25 Fields Medalists Warn AI's Push Into Mathematics Is 'Severely Misaligned' With the Field's Goals

The statement was posted at mathandai.org after about a week of urgent discussion among its initiators, who bypassed the usual lengthy consultation process to respond quickly to what they describe as a crisis. It does not call for halting AI in mathematics, nor does it dispute the results AI systems have produced. The signatories' concerns center on three points: that AI is solving problems faster than the mathematical community can digest the results; that companies optimize for benchmark scores while mathematicians pursue method, understanding and the transmission of knowledge; and that priority, training and the field's open culture will need new rules once AI can rapidly dispose of open problems.

The statement follows a run of rapid AI advances in mathematics. In May, an internal OpenAI model produced a counterexample to the Erdős unit distance conjecture. In July, Claude was involved in overturning the Jacobian conjecture. In early September, GPT-6 Astra made progress on the twin prime conjecture, using a Lean formalization to push the upper bound on consecutive prime gaps from 246 to 186. This week, OpenAI said it had used 10,000 agents running for 88 hours to produce a Navier-Stokes proof, a result that set off a dispute involving OpenAI, Anthropic and two mathematicians.

That episode became the direct trigger for the statement. OpenAI's announcement concerned constructing a smooth external force to make a fluid blow up in finite time, matching cases C and D of the Clay problem. The ensuing argument drew in Tristan Buckmaster, a mathematician at New York University, and Levent Alpöge, a researcher at Anthropic, and raised a series of questions: whether a prompt a researcher types into an AI tool counts as unpublished research material; whether a model company, knowing a mathematician's ideas and progress, used tens of thousands of agents to brute-force the problem and preempt the result; whether OpenAI's request to exclude Alpöge from the author list violates the norms of mathematical research; how a proof can be shown to have been generated independently when top models are trained on user data; who is responsible for turning a proof into mathematics humans can understand; and whether it is reasonable to announce a brute-force proof under a model's name while leaving verification to human mathematicians.

The affair also spread alarm through the mathematical community about companies monitoring prompt data, taking ideas and using raw compute to race ahead. Researchers may hesitate to reveal half-formed thoughts in a chat box, pushing a field that has prized open sharing toward defensive isolation.

In the statement, the signatories describe what mathematics, mathematical problems and proofs mean to them. A famous problem is a landmark and a lighthouse, they write; mathematicians solve it to test how well they understand a region of mathematics. Research usually continues long after a major problem falls. The community must understand new proofs, identify the new methods in them, connect those methods to existing knowledge and digest them through talks, discussion and simplification, ideally until the material can be taught to graduate or even undergraduate students. Some mathematical ideas keep spreading for decades or centuries and eventually become tools ordinary people can use. Solving problems is only a tool and a proxy, they argue; the deeper goal is conceptual understanding and insight.

The statement sets out concerns in three areas. On process and compliance, it says AI-generated solutions are often announced hastily to the media without time for a rigorous paper, and that AI and the institutions behind it fail to cite and credit prior work properly, creating authorship and potential plagiarism disputes. On the exhaustion of open problems, it says AI is rapidly solving or counterexample-ing long-standing open questions across fields; killing problems for the sake of killing them amounts to a utilitarian depletion of the stock. AI lacks the ability for forwards exploration, the statement says, meaning it cannot sense the mathematical landscape and pose new open problems of lasting value. On training and transmission, it says years of academic training exist not only to produce final answers but to build the human capacity for deep understanding and for asking new questions, and that direct output from AI undermines this. Mathematics depends on a human community digesting ideas through reports, discussion and simplification and integrating them into textbooks and teaching; if no human mathematicians take over and fold AI-generated ideas into the canon, those ideas will not come alive, and the human transmission chain between generations will break.

The statement concludes that these problems must be addressed urgently by the mathematical community, by the companies developing the technology and by wider society, because many other forms of intellectual work will face similar issues. The first 25 signatories span algebraic geometry, number theory, dynamical systems, probability, partial differential equations and mathematical physics, covering many of the core breakthroughs of the past half century.

Tao has been among the first mathematicians to use AI actively in his own research and has described it as an excellent research assistant, strong at code generation, literature retrieval and formal proof verification with tools such as Lean. He has nonetheless warned against mythologizing AI, and his concerns have extended to academic ethics and rule-making. Deng has said he uses AI to verify special cases, find literature and check local logic, and that he is more interested in the mathematical foundations underlying AI than in using it directly. He has said AI has lowered the threshold for attacking hard technical details, that mathematics may enter a period of rapid development in the next three to four years, and that mathematicians and AI will move toward human-machine collaboration. A passage he wrote on WeChat Moments a week before signing circulated widely.

In June, the Leiden Declaration on AI and Mathematics was released, calling for action on the use of AI in mathematical research and for norms that keep AI as an auxiliary tool and protect mathematics as a core human intellectual activity. It involved about 60 mathematicians, computer scientists and scholars from 10 countries, was drafted over eight months by a six-person working group, and was endorsed by the International Mathematical Union, with many mathematicians, including Tao and Peter Scholze, signing in support.