A group of 25 Fields Medalists, including Terence Tao and Yu Deng, issued a statement on Sept. 11 local time titled A Serious Misalignment of AI in Mathematics, escalating an already tense dispute between the mathematics community and AI companies such as OpenAI and Anthropic. The statement says the practice of treating major unsolved math problems as benchmarks for model capability has damaged both mathematical science and the mathematical community, and has drifted away from the field’s core goal of pursuing conceptual understanding.
The split has become more visible in recent days. On Sept. 8, OpenAI said an undisclosed internal AI model solved the Navier-Stokes existence and smoothness problem in 88 hours. The Navier-Stokes equations describe fluid motion and are widely used in areas including weather forecasting and aircraft design. In 2000, the Clay Mathematics Institute, or CMI, listed the existence and smoothness problem as one of its seven Millennium Prize Problems and attached a $1 million award to it.
That claim arrived after New York University mathematician Tristan Buckmaster and Anthropic researcher Levent Alpoge had already made key progress on a related problem and released their result on Sept. 7. Buckmaster later criticized OpenAI, saying the company intensified its work only after learning of his team’s progress. He also said he had used OpenAI’s coding tools with unpublished drafts and derivations and suspected the model may have "looked at" them.
OpenAI denied that accusation, but said it could not completely rule out the possibility that user data might have had an indirect role in model training. The company is not planning to claim the CMI prize, and the mathematics community has not formally recognized OpenAI’s proof.
A debate over priority, data ethics and the limits of AI research
OpenAI’s move quickly turned into a broader fight over academic priority, data ethics and the proper boundary of AI-led research. Since May this year, the report says, several mathematical problems have been solved by AI. OpenAI recently disclosed that it has also turned its attention to another Millennium Prize Problem, the Hodge conjecture.
Stanislav Smirnov, a professor at the University of Geneva in Switzerland and a 2010 Fields Medalist, was one of the 25 signatories. In an interview with China Newsweek on Sept. 12, he explained why the statement was drafted and published within just a few days.
Smirnov said most of his peers had not expected events to move so quickly or trigger such a large controversy. Because AI is developing at high speed, he said, the community now needs to move quickly as well and set rules for the future.
Smirnov rejects the "excavator" analogy in its usual form
Asked what the statement meant by a "serious misalignment," Smirnov said the first question is what society supports mathematical research for. In his view, mathematics, like music and art, is an important part of human culture and also a foundation for many other disciplines and technologies. For many mathematicians, he said, the cultural and artistic value of mathematics matters most.
Many practical applications rooted in mathematics — from phones and airplanes to machine learning itself — began as efforts driven by scientific beauty, he said. Using mathematics to test large language models is understandable to a point, because these systems have become so capable that suitable benchmarks are hard to find. Still, he said, the current approach often rewards the production of long proofs for famous conjectures, while the ideas that emerge in the process of exploring those conjectures may matter more.
Smirnov said two friends had compared mathematicians’ complaints about AI-generated proofs to ditch diggers complaining about being replaced by excavators. He said the metaphor works better if moved into archaeology. An excavator is faster, he said, but it may destroy precious artifacts; a slower group of workers may preserve them.
He argues for rules, not a blanket rejection of AI
On the dispute around OpenAI’s Navier-Stokes announcement, Smirnov said the community has already seen cases in which large models appropriate other people’s ideas without attribution or make use of unpublished thinking. If a human mathematician did that, he said, it would be treated as a serious breach of academic ethics. He also said he does not agree with the view that it is acceptable when AI copies humans.
At the same time, he said the more urgent issue is that different groups and individuals hold sharply different views on these questions. New rules are needed to deal with those conflicts. He added that continued AI development may significantly change how these systems operate, which means the public understanding of AI will also need regular revision. In a more constructive reading, he said, there is still room to seek dialogue and balance among all stakeholders, though that will take work.
Smirnov said the statement does not call for eliminating AI and explicitly recognizes its potential to help and speed up mathematical research. As he described it, AI is strong at understanding known information, running experiments and testing whether existing methods can solve current problems. It is much weaker at judging whether a new method is sound or at producing genuinely novel ideas. Even so, he said, those systems are improving quickly, and traditional research methods may need adjustment in the next few years.
His core concern is understanding, not just speed
Asked which recent AI-driven mathematical breakthrough had surprised him most, Smirnov said he had not yet seen anything especially surprising. Some of the questions that truly interest him still appear beyond AI’s reach. What worries him more is the growing emphasis on producing proofs rather than understanding the research goal itself, a shift he said could damage science and its possible applications.
He also said AI can harm mathematical training, even for experienced researchers. He pointed to one scholar friend who said that after a year of using AI to generate course exercises and answers, his own ability to solve student-level problems had deteriorated. Smirnov added that most students seem aware of that risk and try to solve problems on their own, using AI only as a prompt.
"Equality of access has not arrived"
On whether large-scale AI production of mathematical results changes the meaning of human mathematical work, Smirnov said AI currently approaches research and breakthroughs in a more formalized way. The final output may eventually be understandable, he said, but the question is who will do the understanding. One possibility, in his view, is that a new kind of scientific labor is emerging: extracting ideas from text generated by AI. Can AI itself produce truly new ideas? For now, he said, the answer appears to be no, though he stopped short of ruling out future change.
He also said AI-generated proofs could, in principle, make proper citation of prior work harder and threaten continuity in human knowledge, especially if people cannot understand the proofs themselves. But if researchers can find ways to avoid that outcome and build a good form of human-machine collaboration, AI could become a very useful tool.
Smirnov said he has tried using AI on his own research problems, but the strongest current models still do not seem very practical for that purpose, perhaps because they lack key forms of understanding. They are, however, excellent tools for retrieving known information in a field and for proofreading papers.
When asked whether the recent run of events reflects a broader democratization of knowledge through AI, Smirnov gave a blunt answer: he has not seen much democratization yet. Most progress, he said, has come from models that are not open to the public. If AI companies shared resources with mathematicians instead of trying to do everything themselves, the situation might look much better. He said he believes that could happen soon, and that some form of consensus between AI companies and mathematicians will eventually emerge, followed by broader access.