OpenAI Says Its AI Just Toppled a Bedrock Assumption of Computer Science
OpenAI claims its internal models disproved the Exponential Time Hypothesis, settled the Kakeya conjecture in every dimension and proved Quantum Chromodynamics exists. None of it is peer reviewed, and the physics proof has not been released.
For 27 years, computer scientists have built on a simple bet: some problems just cannot be solved fast. OpenAI now says one of its internal models has proved that bet wrong. The people who first wrote that bet down now have to check the work.
In a blog post published Monday, OpenAI announced three claimed discoveries at once. In computer science, it says its system refuted the Exponential Time Hypothesis. In mathematics, it says its models proved the local smoothing conjecture in every dimension, which would also settle the Kakeya conjecture and Stein restriction conjecture in all dimensions. In physics, it claims a rigorous existence proof for certain four-dimensional quantum field theories, including Quantum Chromodynamics. None of it has been peer reviewed. For now, all three are claims from the lab that built the machine.
The ETH result is the one with the sharpest edge. Proposed in 1999 by Russell Impagliazzo, Ramamohan Paturi and Francis Zane, the hypothesis says 3-SAT, a classic logic puzzle, cannot be cracked in subexponential time. OpenAI says hundreds of papers lean on it. Its write-up describes a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space. OpenAI says the model found the disproof on October 16 and the company formalized it in Lean the next day. Both files are on GitHub.
Impagliazzo and Paturi, both at UC San Diego, will lead the review with MIT computer scientist Ryan Williams. They are careful not to cheer yet.
"Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny." Russell Impagliazzo, Ramamohan Paturi and Ryan Williams
Williams wrote on Bluesky that the group signed no NDAs and will receive no compensation, and that OpenAI agreed to release its raw ETH data and fund a conference for the field. A Lean check shows a proof is internally sound. It does not show the formal statement matches what humans mean by ETH, which is where reviewers will poke first.
The math and physics claims are harder to check
The Kakeya angle stings in a different way. According to The Verge, NYU mathematician Hong Wang won a Fields Medal months ago for resolving the Kakeya conjecture in three dimensions, work she did with a co-author. OpenAI now says its models went to every dimension in one shot, using what it calls a novel auxiliary partial differential equation. The raw model output and a Lean proof are public.
Alex Iosevich, a harmonic analyst at the University of Rochester, told Al Jazeera that OpenAI appeared to have cracked the problem.
"The conjecture was formulated by my PhD adviser, Chris Sogge, so it is near and dear to my heart, and the news was a shock at first." Alex Iosevich, University of Rochester
The physics claim is the biggest and the least visible. OpenAI says the work includes a proof that pure Yang-Mills theory exists, part of a Clay Millennium Prize problem. You cannot read it. The shepherding group, led by Nobel laureate David Gross with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, chose to hold back the AI material and write it up themselves.
The shepherd model itself is already contested. The Verge notes that OpenAI's own AGMAI panel of math advisers said just a day earlier that "we recommend that AI companies do not adopt" the practice of picking select people to receive output first. OpenAI concedes the point in its post, saying that choosing shepherds "creates asymmetry of information."
That fight over credit and access is not new. OpenAI's earlier Navier-Stokes claim sparked a bitter credit fight of its own. This time OpenAI says it seeks no academic credit at all and has put $5 million into a Simons Foundation fund for researchers who study AI results. Generous, sure. But the only question that matters is still open. Are any of these proofs right?
The ETH reviewers put the stakes plainly: "If the claim is correct, it will change an important part of theoretical computer science." That if is carrying the whole story.
