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# OpenAI says its AI disproved the Exponential Time Hypothesis, and the people who proposed it will check
- URL: https://www.skimwire.com/openai-ai-disproves-exponential-time-hypothesis-kakeya-claims/
- Published: 2026-10-27T12:55:22.000Z
- Updated: 2026-10-27T12:55:22.000Z
- Description: OpenAI claims AI-found proofs that ETH is false and the Kakeya conjecture holds in all dimensions. Independent experts are now reviewing them.
- Author: Jeremy Moon
- Tags: AI

## The skim

- OpenAI says an internal model has disproved the Exponential Time Hypothesis (ETH), a decades-old assumption about how hard certain logic problems are. If that holds up, a lot of theoretical computer science has to be rethought.
- Two of the three researchers who proposed ETH, Russell Impagliazzo and Ramamohan Paturi of UC San Diego, will lead an open review with MIT's Ryan Williams. They say their involvement "should not be taken as certification of the claim."
- OpenAI also claims proofs that would settle the Kakeya conjecture in every dimension and establish that quantum chromodynamics exists as a rigorous mathematical theory. None of the three results has been independently confirmed.

## What OpenAI is claiming

In a [blog post Monday](https://openai.com/index/building-scientific-understanding-with-academic-communities/?ref=skimwire.com), OpenAI described three results from its internal models. It says the math and computer science proofs, and the Yang-Mills part of the physics work, were formalized in Lean, a language that verifies proofs by machine.

The biggest is in computer science. ETH says that problems like 3-SAT, which asks whether a logic formula can be made true, can't be solved much faster than by trying exponentially many combinations. OpenAI says hundreds of papers rely on it to show that problems in fields from graph theory to databases can't be solved quickly. OpenAI says the model found the disproof on Oct. 16 and that it was formalized in Lean the next day. The write-up and Lean files are [public on GitHub](https://github.com/openai/math?ref=skimwire.com).

The math result is a proof of Christopher Sogge's 1991 local smoothing conjecture in every dimension, which would also resolve the Kakeya and Stein restriction conjectures. Mathematicians had proved local smoothing only in two spatial dimensions (2019) and Kakeya in three (2025). The physics claim is an existence proof for certain four-dimensional quantum field theories, including quantum chromodynamics (QCD), the theory of quarks and gluons. That includes pure Yang-Mills theory, which OpenAI describes as part of a Clay Millennium Prize problem, not the whole problem.

## Who checks the work

OpenAI recruited outside "shepherds" this time. Impagliazzo, Paturi and Williams say they signed no nondisclosure agreements and aren't being paid. At their request, OpenAI agreed to make all raw data public and to fund a conference on the result. "The ETH has been widely believed true since the late 1990s and a great deal of theoretical computer science was built on it being true," Williams [told Al Jazeera](https://www.aljazeera.com/economy/2026/10/27/ai-makes-discoveries-in-mathematics-computer-science-physics-openai-says?ref=skimwire.com).

A group led by Nobel laureate physicist David Gross will write up the physics result itself and is holding back the AI output for now. OpenAI says it doesn't want academic credit for any of the three results and has given $5 million to the Simons Foundation for workshops on AI-produced results.

## Why it matters

Machine-checked doesn't mean settled. Lean confirms the logic is valid, but experts still have to confirm that the formal statement says what the paper claims. OpenAI's record is mixed: it withdrew three papers from its Oct. 6 batch of 722 AI-written manuscripts a day after release, after a sign error was found, [Retraction Watch reported](https://retractionwatch.com/2026/10/08/openai-withdraws-preprints-722-manuscripts-unsolved-math-problems/?ref=skimwire.com). The release process is also under fire. According to [The Verge](https://www.theverge.com/ai-artificial-intelligence/1019143/openai-eth-kaseya-science-math-physics?ref=skimwire.com), OpenAI's own panel of math advisers recommended a day earlier that AI companies stop giving chosen experts first access to results.

"If the claim is correct, it will change an important part of theoretical computer science," the three reviewers wrote in their letter. The next signal is whether other complexity theorists can follow the proof and confirm it.

*Sources:* [*OpenAI*](https://openai.com/index/building-scientific-understanding-with-academic-communities/?ref=skimwire.com)*,* [*OpenAI on GitHub*](https://github.com/openai/math?ref=skimwire.com)*,* [*Ryan Williams*](https://bsky.app/profile/rrwilliams.bsky.social/post/3myspd26qjk2c?ref=skimwire.com)*,* [*The Verge*](https://www.theverge.com/ai-artificial-intelligence/1019143/openai-eth-kaseya-science-math-physics?ref=skimwire.com)*,* [*The Next Web*](https://thenextweb.com/news/openai-exponential-time-hypothesis-false-kakeya-yang-mills?ref=skimwire.com)*,* [*Al Jazeera*](https://www.aljazeera.com/economy/2026/10/27/ai-makes-discoveries-in-mathematics-computer-science-physics-openai-says?ref=skimwire.com) *and* [*Retraction Watch*](https://retractionwatch.com/2026/10/08/openai-withdraws-preprints-722-manuscripts-unsolved-math-problems/?ref=skimwire.com)*.*