How OpenAI Responds to Claims It Used Academics’ Work

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How OpenAI Responds to Claims It Used Academics’ Work in the Navier–Stokes Breakthrough

The controversy surrounding OpenAI's claimed progress on the Navier–Stokes Millennium Prize problem has developed into a wider debate about artificial intelligence, academic credit, unpublished research, and the increasingly powerful role of AI laboratories in mathematics.
Mathematician Tristan Buckmaster and other academics have raised concerns about how OpenAI arrived at its result, particularly because Buckmaster and collaborator Levent Alpöge had themselves been working on closely related problems while using OpenAI's Codex system.
However, it is important to distinguish between the different allegations. There is currently no established evidence that OpenAI simply copied or "stole" Buckmaster and Alpöge's unpublished proof.

1. OpenAI denies using Buckmaster's private Codex work
OpenAI has issued a direct denial that Buckmaster's recent private Codex interactions contributed to the Navier–Stokes result.
According to OpenAI, an internal investigation found that Buckmaster's Codex prompts from the period before the announcement:

"could not have influenced the system in any way, including through training."

OpenAI also says that neither its researchers nor the AI agents involved in the project had access to Buckmaster and Alpöge's unpublished research before it became public.
This represents a stronger position than OpenAI initially took.
Early in the controversy, OpenAI reportedly acknowledged that it could not completely exclude the possibility that de-identified product-use data might indirectly have contributed to model improvement.
After investigating the specific case, however, OpenAI stated that the relevant Codex sessions could not have affected the model responsible for the mathematical result.
Source:
[url=https://openai.com/index/navier-stokes-solution/]OpenAI — Navier–Stokes Solution[/url]
[url=https://www.wired.com/story/openai-navier-stokes-math-discovery-academics/]WIRED — OpenAI, Navier–Stokes and academic concerns[/url]

2. OpenAI admits that news of academic progress triggered its effort
One important part of the story is not disputed.
OpenAI acknowledges that its intensive Navier–Stokes effort began after researchers at the company heard that major progress had apparently been made on a Millennium Prize problem.
The company says that on September 1 it began directing substantial AI resources toward the problem.
It later became clear that the mathematical progress being discussed involved Buckmaster and Alpöge.
This means that OpenAI is not claiming that its effort was completely unrelated to the academics' work.
Rather, its position is that hearing that progress existed encouraged OpenAI to investigate the mathematical area independently.
This creates an important distinction.
The allegation is no longer simply:

"Did OpenAI copy the unpublished proof?"

There is also a broader ethical question:

"Should an AI laboratory use information that academics are close to an important breakthrough as a signal to deploy enormous computational resources and attempt to reach the result first?"

Some mathematicians regard this as a modern form of academic "scooping", even if no confidential mathematical details were directly used.

3. OpenAI argues that the mathematical results are different
OpenAI also argues that its mathematical result is substantially different from the work carried out by Buckmaster and Alpöge.
Buckmaster and Alpöge had obtained results involving the Euler equations with external forcing.
OpenAI says its AI-assisted approach went further by finding a construction without the same external forcing, eventually producing what it claims is a route toward the Navier–Stokes problem.
If correct, this would mean that OpenAI did not simply reproduce Buckmaster and Alpöge's proof.
This part of the controversy is potentially easier for the mathematical community to evaluate, because researchers can compare the published mathematical arguments directly.

4. The dispute over academic credit
Another controversial issue concerns authorship and academic recognition.
Buckmaster has described discussions with OpenAI researchers concerning how the respective results might be presented.
According to Buckmaster, OpenAI proposed arrangements under which he could potentially be connected to OpenAI's paper, while Alpöge — who works for Anthropic — would not necessarily appear in the same way.
Buckmaster also reported a particularly tense conversation in which OpenAI researcher Sébastien Bubeck allegedly asked:

"Why would you ruin your career?"

Buckmaster interpreted the conversation as pressure.
Bubeck disputes that interpretation.
He says he was not asking Buckmaster to remove Alpöge from their own academic research. Rather, according to Bubeck, the discussion concerned authorship of OpenAI's separate work.
Bubeck has also apologized for the wording concerning Buckmaster's career, describing it as a poor choice of words rather than a threat.
Source:
[url=https://www.abc.net.au/news/2026-09-10/openai-navier-stokes-millennium-problem-claims/107132242]ABC News — Navier–Stokes dispute[/url]

5. Buckmaster has stopped short of accusing OpenAI of theft
Despite the strong reaction surrounding the controversy, Buckmaster himself has been relatively careful in his public statements.
He has said:

"I do not know whether our data was used."

He has also stated:

"I am not accusing anyone of anything."

His argument is essentially that the timeline and circumstances were unusual enough that they deserved public scrutiny.
Therefore, the statement:

"Buckmaster proved that OpenAI stole his proof"

would currently be inaccurate.
A more precise description would be:

Buckmaster raised concerns about whether unpublished AI-assisted mathematical work could have indirectly influenced OpenAI's project and questioned the way OpenAI responded after becoming aware of his team's progress.

6. Criticism from the wider mathematical community
The controversy has expanded beyond Buckmaster.
A number of mathematicians have expressed concerns about the way large AI laboratories are entering mathematical research.
An open letter associated with members of the Caltech and broader mathematics community criticized the increasing pressure to rapidly announce AI-generated mathematical discoveries.
Critics argue that AI laboratories can deploy enormous amounts of computing power after hearing that traditional researchers are approaching an important result.
Some mathematicians have also complained that the academic community is then expected to spend significant amounts of unpaid time checking extremely long AI-generated proofs.
The open letter reportedly described some of these practices as potentially amounting to:

"research misconduct."

OpenAI subsequently withdrew its sponsorship of a Caltech mathematics event following the controversy.
Sources:
[url=https://proofsandprompts.com/2026/09/10/open-letter-about-the-mathathon/]Open Letter About the Mathathon[/url]
[url=https://www.businessinsider.com/openai-caltech-ai-math-hackathon-backlash-anthropic-2026-9]Business Insider — OpenAI withdraws from Caltech math event[/url]

7. Questions about citations and attribution
A separate controversy also emerged concerning references in OpenAI's mathematical paper.
Reports stated that the original version did not properly cite earlier work by mathematicians Diego Córdoba and Luis Martínez-Zoroa, whose techniques were considered relevant to the construction.
Those references were subsequently added.
This does not demonstrate that OpenAI copied Buckmaster's research.
However, it has contributed to concerns among mathematicians that the speed of AI-generated mathematical research may sometimes come at the expense of careful attribution.
Source:
[url=https://elpais.com/tecnologia/2026-09-10/openai-corrige-de-tapadillo-su-prueba-del-milenio-para-citar-a-los-
matematicos-clave-que-ninguneo-al-anunciar-el-descubrimiento.html]El País — OpenAI adds mathematical citations[/url]

Where does the evidence currently stand?
At present, there is no publicly demonstrated evidence that OpenAI directly stole Buckmaster and Alpöge's unpublished proof.
Two important facts, however, appear to be established.

• OpenAI learned that another group had made significant progress and then deliberately launched a very large computational effort toward the same general mathematical problem.
  
• Buckmaster had been using OpenAI's Codex system while conducting unpublished mathematical research, which naturally raised questions about whether those interactions could somehow have influenced OpenAI's models.
  

OpenAI now says that its investigation has ruled out the second possibility for the relevant prompts.
The remaining difficulty is independent verification.
Outside mathematicians can compare the mathematical proofs themselves, but they cannot independently reconstruct OpenAI's internal training pipeline or determine precisely what information was available to every system involved.
Conclusion
The controversy therefore appears to be shifting away from the simple question:

"Did OpenAI steal Buckmaster's proof?"

OpenAI has issued a fairly specific technical denial of that allegation.
The more difficult question may instead be:

"What should happen when AI laboratories hear that academic researchers are approaching a major breakthrough and can immediately deploy thousands of AI agents and enormous computational resources toward the same target?"

That question is likely to become increasingly important as AI systems become capable of carrying out more sophisticated mathematical research.
Traditional academic norms developed in a world where competing researchers generally had comparable human limitations.
AI laboratories operate under very different conditions.
The Navier–Stokes controversy may therefore become an early example of a much larger debate about authorship, priority, research ethics and the future relationship between mathematicians and AI laboratories.