making the panel about as close to the source of the conjecture as it’s possible to get. OpenAI says it has agreed to the group’s request that all raw data behind the result be made public so the broader community can independently verify it, and that it will fund a conference dedicated to working through what the disproof means for the field. The group is inviting researchers to help organize that examination and to weigh in on the harder questions an AI-generated complexity result raises around verification, credit, and access. ## Part of a broader release, with different rules for each result The ETH disproof is one of three results OpenAI announced together, alongside the Kakeya conjecture proof in mathematics and an existence proof for interacting quantum field theories — including Quantum Chromodynamics and a unified completion of the Standard Model of particle physics — in theoretical physics. For the physics result, OpenAI has gone a step further than the ETH case and is deferring entirely to its external group, led by Nobel laureate David Gross, on if and when to release the underlying AI-generated materials at all. OpenAI frames all three collaborations around the same four principles: transparency about the arrangement, no academic credit claimed for the model’s output, recognition for the external researchers who do the work of explaining and contextualizing the results, and independence, in that the working groups’ conclusions are their own and don’t represent OpenAI. The ETH release follows a pattern the company has been building toward for months. OpenAI’s [October 6 math drop included proofs touching 23 problems from the Erdős problems database](https://officechai.com/ai/openai-has-also-included-proofs-for-23-erdos-problems-in-its-latest-math-proof-drop/), a release that drew [pushback](https://officechai.com/ai/terrance-tao-explains-how-ai-powered-math-proofs-could-be-a-net-negative-for-math/) from mathematicians including Terence Tao over the sheer volume of claims put out at once without the kind of structured verification process OpenAI is now using for the ETH and physics results.