If the claim holds, one of complexity theory’s most heavily used assumptions is dead. OpenAI says its system disproved the Exponential Time Hypothesis, and that a Lean formalization verified the result. That is a big sentence. The more interesting part of the announcement, though, is how the company plans to get anyone to believe it.
In a post dated October 26, 2026, OpenAI announced three results spanning harmonic analysis, complexity theory, and quantum field theory. It calls the manuscripts “raw research data” and says turning them into scientific understanding is a job for outside experts.
The three results
The math result concerns the local smoothing conjecture, proposed by Sogge in 1991. It says the most extreme focusing of waves is short-lived. Guth, Wang, and Zhang proved the two-dimensional case in 2019, and Wang and Zahl proved the Kakeya conjecture in three dimensions in 2025. OpenAI says its models proved local smoothing in every dimension, which would also settle the Kakeya and Stein restriction conjectures in all dimensions. The proof reportedly rests on a new auxiliary partial differential equation. The AI output arrived October 18 and was formalized in Lean the next day.
The computer science claim is the loudest. The ETH says Boolean satisfiability cannot be solved in sub-exponential time, and hundreds of papers use it to argue that problems in graph theory, databases, computational biology, and geometry are hard. OpenAI says its system found a disproof on October 16, with a Lean check on October 17. The company is careful here: a refutation reopens questions about how fast these tasks could become, but practical algorithms would need significant further research. Don’t expect your solver to speed up next week.
The physics result is about the existence of quantum chromodynamics and completions of the Standard Model. The post gives the least detail on it, and that group has chosen not to release the AI artifacts yet.
A different release model
OpenAI asked outside experts to act as shepherds, and they recommended three strategies. Math gets a plain release of the AI output. Computer science gets an external group plus public materials. Physics gets an external group that controls the release. The natural language proof and Lean formalization for the ETH result are already on OpenAI’s GitHub.
The ETH group is credible. It is led by Russell Impagliazzo and Ramamohan Paturi, who proposed the ETH with Francis Zane, and Ryan Williams of MIT, who has refuted strong versions of it. Testing a claim like this with its own authors is a good sign. OpenAI also agreed to fund a conference on the implications.
The collaborations follow four stated principles:
- Transparency: no nondisclosure agreements, and members can publish freely.
- No academic credit sought by OpenAI for discoveries from its models.
- Recognition for the groups’ writeups and understanding.
- Independence: participation is voluntary and unpaid, and members do not speak for OpenAI.
Why it matters
Compare this with Google DeepMind’s AlphaProof and AlphaEvolve work, which mostly announced results on its own terms. OpenAI is instead admitting that generating a proof is now cheaper than understanding one. Lean helps, since a formal check removes doubt about correctness. It does not explain why the result is true, or whether the formal statement matches the conjecture people care about. That second question is where experts will earn their keep.
There are real weak spots. Unpaid volunteers carry the verification burden. Choosing the first shepherds decides who gets early access, and OpenAI itself concedes that creates information asymmetry. And the physics claim is the hardest to judge from the outside while its artifacts stay private.
Still, this matters more than a typical benchmark brag. If the ETH result survives scrutiny, it is a landmark. If it doesn’t, the public Lean files will make that obvious fast. Either way, the verification process is the real story.
