A fight over work related to the Navier-Stokes equation has turned into a much larger argument about AI, scientific credit, and the future of open research.
At the center of the dispute is a claim that OpenAI’s internal model solved the Navier-Stokes equation, one of the Millennium Prize Problems. That was followed by public allegations from New York University mathematician Tristan Buckmaster, who said that after he and Leven Alpöge had identified a promising route, OpenAI learned of that direction in the “last few days” and pushed its latest model along the same line with overwhelming compute.
According to the account cited in the source text, Buckmaster also alleged that when OpenAI approached the NYU team, it tried to control how the research would be released and said that any joint publication would require the removal of Anthropic collaborators from the author list. OpenAI researcher Sebastien Bubeck responded publicly, calling those allegations false.
The exact sequence of events remains disputed. The source text says one version that may be closer to reality is that Buckmaster did not get to the finish line first, OpenAI did, and the method used by OpenAI may not have been entirely invented by OpenAI itself.
A century-old math problem is now part of a fight over research norms
The Navier-Stokes equation has long been treated as a central challenge in fluid dynamics. It is also one of the seven Millennium Prize Problems listed by the Clay Mathematics Institute, and the problem has resisted resolution for more than a century.
Several months ago, Buckmaster and Leven Alpöge teamed up to use AI on important problems in fluid dynamics. The source text says that after months of work, they found a route that looked highly promising. What followed was a public clash over how that direction became known, whether an AI company moved quickly to publish ahead of the original researchers, and whether authorship was part of the negotiation.
Hugging Face co-founder Thom Wolf reacted on X with a sharply critical post, questioning that treatment of mathematicians and scientific communication and criticizing the idea of taking someone else’s work and then suggesting a joint paper.
Terence Tao says the deeper risk is the collapse of open science
Fields Medalist Terence Tao entered the debate with a long post that shifted attention from one contested result to the structure of research itself. His argument was not limited to one company or one equation. He warned that AI may be damaging the open-science tradition that mathematics has relied on for centuries.
Tao used an analogy: a country can be surrounded by ocean and still suffer from a shortage of drinkable water. Mathematics, in his view, is not short of problems. What is scarce is the ability to identify which problems are worth serious effort. That judgment is slow, careful, and often subjective.
He described traditional mathematical research as having a “terrain of difficulty.” Some problems are flat ground and can be handled with existing tools. Some are mountains that demand major effort. Others are chasms that cannot yet be crossed. That uneven terrain helps mathematicians see which directions matter and how different fields connect to each other.
His warning is that the AI era may flatten that terrain. Powerful tools, especially black-box systems whose inner workings are opaque, can act like a steamroller. In that setting, the problem is not simply that more questions get solved. It is that researchers lose the ability to distinguish promising lines from dead ends.
For Tao, the rarest resource in science today is not an answer but a promising question. In earlier periods, mathematicians who found a useful direction would often discuss it at conferences, in seminars, or with peers. That habit of exchanging partial ideas is one of the foundations of open science.
If sharing a direction becomes risky, secrecy becomes rational
Tao wrote: “We have already seen that even mere rumors that someone is working on a problem can trigger enormous AI-driven efforts that flatten the original project before it has had the chance to realize its potential.”
That warning goes to incentives. If a company with access to vast compute can seize on an early research lead and run thousands of fast iterations through a model, then years of human intuition and pathfinding can be turned into a published result on a much shorter timeline.
In that environment, public discussion stops looking generous and starts looking dangerous. Tao’s conclusion is that the current incentive structure is moving toward a world in which researchers stop sharing promising directions with the broader academic community. He said that would reverse centuries of open-science practice and cause serious long-term damage.
If that shift takes hold, the consequences would extend past one disputed paper. Researchers would keep ideas private, discussions would move underground, and conferences would turn into places where finished results are presented after the real intellectual exchange has already been withheld.
The dispute is also about whether science values answers or understanding
Tao’s post was widely amplified, including by François Chollet and Gary Marcus. Marcus backed Tao and said AI companies should compete on who can bring genuine scientific insight, not on who can use a compute advantage to announce a solution first.
That response pushed the debate toward a basic question: in research, is the goal only to reach an answer, or to extract wisdom, methods, and structure from the path toward that answer?
The source text argues that in foundational disciplines such as mathematics and physics, the proof process often matters more than the final statement. It cites Fermat’s Last Theorem, whose proof helped produce important tools in modern algebraic geometry, and the Poincaré conjecture, whose pursuit advanced topology.
One commenter under Tao’s post, as quoted in the source, put it this way: “No one ever said the answer was the most important part. We need to focus on understanding why these problems were difficult in the first place.”
Tao’s criticism is that if AI companies use black-box systems to assemble answers without releasing negative results or exposing the route taken, those outputs may serve a short-term goal while leaving little durable knowledge behind for future researchers.
He wrote that the indiscriminate use of powerful problem-solving tools may achieve the immediate objective of solving the problem at hand, but only at the cost of the ecosystem that supports the next wave of progress.
In his framing, raw solutions that do not come with careful analysis or new insight may have very limited value for the long-run development of human science and could even contaminate the field.
Tao calls for new social norms
The dispute tied to this fluid-dynamics problem is still unresolved. Yet regardless of what ultimately proves true about the episode, the argument has already exposed a deeper fracture around AI ethics and how research communities defend themselves.
Tao ended with a proposal for new norms. Academic communities, he said, should reject answers produced mainly through black-box brute force when those answers do not carry meaningful insight.
He compared that to modern food donation programs, which no longer accept just any donation, even if it is edible, but instead maintain standards accepted by society. The implication is that science should not be satisfied with output alone. It should also care about method, transparency, and knowledge value.
What exactly happened among OpenAI, the NYU team, and collaborators has not been fully established in public. Tao’s warning, though, is already clear: if mathematicians no longer feel safe discussing where research should go, then what is at risk is not only authorship on one paper, but the open-science tradition itself.