A claim that stunned mathematics
In September, OpenAI announced that its artificial intelligence agents had solved one of mathematics' great unsolved problems. The problem concerns the Navier-Stokes equations, the set of equations that describe how fluids move, from water in a pipe to air flowing over an aircraft wing. Mathematicians have wrestled with these equations for about 90 years, and a related question is one of the seven Millennium Prize Problems set by the Clay Mathematics Institute, each carrying a $1 million prize.
OpenAI said its agents cracked the problem in 88 hours. The company described a run involving about 10,000 AI agents, millions of exchanged messages and around 130 billion output tokens. It said the work resolved key parts of the problem, showing that a smooth fluid flow can develop a singularity, a point where speeds grow without bound, in finite time. The body that runs the prize said the problem had apparently been settled, but added that its review would take time. That caution matters, because a claim of this size is not settled by announcement alone. It has to survive close checking by independent mathematicians, a process that can take months or years.
The announcement landed as a showcase for what AI can now do in research. Mathematics has become a favourite testing ground for AI companies, because problems there have clear right answers and proofs can, in principle, be checked step by step. A system that can produce a long, formal proof looks like a powerful research tool, and OpenAI presented its result in exactly those terms: a demonstration that AI agents can now tackle problems that have resisted human effort for decades. For readers following technology news and science news, the claim was striking on its own. What followed made it a much bigger story.
The question Buckmaster raised
Hours before OpenAI's announcement, Tristan Buckmaster, a mathematician at New York University, went public with concerns of his own. Buckmaster had formed an independent team with Levent Alpoege, a mathematician employed by the rival company Anthropic. The pair had been working towards the same goal, and they had kept their drafts in OpenAI's coding tool, Codex. Buckmaster said his co-researcher had been tipped off that news of their progress had reached OpenAI, though he did not specify how that information had travelled.
Buckmaster asked whether research stored in Codex could have fed into OpenAI's own work. He was careful about how he put it, stressing that he was not accusing anyone of anything. That distinction is important, and it has been preserved in reporting of the row ever since. Buckmaster raised a question about process and access, not a direct charge of copying. The question was still uncomfortable for OpenAI, because it touched on a basic issue in science: when researchers store unpublished work in a tool run by a company that is also competing in the same field, who can see that work, and what safeguards separate one team's drafts from another team's research?
OpenAI rejected the suggestion that it had used the other team's work. The company said nobody at OpenAI, human or AI, saw the other teams' work before it was published. At first, it added that it could not rule out that anonymised data from use of its products may have helped improve its models. Days later, it went further, saying that Buckmaster's Codex prompts from the two months before the announcement could not have influenced the system in any way. That shift, from a qualified denial to a firmer one, has itself become part of the story, because it shows how hard it can be for outsiders to judge what happened inside a closed system.
The full picture remains unclear, according to BBC reporting and other coverage of the dispute. The two sides also disagree about substance, with some reports noting that the methods used were similar in places, while OpenAI has said the proofs differ significantly. What is not in dispute is the timing: two efforts on closely related problems reached public attention within days of each other, and one of them was built using the other company's tools. That sequence alone was enough to shake confidence among mathematicians who had already been uneasy about AI companies racing to solve famous problems.
A mathematics lecture taking place in a university lecture hall
Credit: Public domain, via Wikimedia Commons.
Why credit matters so much in mathematics
In most fields, being first matters. In mathematics, it matters in a particular way, because a proof is a permanent contribution to a shared body of knowledge. Credit decides who is remembered for a breakthrough, who gets invited to speak, who wins prizes and who secures funding for the next project. When a result is produced by a large team of AI agents, those questions become harder. Who is the author? Is it the company, the researchers who set the problem, the engineers who built the system, or the agents themselves? And when an independent team has been working on the same problem in private, how should a company handle the news that a rival effort is close?
The row has also revived an older argument about what mathematics is for. Some mathematicians, including Fields Medal winners who signed a declaration on AI in mathematics, argue that solving a problem is not the same as advancing the field. On this view, the value of a proof lies in the ideas it introduces, the connections it reveals and the understanding it leaves behind for others to build on. A long, machine generated proof that few people can read or learn from may settle a question without doing that wider work. Others take a different view, arguing that new results, however they are produced, create new territory to explore and that understanding can follow from a solution rather than precede it.
That disagreement was on display at the Heidelberg Laureate Forum, where mathematicians debated OpenAI's claim in public. Jacob Tsimerman, a Fields Medal winner who joined OpenAI as an AI safety researcher, emphasised the scale of the claimed achievement. Peter Scholze, another Fields Medal winner, argued that solving famous problems matters because the methods can illuminate related questions and deepen human understanding, and that a lengthy machine generated proof may contribute less to that goal than its headline suggests. Both positions were reported in coverage of the forum, and neither side has conceded ground. The debate is genuine, not a misunderstanding, and it will shape how mathematics treats AI results for years.
A wider worry about trust in research
The Navier-Stokes row is only one part of a larger concern. Researchers and journal editors say AI is already changing how science is produced and checked, and not always for the better. One problem is volume. AI tools can generate papers, drafts and submissions at a speed that peer review was never designed to handle. Editors describe a rising tide of submissions that need careful checking, including papers with invented references, plausible sounding claims that do not hold up, and results that look stronger than the evidence supports.
A second problem is detection. A computer scientist at Ghent University searched more than a million biomedical research papers for wording patterns favoured by AI writing tools and found that by December last year, nearly 90 percent showed AI fingerprints, according to reporting that summarised the study. AI detection tools are imperfect, and that figure should not be read as proof that 90 percent of papers were written by AI. It does suggest, however, that AI assistance is now widespread in scientific writing, and that journals cannot assume a submitted paper was produced in the traditional way.
A third problem concerns novelty. Google DeepMind, another AI lab, has claimed striking results in predicting new crystal structures for materials science. Researchers Anthony Cheetham and Ram Seshadri sampled the supposed new crystals and reported that they had yet to find any strikingly novel compounds, describing many as trivial adaptations of known materials. DeepMind rejected that charge, saying it had tested each compound for novelty and arguing that dismissing unfamiliar structures for looking familiar misses the point. The exchange shows how hard it can be to judge an AI claim from outside: the data, the methods and the checks are often controlled by the same company making the claim.
Dalmeet Singh Chawla, a science journalist who covers research integrity, has argued that generative AI has basically disrupted the whole scientific process, and that publishers' integrity teams will need to increase their efforts sharply to keep up. That warning captures the mood among many researchers. The fear is not that AI will replace scientists, but that it will wear down the systems that let scientists trust each other's work: peer review, replication, citation and the slow accumulation of checked results.
The backlash, and the case for AI
The backlash has taken organised form. The Association for Human Mathematics was created in the wake of controversial AI releases, including an OpenAI release covering 377 mathematics problems in more than 700 files. The group has called for a boycott of OpenAI, according to WIO News reporting on the boycott call, and says mathematicians did not ask for the work to be done, describing the mass release as a demonstration of power rather than scholarship. More than 1,000 mathematicians have pledged, to varying degrees, not to work for AI companies and to avoid using their models in research, according to New Scientist reporting. Terence Tao, a leading mathematician at the University of California, Los Angeles, has warned that results dumped on the mathematical community in hasty, hard to read form can harm the field, even when the results themselves are formally correct.
OpenAI and other AI companies reject that framing. They argue that their systems are producing real results, that formal verification in systems like Lean provides a stronger check than traditional peer review alone, and that mathematicians who refuse to engage with AI will be left behind. They also point out that AI tools are already used widely by researchers for coding, drafting and searching the literature, and that drawing a hard line against them would be impractical. From this perspective, the task is to build better norms for AI assisted research, not to boycott the tools outright.
Both sides have a point, and that is why the argument is unlikely to end soon. AI systems are genuinely capable in mathematics, and their results deserve serious attention. At the same time, the systems are run by companies with commercial interests, their inner workings are often opaque, and the traditional safeguards of science were built for a slower, more transparent world. The Navier-Stokes dispute brought those tensions into the open, but it did not create them. It gave researchers a concrete case to argue about, with named people, a famous problem and a question about access that remains unanswered.
What happens next
Several questions will decide how this story ends. The first is verification: will independent mathematicians confirm OpenAI's Navier-Stokes proof, and will the Clay Mathematics Institute accept it as a solution to the prize problem? That process will take time, and the institute has already signalled that its review will not be rushed. The second is transparency: will OpenAI provide a fuller account of how its system was run, what data it used, and how it separated its own research from work stored in its tools by outside researchers? The third is governance: will journals, universities and prize bodies set clearer rules for AI assisted work, including disclosure of AI use, access to underlying data and standards for readable proofs?
For now, the dispute stands as a warning and a test case. It shows that AI can produce results at a scale and speed that traditional science struggles to absorb, and that questions of credit and access become sharper when the tools belong to the competitors. It also shows that mathematicians are willing to organise in defence of their norms, even at the cost of turning away from powerful new tools. Whether that stance holds, or whether new rules emerge that let researchers use AI with confidence, will shape not just mathematics but every field where AI is now doing research. Readers can follow more science coverage on the Verity homepage and find contact details for the newsroom.
