OpenAI's New Science Claims Put Independent Review in the Spotlight

Three claims, and the checking still ahead

The short version fits in a few sentences. On October 26, OpenAI announced three results it says its internal models produced, one each in mathematics, theoretical computer science, and physics. It also announced who would help the scientific community make sense of them. No source we read reports a finished independent assessment of any of the three.

That is why the argument now is less about the results than about the process. Who sees the evidence first? Who organizes the checking? And who decides when the rest of us get to look?

What is being claimed

The mathematics claim concerns a conjecture Sogge proposed in 1991 about "local smoothing," which describes how waves focus. Think of ripples converging on one spot. The conjecture says extreme focusing can last only briefly, so at a typical moment the concentration is far weaker than at its worst. Researchers proved it in two dimensions in 2019. OpenAI says its models proved it in every dimension, and that this settles two other well-known conjectures, Kakeya and Stein's restriction conjecture, in every dimension too.

The computing claim concerns the Exponential Time Hypothesis, or ETH. It is an assumption that certain logic puzzles cannot be solved quickly, and hundreds of papers rest on it. OpenAI says its system refuted the hypothesis. If that holds up, it could point toward faster algorithms. OpenAI itself adds that turning theory into practical gains would take significant further research.

The physics claim is a mathematical existence proof for certain four-dimensional quantum field theories, including quantum chromodynamics, which describes the strong force between quarks and gluons. The work includes pure Yang-Mills theory, which is part of a Clay Mathematics Institute Millennium Prize problem. The sources do not say whether the claim would meet that prize's requirements.

All of this is what OpenAI announced. None of it is confirmed.

What a machine check settles, and what it does not

OpenAI says it also formalized the mathematics and ETH proofs, and the Yang-Mills part of the physics work, in Lean, software that checks formal mathematical proofs line by line. That sounds like the end of the story. It is closer to the beginning.

AI Ping, in an October 27 report on the ETH material, points out a gap. The statement formalized in Lean gives a weaker running-time bound than the sharper one in the revised October 25 manuscript. Both fall in the "subexponential" family, meaning the time grows more slowly than the exponential growth the hypothesis concerns. But reading the sharper bound as fully machine-checked would stretch the facts.

AI Ping also notes that the manuscript covers a specific case: counting the solutions of logic formulas whose clauses have a fixed length. By the manuscript's own account, the result does not carry over to all hard problems of this kind, and it does not by itself show that P equals NP. Lean's comparison tool checks that a proof establishes the stated target, uses only permitted axioms, and is accepted by the system's core checker. People must still judge whether the formal statement matches the claim in ordinary mathematical language.

A checked statement is good evidence. Readers need to know exactly which statement was checked.

The researchers leading the ETH review are Russell Impagliazzo, Ramamohan Paturi, and Ryan Williams. According to AI Ping, they say their participation should not be read as certifying that the claim is correct. Their task is to find out what the argument shows, where it stops, and whether others can rebuild it.

Three ways to release

OpenAI describes three arrangements. For mathematics, it posted the model output and left researchers to organize their own efforts. For computing, it formed an outside group that develops explanations while the output stays public. For physics, it formed a group led by David Gross and left the publication decision to the group. As OpenAI describes it, that group has decided not to release the AI-produced materials for now and to write up the results itself. As Engadget reported on October 27, the group has so far published nothing and has set up an email address for questions.

OpenAI says participants sign no confidentiality agreements, serve without pay, and speak for themselves, not for the company. It says it will not claim academic credit for the discoveries. It also concedes the trade-off: choosing the first reviewers shapes who joins in early and creates unequal access to information. The company asks for feedback on broadening participation and says it does not yet know which approach will work best.

Why mathematicians object

The Advisory Group on Mathematics and Artificial Intelligence, or AGMAI, is a group of nine researchers, including Timothy Gowers, Martin Hairer, and Edward Witten. It says it works independently of AI companies and takes no payment, though it formed after OpenAI approached some of its members about an advisory board.

On October 26, AGMAI called on OpenAI to publish the natural-language and Lean materials for the Yang-Mills and QCD results without delay. The group argues these are mathematics questions as well as physics ones. It notes OpenAI said it was waiting for the Lean formalization, which OpenAI reports finishing for Yang-Mills on October 16. AGMAI concludes there is no scientific reason for further delay. The sources do not say how far the formalization of the QCD result has come.

Note a small mismatch in the accounts. OpenAI says the physics group chose to hold the materials back. AGMAI addresses its demand to OpenAI. The sources do not tell us how those two positions fit together.

A day earlier, on October 25, AGMAI published a broader statement. It grants that designating experts puts knowledgeable eyes on results early and can produce a better first write-up. But it lists the costs. Chosen researchers get a head start. Others may be discouraged from contributing. The selection reflects the company's networks and priorities. And the chosen names can end up vouching for a release and shielding the company from criticism. AGMAI says the chosen researchers acted in good faith and did valuable work. Its objection is to the arrangement. Its statement is aimed at mathematics, not necessarily other sciences.

AGMAI had a related warning on October 6, after an earlier OpenAI release. Releasing results, it said, is the start of human understanding, not the end. It added that mathematicians must be free to pursue their own questions, with fair access to powerful tools and computing power. That statement does not assess the new claims. It does explain why the dispute reaches past one proof.

Our view

We welcome serious claims being put where independent researchers can challenge them. We prefer public evidence, clear statements of scope, and explanations that people outside the first group can follow. Those conditions make a result more useful whether scrutiny confirms it, narrows it, or finds a mistake.

We also think the access dispute deserves as much attention as the headlines. Respected reviewers can help organize hard work, and OpenAI says it is open to changing the process. Still, a reviewer's name should never weigh more than the evidence behind it. Calling the arrangement a collaboration is accurate. For now it also works like a waiting line, and that is the part worth watching.

The open questions are concrete. What survives independent examination? When do the physics materials become public? And does the understanding spread beyond the first people given access?