OpenAI says its AI disproved the Exponential Time Hypothesis

OpenAI says one of its internal AI systems has shown that the Exponential Time Hypothesis, a core assumption in computer science, is false. The company also claims new results in harmonic analysis and quantum field theory, for three discoveries in all.

None of the three claims has been confirmed by an independent group yet. OpenAI says it is handing the work to outside experts to check, and that their conclusions will be their own.

Key facts

• The company says it checked the proof in the Lean proof language on Oct. 17, 2026.
• The ETH is a long-standing guess about how hard it is to tell whether a Boolean formula can be satisfied, OpenAI says.
• Russell Impagliazzo and Ramamohan Paturi, both of UC San Diego, will lead the review of the ETH work alongside MIT's Ryan Williams.
• OpenAI also says its models proved the local smoothing conjecture for all dimensions, a result it says settles the Kakeya and Stein restriction conjectures too.
• In physics, OpenAI claims a rigorous proof that some four-dimensional quantum field theories exist, including pure Yang-Mills theory.

Background

OpenAI says the ETH has long been widely accepted and has served as a building block in hundreds of papers. Researchers in databases, graph theory, computational geometry and computational biology have leaned on it to show that some problems are probably hard, the company says. Impagliazzo and Paturi helped first propose the ETH in 1999, according to The Verge.

The Verge reported that a GitHub summary from OpenAI describes a deterministic algorithm for fixed-width CNF formulas. The algorithm counts every satisfying assignment exactly, using polynomial space and subexponential time, according to The Verge. According to that summary, the special case of 3-SAT is what breaks the ETH. "Surprisingly, our system has recently proved that the ETH is false," OpenAI wrote.

The math claim centers on the local smoothing conjecture, which Sogge proposed in 1991, according to OpenAI. OpenAI's post says the two-dimensional case was proved in 2019 by Guth, Wang and Zhang, and that Wang and Zahl settled the Kakeya conjecture for three dimensions in 2025. OpenAI says it got the AI output for this proof on Oct. It says it then finished a Lean version and posted both files on its public GitHub page.

[The physics claim covers four-dimensional theories including Quantum Chromodynamics, or QCD, and pure Yang-Mills theory, which falls under one of the Clay Mathematics Institute's Millennium Prize problems, OpenAI says](https://openai.com/index/building-scientific-understanding-with-academic-communities/). A Yang-Mills proof came out of OpenAI's models on Sept. 9, 2026, the company says. The company says it completed the Lean check of Yang-Mills existence on Oct.

The physics work will be guided by a group under Nobel laureate David Gross, with Arthur Jaffe, Michael Douglas, Nikita Nekrasov and Igor Klebanov as members, OpenAI says. OpenAI says the group has chosen to hold back the AI-produced materials for now.

These claims follow a busy month. The Verge reported that OpenAI put out nearly 400 AI-generated results earlier in October, spread over more than 700 manuscripts. Of the 719 manuscripts in that batch, just 300 top-line results had been formalized, roughly 42 percent, The Verge reported.

What it means for you

For most readers, nothing changes today. OpenAI says that building faster algorithms and turning theory into practical gains will take a lot more research. The sources do not say what a disproof would mean for real-world software or for encryption.

For researchers, OpenAI says the result reopens the question of how much faster some tasks could get, and it could point the way toward better algorithms. Work in the fields OpenAI lists, from graph theory to computational geometry, could be affected because many results there assumed the ETH holds.

The bigger story may be how AI results get checked. OpenAI says outside collaborators sign no nondisclosure agreements, take part by choice and without pay, and that OpenAI is not seeking academic credit. OpenAI says it accepted two requests from the ETH group: publish all raw data so others can verify it, and pay for a conference on what the work means.

There is also a dispute over process. Princeton's Institute for Advanced Study hosts AGMAI, a nine-person panel of math advisers, The Verge reported. The Verge reported that the panel, which OpenAI assembled, advised AI companies against choosing certain people to get AI output first. The panel cited biased selection, unequal access and borrowed reputation as concerns, according to The Verge. OpenAI used that kind of early-access approach for the computer science and physics results, The Verge reported.

Practical steps

• Read the source material: OpenAI says the ETH proof, in both plain language and Lean, is on its public GitHub repository.
• Join the review: the ETH working group is inviting the wider community to help set up an open look at the claim.
• Weigh in on the rules: the same group wants to talk through how AI-produced breakthroughs should be verified, who gets access and who gets credit.
• Keep in mind that OpenAI says outside experts will review the work, and their verdicts are still to come.

What happens next

The ETH group led by Impagliazzo, Paturi and Williams will check the disproof. It is not known whether it will confirm the result, or when.

OpenAI says Gross's group will write up the Yang-Mills and QCD result itself rather than release the AI-produced files now. It is not known when, or whether, those AI materials will come out. Whether the Millennium Prize will come into play for the Yang-Mills claim is also unknown.

OpenAI is putting $5 million into a $15 million Simons Foundation initiative that Anthropic is also funding, a push to help mathematicians understand AI-generated research, The Verge reported. OpenAI says its share will fund workshops, conferences and special programs.

FAQ

Has anyone confirmed the ETH disproof? No. OpenAI says outside experts will review it, and no independent group has published a verdict yet.

Does this mean computers will solve these problems faster soon? Not soon. OpenAI says faster algorithms and real-world gains will need significant further research.

Does OpenAI pay the outside reviewers? No. OpenAI says taking part is unpaid and voluntary, and members reach their own conclusions.

Where is the ETH proof posted? OpenAI says it put the plain-language proof and the Lean version on its GitHub repository.

Which AI model did the work? That is not known. OpenAI's post mentions only internal models.