OpenAI Claims Its AI Disproved a Core Assumption of Computer Science

OpenAI says its internal AI models have disproved the Exponential Time Hypothesis (ETH), one of the most widely accepted assumptions in computer science, and proved the existence part of a Millennium Prize Problem in mathematical physics. The company published three results spanning mathematics, computer science, and physics in a blog post, and it has asked outside experts — including 2004 Nobel laureate David Gross — to check whether the proofs hold. OpenAI calls the manuscripts raw research data that still needs to be understood.

The stakes are considerable. Hundreds of published papers in graph theory, computational biology, databases, and computational geometry build on the ETH. A proof that the assumption is false would strip those results of their foundations — not render them wrong, but unproven. Quantum field theory, the framework at the center of the physics result, is what OpenAI calls the most important framework in modern theoretical physics, yet it has never had an exact mathematical basis.

What does the computer science result claim?

The ETH concerns the Boolean satisfiability problem, or SAT: given a logical formula whose variables can only be true or false, can you set the variables so the whole formula comes out true? With few variables, you can try every combination. Each added variable doubles the possibilities. At 100 variables, the count reaches a 31-digit number.

The ETH says there is no real shortcut: in the worst case, computing time grows exponentially by a fixed factor with every added variable. OpenAI says its system has now proved the ETH false.

SAT connects directly to the P versus NP problem, the famous open question of whether a problem whose solution can be checked quickly can also be solved quickly. Checking a SAT assignment is easy; finding one is the hard part. A fast method for SAT would make thousands of other problems fast to solve too. Most experts believe no such method exists — the shorthand is "P does not equal NP."

The ETH goes further than that conjecture. It specifies not only that SAT is hard, but how hard. If the ETH falls, P could still differ from NP, so hard problems would not automatically become easy.

Who is checking the claim?

MIT professor Ryan Williams will independently verify and explain the result together with Russell Impagliazzo and Ramamohan Paturi of UC San Diego. Impagliazzo and Paturi originally proposed the ETH along with Francis Zane. Williams writes that the group has signed no nondisclosure agreements, is working unpaid, and plans to share interim findings as they go.

In an open letter, the three state that their involvement is not an endorsement of the claim. A result this big needs careful, independent review, they write.

At the group's request, OpenAI is publishing all the raw data, including the written proof and a Lean proof. Lean is a programming language that lets a computer check every step of a proof. That check has limits: Lean only verifies that the proof establishes the statement as written in Lean, and experts must still decide whether that statement captures the intended problem.

OpenAI has also committed to funding a conference on what the result means for the field.

Would developers notice anything?

Probably not immediately. Specialized programs called SAT solvers already handle formulas with millions of variables when checking chip designs for errors and testing software. Real-world formulas are usually much easier than the worst case the ETH deals with, so a worst-case speedup would not automatically help those programs.

Williams struck the same cautious tone on X. Asked what everyday developers would notice first, he said nobody knows yet. At the current pace, he said, it is plausible that practical SAT solving could see serious progress within 12 months. "Or we may see nothing of the sort. I really don't know," he admitted.

The theoretical fallout would reach complexity theory itself, specifically the study of circuits — networks of simple logic gates like AND, OR, and NOT. If the result holds, Williams says it would follow that a certain class of very demanding problems cannot be solved with small circuits, meaning circuits that need at most about twice as many gates when the input doubles in length.

What is the mathematics result?

The math proof targets the local smoothing conjecture, proposed by mathematician Christopher Sogge in 1991. Waves — sound, light, earthquakes — can concentrate at a single spot, like light at the focal point of a magnifying glass. The conjecture says that extreme concentration lasts only briefly, and that waves, averaged over time, behave more smoothly than the extreme case suggests.

Until now, the conjecture had been proven only in two dimensions, for waves on a surface like water, by Guth, Wang, and Zhang in 2019. OpenAI says its models have produced a proof for every dimension, including waves in space and in hypothetical spaces with more dimensions.

The reach extends beyond waves. Because the local smoothing conjecture is so basic to the field, two other well-known conjectures follow from it: the Kakeya conjecture from geometry and Stein's restriction conjecture from Fourier analysis, which breaks signals like sounds into individual oscillations. According to OpenAI, both would now be solved in all dimensions. The difficulty of that is measurable: Wang and Zahl proved the Kakeya conjecture only for three dimensions in 2025.

No dedicated group is shepherding this proof. OpenAI says it reached out to an outside expert to discuss such a collaboration, but on that person's advice it published the proof text and the Lean proof directly, letting researchers decide for themselves how to check the result.

What did the physics proof establish?

The physics result concerns quantum field theory, the framework physicists use to describe elementary particles and the forces between them. Its predictions are extremely accurate, but the theory lacks an exact mathematical basis; physicists work with approximations, such as an imaginary lattice of points made progressively finer. Whether that process produces a unique, consistent theory — whether a theory "exists" in the mathematical sense — has remained open.

OpenAI says its AI has proved that certain quantum field theories exist in four dimensions, meaning three of space plus time. Nobody has previously achieved such a proof in four dimensions for theories where particles interact with each other.

The proof centers on the strong force, which binds quarks into protons and neutrons and holds atomic nuclei together, carried by particles called gluons. It covers three theories that build on each other:

• Yang-Mills theory, which describes only gluons, without quarks, and is tied to one of the seven Millennium Prize Problems, each carrying a $1 million prize from the Clay Mathematics Institute. OpenAI says it has solved only the existence part of that problem; the second part, the mass gap, remains unproven. The mass gap is the distance between zero mass and the smallest possible mass of gluon clumps, a puzzle because massless carriers like light carry long-range forces while the strong force acts only over tiny distances.
• Quantum chromodynamics (QCD), which adds quarks and gives a complete description of the strong force.
• The simplest grand unified theory, which reduces the three forces to a single one and includes the Standard Model's force and matter particles. The Standard Model itself cannot be extended to arbitrarily small distances because some of its forces get stronger, not weaker, at small distances.

OpenAI says both Yang-Mills theory and QCD can exist mathematically mainly because of asymptotic freedom — the strong force gets weaker as particles get closer — which keeps the math manageable as the lattice gets finer.

A group led by David Gross, who shared the 2004 Nobel Prize in Physics for his work on asymptotic freedom, will shepherd the work. The group includes Michael Douglas, Arthur Jaffe, Igor Klebanov, and Nikita Nekrasov; Jaffe helped write the Millennium Prize Problem on Yang-Mills theory. OpenAI has already translated the Yang-Mills proof into Lean, but this group is holding back the AI's materials for now and plans to write up the result itself.

If the proof holds, all three steps would gain a mathematical foundation. That would not change any of physics' predictions, but OpenAI hopes it will turn quantum field theory into a mathematically rigorous discipline.

What are the open questions in OpenAI's process?

OpenAI admits the review process carries trade-offs. Whoever picks the first shepherds helps decide who gets involved first, the company writes, and some people end up knowing more sooner than others. OpenAI also says it is not yet clear which of the three field-specific approaches works best.

The company says it is not claiming scientific credit for the discoveries; credit should go to the groups explaining the results. That position appears to respond to criticism following the PR disaster over Navier-Stokes. OpenAI has also pledged $5 million to the Simons Foundation to fund workshops and conferences on AI results.

Williams' group, in its open letter, calls for a debate that goes beyond this review: how to verify AI breakthroughs, who gets access to them, and who deserves the credit.