OpenAI says its AI refuted a core complexity hypothesis and proved two other results

Greg Brockman, OpenAI’s president, announced on X three scientific discoveries, one each in harmonic analysis, complexity theory and quantum field theory. The headline claim, according to secondary reports, is that an OpenAI model refuted the Exponential Time Hypothesis.

Brockman’s post is short. He wrote that the work shows “AI starting to help us improve our understanding of the universe!” The post links to the technical material, which could not be opened for this article, so the details below come from outlets relaying OpenAI’s claims. They have not been confirmed independently.

Three claimed results, two reportedly checked by machine

According to a report relayed by KuCoin News, citing ChainCatcher and Jin10 Data, the mathematics result is a proof of the local smoothing conjecture in all dimensions. The same report says it settles the Kakeya conjecture and the Stein restriction conjecture, two well-known problems in harmonic analysis. A separate summary describes the result as Sogge’s local smoothing for waves, which would also yield Kakeya maximal estimates. A DEV Community write-up gives the proof’s title as “Local smoothing for the Euclidean wave equation”.

In computer science, OpenAI is said to have refuted the Exponential Time Hypothesis. That is a widely used assumption that some hard problems cannot be solved much faster than by brute force. One summary says the route is a deterministic algorithm that counts satisfying assignments of fixed-width formulas in subexponential time. The KuCoin report says the result may point to faster algorithms than researchers expected.

The physics claim is the boldest. The KuCoin report says the AI produced rigorous existence proofs related to quantum chromodynamics and Yang-Mills theory, which it calls one of the seven Millennium Prize Problems. Another summary describes it as proofs for certain interacting four-dimensional theories with gauge fields and fermions. The two descriptions differ in scope, so the exact statement needs to be read from OpenAI’s own paper.

What has been checked and what has not

The reports draw a clear line. The mathematics and computer science results are said to be formally verified in Lean, a proof-checking program, with the proof materials made public. The physics result is described as under review by experts, including Nobel laureates in physics, with no outcome yet. One summary names physicist David Gross as leading a review group. That detail could not be confirmed from a page I read.

The DEV Community post adds that outside experts, which it calls “shepherds”, guided the computer science and physics work before publication. It does not name them. Neither it nor the KuCoin report names the model used, and the repository location was not available in any source I could read.

For readers, the practical point is that nothing here is a product. These are research claims, and OpenAI has not said whether the models behind them will reach ChatGPT or the API. A Lean-checked proof is strong evidence that the argument is correct. It does not show that the formal statement matches the problem mathematicians care about, which is why experts will still read the statements closely.

A second batch after the August problem set

This is not OpenAI’s first claim of this kind. On August 4, The Quantum Insider reported that OpenAI said an internal model solved ten major open problems in mathematics and quantum complexity. A search summary of that coverage notes that detailed proofs and peer review had not been released at the time. The DEV Community post says this latest release came less than a month after OpenAI published hundreds of manuscripts claiming solutions to long-standing math problems.

The new batch differs in two ways, going by the reports. It reaches into physics, and two of the three results are said to arrive with machine-checkable proofs instead of manuscripts alone. That answers the main criticism of the earlier round.

The release also sits alongside OpenAI’s commercial work. Days earlier the company put GPT-6.1 Terra in the API and Codex, rated Critical for cyber risk, so the research claims and the product line are moving at the same time. OpenAI has not said whether the discoveries came from that model.

What to watch is the physics claim. Existence proofs for gauge theories like those behind quantum chromodynamics would be a major result if they hold. The review described in the reports has not reported back, and none of the sources I read include comment from independent physicists or mathematicians.