AI Research Scooping: OpenAI's Navier-Stokes and Anthropic's Enzyme Claims Spark Priority Disputes with Scientists

Two announcements, five weeks apart, arrived with the same shape. On 8 September, OpenAI said an internal model had produced a proof that the three-dimensional Navier–Stokes equations can develop a finite-time singularity under smooth external forcing. On 23 September, Anthropic said roughly 950 Claude agents had identified a previously uncharacterised enzyme system — array-associated reverse transcriptases, or ARTs — in viruses that infect bacteria. Both companies called the result a milestone for AI in science.

Each claim landed next to a working researcher. Tristan Buckmaster, a mathematician at New York University, had spent about a year with Levent Alpöge, an Anthropic mathematician, pushing a related fluid-dynamics program toward the same prize problem. Mario Rodríguez Mestre, a computational biology PhD candidate at the University of Copenhagen, says his group has studied the very enzymes Anthropic named ARTs since 2022, calling them “jumbotrons.” Both men had used the announcing company's own models while doing the work.

That is the part worth sitting with. Neither researcher has produced evidence that a company read specific drafts or conversations. The disputes are about priority and provenance, and about what “independent discovery” can even mean when the tool and the competitor are the same organisation.

A proof, a prize, and a phone call

The Navier–Stokes equations describe how fluids move, and since Jean Leray's foundational work in 1934 mathematicians have asked whether initially smooth three-dimensional flow can blow up to infinite speed in finite time. The Clay Mathematics Institute put a US$1 million prize on the question in 2000. OpenAI's result is narrower than the first headlines suggested: the company proved finite-time blowup for the forced variant of the problem — Clay statements C and D — where a smooth external force is allowed to stir the fluid. The unforced physical equations, statements A and B, remain open.

The method was the story in itself. OpenAI said about 10,000 concurrent agents worked for roughly 88 hours and generated around 130 billion output tokens, and that a separate pass with GPT-6 Astra spent 17 hours checking the argument in the Lean proof assistant. One outside estimate, from University of Michigan engineer Karthik Duraisamy, put comparable compute at about US$6 million at retail rates — several times the prize OpenAI says it will not claim. The company posted a 166-page manuscript and a Lean formalisation on 9 September.

Buckmaster's account fills in the human side. He and Alpöge, working as a personal collaboration with no institutional backing, had made what Buckmaster called “real progress” on 15 August and verified it in Lean by 22 August, using a niche approach built on work by Diego Córdoba and Luis Martínez-Zoroa. They posted their preprints, with Lean formalisations, on 7 September — the day before OpenAI's announcement — covering the incompressible porous media equation, the two-dimensional Boussinesq system and the three-dimensional Euler equations, with a fourth result on hypo-dissipative Navier–Stokes held back while its Lean check ran. On 3 September he emailed OpenAI. On 6 September, by his account, he took two Sunday calls with OpenAI's Sébastien Bubeck and another mathematician. Buckmaster says OpenAI offered him sole authorship on a joint announcement while leaving Alpöge off, and that when he threatened to go public he was asked why he would “ruin your career.” He says his questions about whether his Codex drafts had been seen or used for training went unanswered.

OpenAI denies that account. Bubeck called the allegations “false and inflammatory” and later described one remark as a “poor choice of words.” Chief research officer Mark Chen said no person or agent searched user data to solve the problem. The company's own statement contains the sentence that keeps the argument alive: while unlikely, it “cannot rule out that de-identified data derived from their usage of our products helped improve our models.” Terence Tao, writing on Mastodon, called the Buckmaster–Alpöge work “a remarkable achievement” and said he saw no fundamental obstacle to extending their approach toward the full Navier–Stokes problem.

The enzyme claim, and a four-year head start

Anthropic's 23 September preprint described a search that began with a single high-level prompt: find unusual reverse transcriptases — enzymes that copy RNA into DNA — in a database of roughly 1.9 billion protein clusters. Around 950 agents ran for about 21 hours and consumed about 210 million tokens. The swarm gathered more than 200,000 reverse transcriptases, narrowed them to roughly 3,500 candidate systems, and sent about 20 of the most promising up for human review. One agent flagged a reverse transcriptase beside a long array of evenly spaced DNA repeats in jumbo phages, a structure that echoes the arrays CRISPR systems use. Anthropic named the system ART.

What ART does is unknown. The enzyme's activity has not been demonstrated, and neither the partner protein's role nor any gene-editing function has been shown. Anthropic itself said the underlying reverse transcriptase had appeared in earlier studies of a jumbo phage; its claim is that Claude was first to recognise the repeat array and a neighbouring protein as one system. A reanalysis of published data from a Staphylococcus lentus phage infection showed the array's transcripts made up as much as 8% of phage RNA 15 minutes after infection — evidence of activity, not of function. Feng Zhang, a CRISPR pioneer at MIT and the Broad Institute, called the finding “genuinely intriguing” and worth investigating. Lucas Harrington, who trained in Jennifer Doudna's lab and founded Mammoth Biosciences, was less generous: finding a strange cluster of genes and repeats, he wrote, “is often the easy part.” David Ricks, the chief executive of Eli Lilly, endorsed that post.

Then Mestre spoke. He told The New York Times his Copenhagen group had been studying the same enzymes since 2022 and had shared drafts and thesis material with Claude across three years of use. He is a co-inventor on a 2023 ReNegade Therapeutics patent covering related reverse transcriptases. “The most important question is not ‘Were ARTs already known?’ They were,” he said. The question, he added, is whether Claude reasoned its way to the result or was guided partly by his own work. Anthropic replied that Claude “was not trained on any user transcripts” and that its molecular biology team has no such access, and said it is unaware of previously published work describing the ART system.

What the re-readings changed

Mathematicians have now had about six weeks with the OpenAI paper, and the picture shifted. In Scientific American's 13 October account, several groups working through the proof concluded it does not, after all, follow the Córdoba–Martínez-Zoroa program that Buckmaster and Alpöge pursued. Gonzalo Cao-Labora, a mathematician at EPFL in Lausanne, put it plainly: “When you go to the details, it is a different approach.” The resemblance that triggered the fight may be superficial.

That does not settle the provenance question; it moves it. The result still depends on an unphysical, finely tuned force that stirs the fluid into a blowup, which is why the unforced problem stays open. A separate concern emerged on the verification side: an October audit posted by researchers including Alexander Bastounis argued that OpenAI's Lean repository does not faithfully match the written manuscript, citing a derivative mismatch in Lemma 8.6 and a different inequality in one uniqueness argument. Camillo De Lellis of the Institute for Advanced Study told Scientific American, “I honestly don't see a factual resolution of this.” A claim about where ideas came from cannot be checked the way a Lean proof can, because it is a claim about a training process no outsider can inspect. The pattern repeated elsewhere, when mathematician Andreas Thom presented evidence that OpenAI's announced solution to the Gromov soficity conjecture rested on a problem he had explored using OpenAI's tools.

The field answers back

On 11 September, 25 Fields Medalists published an open letter, “A Severe Misalignment of AI in Mathematics,” arguing that the goals of AI companies and the mathematical community are “severely misaligned,” and that rushing famous problems as model benchmarks is “detrimental to the science of mathematics.” Hugo Duminil-Copin's image — air-dropping someone on the summit of Everest is not the same as climbing it — captured the objection. The letter's sharpest point was that the profession's most precious resources are students and ideas. OpenAI responded by convening an independent advisory group on mathematics and AI, to be hosted at the Institute for Advanced Study, with initial members including Timothy Gowers, Edward Witten, Ravi Vakil and Martin Hairer. The company said the group would not advise on how fast OpenAI moves.

The concern has spread beyond mathematics. The French Mathematical Society issued a statement flagging what it called bibliographic plunder and energy costs, along with “rumours of coercion.” A 16 September editorial in Nature urged AI companies and the scientific community to agree on reliable, transparent ways of recognising contribution. In biology, the Copenhagen dispute pushed researchers to change their habits, as Nature reported on 7 October: Sandra Laurentino at the University of Münster now renames variables before pasting code into a model, and Samuel Mehr at the University of Auckland wrote a lab policy forbidding students from uploading protected material to commercial tools. Funders are moving too — Wellcome, a signatory to the UK Research Funders Policy Group statement, bars reviewers from inputting confidential grant applications into generative AI, and reported in June that about a quarter of applicants to its early-career awards disclosed using generative AI.

What this means for your lab

Set the base rate before the exception. In five weeks, two researchers said a company's announced result looked like work they had already shared with that company's tool; in neither case has anyone shown that a specific conversation or draft was read or directly used. The exception is what the companies concede themselves: OpenAI says it cannot rule out that de-identified usage helped improve its models, and Anthropic's own note shows the agent swarm missed the repeat array in ten repeat runs. A discovery that does not reproduce is a lead, not a result.

That asymmetry — you cannot prove what happened inside the model, and the vendor cannot fully disprove indirect influence — is what the new provenance standards are trying to address. It is also why journals keep tightening their generative-AI policies for peer review, since reviewers hold the same confidential material researchers do. For a working lab, the practical steps are less dramatic than the headlines. A postdoc I work with — call her Dr. R — stopped pasting unpublished figures into a consumer chat window the week the Copenhagen dispute broke. Her group now keeps a one-line log of which model saw which file and when. It took an afternoon.

• Use enterprise or API tiers, which generally exclude inputs from training by default, and confirm that in writing.
• Check whether an opt-out has a feedback exception that can still route a conversation into training.
• Keep local records of prompts, uploaded files, model versions and outputs — the audit trail the dashboards do not give you.
• Rename variables and strip identifiers before anything touches a model, the way Laurentino does.

One next step

Before your next grant cycle or manuscript submission, sit down with your lab's AI accounts and get four answers in writing: whether inputs train models, whether opting out has a feedback exception, how long prompts are retained, and who inside the vendor can review stored conversations. If you cannot get all four, treat the tool as a public notebook.

Photo by Brecht Corbeel on Unsplash