OpenAI’s three claimed breakthroughs face researcher resistance

By Sophie Lindqvist

OpenAI announced three results on Monday: a claimed all-dimensional solution to Kakeya, a claimed disproof of the exponential time hypothesis, and a physics result on quantum chromodynamics and Yang–Mills theory.

The company paired the announcement with an evolving disclosure policy. OpenAI says outside expert “shepherds” will help decide how to release each result, after months of friction over hundreds of AI-generated preprints sent to mathematicians at the start of October.

The Verge’s interviews frame the dispute as more than a scheduling problem. Researchers said OpenAI would control the first audience for consequential work, repeating a pattern they described as exhausting after months of AI-generated findings.

What did OpenAI release?

Following advice from its “shepherds,” OpenAI assigned each result a different release route:

• Mathematics: OpenAI released the AI-generated output, “leaving researchers free to organize their own efforts to explain the result.”
• Computer science: OpenAI will assemble an external group of researchers “to explain the result.”
• Physics: OpenAI released nothing and said it would “defer” to an external group of experts about how to release the materials.

OpenAI said all three concern some of the most consequential unsolved problems in mathematics, computer science, and physics. According to the company, some extend earlier work, while others break new ground.

The Verge said uneven disclosure and technical complexity make full judgment difficult. Even with all information available, evaluation would take time, though experts still described the results as “huge,” “major breakthroughs,” and “significant.”

The plan creates three access tiers: an open mathematics output, an external group for computer science, and no physics materials.

Why do the three results matter?

OpenAI’s mathematics output purports to resolve the Kakeya conjecture in all dimensions. In rough terms, the problem asks how little space is needed to rotate a needle or pencil in every direction.

A proof of the three-dimensional version was among the achievements for which NYU mathematician Hong Wang received a prestigious Fields Medal earlier this year. OpenAI’s claim under review covers all dimensions.

Brown University mathematics professor Brendan Hassett told The Verge OpenAI’s claim “looks well supported.” He had not yet checked the Lean formalization, which The Verge described as a means of computationally verifying results.

The physics result explores the Standard Model, which The Verge described as physics’ most successful and complete theoretical framework. It focuses on quantum chromodynamics and that field’s relationship to Yang–Mills theory.

Quantum chromodynamics describes the strong nuclear force, one of nature’s four fundamental forces alongside gravitational force, electromagnetic force, and weak nuclear force. Yang–Mills theory is also a cornerstone of modern particle physics.

Yang–Mills theory sits at the heart of one of the seven Millennium Prize Problems in mathematics. OpenAI said its physics work does not address the unresolved mass gap.

The computer science result claims to disprove the exponential time hypothesis, a widely held assumption that certain problems cannot be solved substantially faster than brute-force approaches. The claim is closely related to P versus NP, another Millennium Prize Problem.

P versus NP asks whether problems whose solutions can be easily checked are also easy to solve. The Verge described it as one of theoretical computer science’s biggest unsolved problems.

The stakes are verification: OpenAI’s uneven release leaves researchers with different amounts of evidence.

Why is selective access drawing resistance?

Constantin Kogler, a researcher at the Institute for Advanced Study, welcomed the manageable batch of three compared with the hundreds released previously. “I am fine with them releasing the problems as they did today,” he said.

But he questioned limiting first access to experts OpenAI chose: “It doesn’t make any sense that first only a few distinguished scientists can look at them.” The experts The Verge interviewed wanted the wider research community to begin the arduous work of scrutiny.

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 argued: “The large labs have enough power as it is. They should not be picking winners and losers.”

Karch initially suggested a “competitive process” for selecting the group, while acknowledging it would likely produce a similar group. He called that likely roster “first rate.”

Karch later asked why OpenAI “can’t release the proof now,” rather than only appointing experts. He said: “This would democratize access while still showing that they care about making the results meaningful and understandable.”

Researchers support outside scrutiny, but they object to OpenAI choosing who enters the process first.

What did AGMAI recommend?

One day before the announcement, the Advisory Group on Mathematics and Artificial Intelligence, or AGMAI, warned against selective first access. OpenAI had previously pledged to consult the group on how to share its findings.

“We recommend that AI companies do not adopt this practice,” AGMAI said. The group called advance access “unnecessary” and said it borrows the reputation of selected researchers.

AGMAI also warned of unequal access, biased selection, and delays. It recommended releasing outputs on scholarly repositories, with formalized proofs and details about how the problems were chosen. The group also called for funding and other support for researchers trying to understand the results.

After publication, AGMAI urged OpenAI to “make public without delay the natural-language and Lean outputs behind its announced” results in physics. The group said OpenAI had delayed release until the Lean formalization was complete.

AGMAI wrote: “While these are central questions in physics, they are also important questions in mathematics. The existence of quantum Yang–Mills theory is part of a Millennium Prize problem and the construction of interacting quantum field theories in four dimensions has been a goal of mathematical physics for decades.”

It added: “We have great respect for the scientists asked by OpenAI to lead this work. But as we explained in our recent statement, understanding should develop in the open, with everyone given the same access.”

AGMAI then noted: “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.”

Brendan Hassett argued that open access could improve science and encourage wider adoption of AI tools. “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.

AGMAI’s position is straightforward: publish the outputs, proofs and access on equal terms.

Can any release process satisfy everyone?

OpenAI says it is experimenting with different approaches and acknowledges that each has tradeoffs. The company still has to choose a process that supports meaningful review without creating another barrier.

Stanford mathematician Jared Duker Lichtman said finding a process that works for fields OpenAI is increasingly encroaching on 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.”

Georgia Institute of Technology mathematics professor Xiaoyu He said, “The results are very impressive,” but warned that OpenAI was “making a show of trying to be responsible and thoughtful about how they release results.”

He said the release process could not fix two deeper problems: “fundamental results are being solved so quickly without human contribution” and “the papers are difficult to read and verify.”

OpenAI’s next decision on the withheld physics materials will show whether its shepherd model broadens research access or merely renames selective review.