Math Advisory Panel Demands OpenAI Release Yang-Mills Paper as Anthropic Posts Its Own ETH Refutation

Since OpenAI announced three claimed proofs on Monday, Oct. 26, in math, computer science and physics, the dispute has moved from what was claimed to how it was handed to the scientific community.

The advisory panel pushes back

The Advisory Group on Mathematics and Artificial Intelligence (AGMAI) is the expert panel OpenAI itself organized after mathematicians criticized its earlier releases. It issued a clarifying statement one day before the announcement. According to Scientific American, OpenAI's approach to two of the three results directly violates that statement, because OpenAI designated specific experts to shepherd the results into public view.

The physics paper is the sharpest example. A group led by Nobel laureate David Gross, with Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, chose not to release the AI-produced material for now and says it will write up the work itself. The claim concerns a rigorous existence proof for four-dimensional quantum field theories, including quantum chromodynamics and pure Yang-Mills theory. Yang-Mills is tied to one of the Clay Mathematics Institute's seven Millennium Prize Problems.

AGMAI wrote that "there is no scientific reason for delaying ... any further" and called on OpenAI to release the paper.

The model behind all three results remains proprietary. The exact prompts, compute time and chain-of-thought outputs have not been made public. OpenAI has not said how the model was built or trained.

Anthropic lands on the same result

A few hours after OpenAI's post, Anthropic published its own refutation of the Exponential Time Hypothesis (ETH), which it says an internal Claude model found on Oct. 16. OpenAI says its model found its disproof the same day and checked it in Lean, a machine proof-verification language, on Oct. 17.

ETH concerns how hard it is to solve Boolean satisfiability, a problem closely tied to P versus NP. Researchers have used it to show that problems in graph theory, computational biology and databases cannot be solved quickly. Hundreds of papers rest on it.

Scientific American reports that two of OpenAI's three results coincide with closely related work involving Anthropic.

What OpenAI says, and who is checking

OpenAI calls the manuscripts "a form of raw research data" rather than finished papers. It says its release process "continues to evolve in response to feedback from the associated academic communities." For the math and computer science results, the write-ups and Lean proofs are on the company's GitHub repository.

For ETH, Impagliazzo and Paturi of UC San Diego and Williams of MIT are organizing the examination. Impagliazzo and Paturi first proposed ETH, along with Francis Zane. In an open letter, the three wrote: "Our involvement should not be taken as certification of the claim. A result of this significance requires careful, independent scrutiny."

Williams said the group signed no non-disclosure agreements and will not be paid. The group asked OpenAI to release all raw data on the ETH result and to fund a conference for the research community. Williams and OpenAI both say OpenAI agreed to both.

The math claim is that OpenAI's models proved Christopher Sogge's 1991 local smoothing conjecture in every dimension. That would also settle the Kakeya conjecture and Stein's restriction conjecture in all dimensions. Mathematicians proved Kakeya in three dimensions last year, work that earned Hong Wang a Fields Medal this summer.

The track record so far

OpenAI's Oct. 6 release was 722 manuscripts in 372 families. Three were withdrawn on Oct. 7 after a sign error. The Oct. 26 update added two manuscripts, bringing the catalogue to 721 manuscripts in 373 families, and added a Lean formalization of an earlier rational Hodge conjecture result that the announcement did not mention.

OpenAI has acknowledged that some released results lack Lean-checked versions and may contain mistakes. A Lean check also has a limit: it confirms the formalized argument is internally consistent, not that the formal statement matches the question the paper claims to answer. That comparison still falls to human mathematicians.

Scooping complaints

The credit questions predate this week. Twelve hours before OpenAI announced on Sept. 8 that it had cracked the Navier-Stokes problem, NYU mathematician Tristan Buckmaster posted that he and Levent Alpöge of Anthropic had reached a partial solution to the same problem using AI tools from both labs. Nature has reported that the circumstances strongly suggest OpenAI got wind of their work. OpenAI says its internal investigation found Buckmaster's prompts could not have influenced its system. The Clay Institute says the problem appears to be settled and that its evaluation will be unhurried.

In a separate case, Mario Rodríguez Mestre, a PhD student at the University of Copenhagen, told The New York Times he had studied CRISPR-like repeated DNA segments in viruses for years, often with Claude, and kept unpublished drafts on a private account. Anthropic later said agents running on Claude had found the same pattern. "I am not claiming that Anthropic deliberately took our work. I cannot demonstrate that," he said. Anthropic says Claude was not trained on user transcripts and that its molecular biology team had no access to his conversations.

Researchers are adjusting. Sandra Laurentino at the University of Münster now substitutes variables before pasting her work into a model. Samuel Mehr at the University of Auckland has told his students not to upload protected information to commercial LLMs. Geoffrey Irving of Resolution in Berkeley put it this way: "They're going to get scooped, because the AIs are very good at solving problems."

What comes next

No independent expert has yet confirmed any of the three claims. The ETH review group, the promised conference and the Gross group's own write-up are the next checkpoints. The Yang-Mills paper remains unreleased, and AGMAI's demand for its publication has no announced response from OpenAI.