Three OpenAI breakthroughs, three release strategies
On Monday, OpenAI announced three OpenAI breakthroughs in mathematics, computer science and physics, produced by its AI models. The mathematics result purports to prove the local smoothing conjecture in every dimension, which OpenAI says would also resolve the Kakeya conjecture. The computer science result claims to disprove the Exponential Time Hypothesis, a 1999 assumption about the limits of computation that hundreds of papers rely on. OpenAI says the physics result is an existence proof for four-dimensional quantum field theories, including quantum chromodynamics and pure Yang-Mills theory. The work does not address the unresolved Yang-Mills ‘mass gap’.
Experts who spoke to The Verge said there are good reasons to take the results seriously, variously describing them as “huge”, “major breakthroughs” and “significant”. But given the varying levels of disclosure, they also said it is difficult to fully judge the findings — and that doing so would take time.
That is where the announcement split in three. For the mathematics result, OpenAI released the AI-generated output, leaving researchers free to organise their own efforts to explain it. For computer science, it published the material alongside an external group of researchers — Russell Impagliazzo, Ramamohan Paturi and Ryan Williams, two of whom first proposed the hypothesis — who released the write-up and a Lean proof on GitHub with an open letter. Physics, meanwhile, has not been released at all. OpenAI said it will defer to an external group of experts, led by David Gross, about how to release the materials.
The 722-paper precedent
Researchers had reason to be wary of the choreography. Mathematicians are still grappling with the hundreds of preprints the company released on 6 October — 722 mathematics manuscripts from an unreleased AI model. This time, OpenAI said it was working with expert “shepherds” to decide how best to share its latest breakthroughs. The batch was smaller — three results instead of hundreds — and the company said it was experimenting with different approaches.
But the researchers’ excitement about the science was tempered by exasperation with OpenAI’s conduct. Many were eager for the wider community to get on with the arduous task of scrutinising the lab’s findings — and questioned why OpenAI was putting up additional barriers by handpicking experts to oversee the process.
The warning that came a day early
It is exactly the kind of gatekeeping the Advisory Group on Mathematics and Artificial Intelligence warned against just a day before the announcement. AGMAI, a group of experts hosted at the Institute for Advanced Study that OpenAI had previously pledged to consult on how to share its findings, published its responsible-release recommendations on 29 September, after receiving more than 600 replies from the mathematical community. The group recommended that AI labs release output on scholarly repositories, with formalised proofs and information on how the problems were chosen, and provide funding and other support for people working on understanding the results.
On 25 October, the day before OpenAI’s announcement, the group went further: “We recommend that AI companies do not adopt this practice,” it said, arguing that selecting certain people to receive the output first is “unnecessary” and risks unequal access, biased selection and delays.
Following the publication of the latest results, AGMAI urged OpenAI to make the physics outputs public without delay: “Understanding should develop in the open, with everyone given the same access. OpenAI have said they delayed release until the Lean formalization was complete. By their own account this is now complete, so there is no scientific reason for delaying the release any further.”
“It doesn’t make any sense”
Most experts The Verge spoke to welcomed OpenAI’s decision to consult outside researchers, but argued that publicly announcing results should also mean making that work available for anyone to scrutinise. Constantin Kogler, a researcher at the Institute for Advanced Study, questioned the decision to restrict access to experts of OpenAI’s choosing. “It doesn’t make any sense that first only a few distinguished scientists can look at them,” he said.
Andreas Karch, a physics professor at the University of Texas at Austin, was blunter. “The fact that they handpick the group is a disaster,” he told The Verge. “The large labs have enough power as it is. They should not be picking winners and losers.” Karch initially suggested selecting researchers through a competitive process, though he acknowledged it would likely produce a similar group, which he described as “first rate”. He argued the proof could be released now as well as appointing the expert group. “This would democratize access while still showing that they care about making the results meaningful and understandable,” he said.
Making the findings openly available could also lead to better science, said Brendan Hassett, a mathematics professor at Brown University, who described the mathematics claim as “well supported” while stressing he had not yet checked the Lean formalisation. “Having many groups around the world wrestle with these results supports rapid adoption of new tools by those that would like to use them,” he said.
OpenAI’s side of it
The case for the shepherds is practical: a small group may be able to coordinate verification faster than an uncoordinated crowd, and explaining results before releasing them may reduce confusion. OpenAI itself says members of the external groups participate voluntarily and without pay, sign no nondisclosure agreements, and can publish their own conclusions — and that OpenAI will not seek academic credit for discoveries produced by its models. OpenAI also acknowledges the awkward part: choosing the initial shepherds “creates asymmetry of information”, and it says it welcomes feedback.
The computer science group underlined its own independence in its open letter: “Our involvement should not be taken as certification of the claim,” Impagliazzo, Paturi and Williams wrote. And as Stanford mathematician Jared Duker Lichtman put it, finding a way to communicate with researchers that satisfies everyone may be impossible. “My sense is that for any approach, there is going to be someone who is upset,” he said. “So it’s just a question of finding the least offensive option.”
The question nobody can answer yet
That leaves the verification bottleneck — the part of the story no release strategy has solved. Even the material that has been released is hard to assess: the public Lean documentation for the computer science result describes formalised subexponential-time results for fixed-width Boolean formulas, while the review group examines whether the work actually refutes the Exponential Time Hypothesis. The formalised content may be narrower than the advertised claim, and only the review will settle it.
Xiaoyu He, a mathematics professor at the Georgia Institute of Technology, thinks the problem runs deeper than how OpenAI chooses to announce its findings. “The results are very impressive,” he said, “but I think they are making a show of trying to be responsible and thoughtful about how they release results while not being able to change the main issues: that fundamental results are being solved so quickly without human contribution, and that the papers are difficult to read and verify.”
That is the question now sitting with the physics result, which has not been publicly released: does the power to decide who sees a result first amount to influence over how it is judged — or does independent verification by the wider community stay fully open once the material is released? OpenAI says it will keep incorporating community feedback and improving its standards for sharing major scientific advances. The researchers who must do the verifying are waiting to see whether that means publishing the physics proof — and when.
