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25 Fields Medalists Warn AI Labs Are Misaligned With Mathematics
Twenty-five Fields Medalists say AI companies are treating famous mathematical problems as performance benchmarks rather than sources of human understanding. The declaration follows a dispute over OpenAI’s Navier–Stokes work and the company
AI.info Team ·
Twenty-five Fields Medalists are accusing AI companies of pursuing mathematical breakthroughs in ways that threaten the discipline’s standards for understanding, attribution and review. Their declaration, published as OpenAI faces a dispute over its work on the Navier–Stokes problem, says the goals of commercial AI labs and research mathematicians are “severely misaligned.”
The signatories include Terence Tao, Peter Scholze, Maryna Viazovska, Cédric Villani, June Huh and 2026 Fields Medalist Yu Deng. Each has received the Fields Medal, widely regarded as mathematics’ highest honor.
The intervention arrives after a week of conflict involving OpenAI, New York University professor Tristan Buckmaster and Anthropic mathematician Levent Alpöge. OpenAI has also withdrawn its sponsorship of a mathematics event at the California Institute of Technology after criticism from researchers there, according to TechCrunch.
Mathematicians reject the scoreboard
The declaration, titled A Severe Misalignment of AI in Mathematics, argues that solving a famous problem is only a proxy for the real purpose of mathematical research. The field’s value, the signatories say, lies in developing concepts, methods and explanations that other mathematicians can study, teach and extend.
“The goals of the AI companies and the goals of the mathematical community are severely misaligned,” the mathematicians write on the declaration’s official website. They warn that rapidly producing true-or-false answers can damage the intellectual environment that turns an isolated result into lasting knowledge.
Research mathematics generally advances through talks, private exchanges, detailed papers and sustained scrutiny. A result that arrives first as a company announcement may establish priority, but it does not automatically provide the exposition or independent checking needed to place the work inside the mathematical canon.
OpenAI’s Navier–Stokes dispute intensifies the argument
Buckmaster and Alpöge said they had been developing results related to the Navier–Stokes existence and smoothness problem, one of the seven Millennium Prize problems. Buckmaster later accused OpenAI of using information about their progress, adopting a similar approach and pressing him to remove Alpöge’s name from a proposed credit arrangement.
OpenAI published its own proof shortly afterward, saying the work came from an unreleased model after an intensive period of computation. OpenAI said its researchers and agents did not see the pair’s work before it became public, while acknowledging that it could not rule out the possibility that de-identified product data had helped improve its models.
TechCrunch reported on September 8 that the week-long push consumed 300 billion output tokens — $22.5 million of compute at then-current Astra rates — across every Millennium problem OpenAI attempted, not Navier–Stokes alone. OpenAI’s own post puts roughly 130 billion of those tokens against Navier–Stokes. The same post says the effort began on September 1, inspired by rumours that two Millennium Prize problems had been solved; that date comes from OpenAI, not from Buckmaster.
Those competing accounts do not establish that OpenAI copied the researchers’ work. They do show why mathematicians are concerned about secrecy, model-training data and priority when a company can spend millions of dollars to pursue a result at machine speed.
A separate AI proof raised the stakes
OpenAI’s dispute follows the company’s announcement that an internal model had disproved a longstanding conjecture in discrete geometry known as the planar unit-distance problem. The problem asks how many pairs of points can be exactly one unit apart among a set of points in the plane, and dates to work by Paul Erdős in 1946.
OpenAI said external mathematicians checked the proof and published companion remarks explaining its significance. The company quoted Fields Medalist Tim Gowers calling the result “a milestone in AI mathematics.” Princeton mathematician Noga Alon described it as an outstanding achievement that settled a long-running open problem.
Those reactions demonstrate that mathematicians are not dismissing AI-generated work simply because a machine produced it. The conflict concerns how results are developed, disclosed, credited and explained. A proof can be correct and still leave open questions about the human work that led to it, the sources used to produce it and the ideas that readers are expected to learn from it.
The declaration asks who controls mathematical research
The Fields Medalists say AI systems are increasingly capable of producing conclusions built from decades of human work without reproducing the training, judgment and question-formulation that produced the field’s deeper ideas. They warn that companies may begin choosing problems because they are easy to automate or advertise, rather than because they matter most to mathematicians.
“Often these solutions are announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others,” the signatories write. They link that pressure to attribution and plagiarism concerns, particularly when models draw on published mathematical literature or private interactions with researchers.
The group also argues that the discipline needs human mathematicians to interpret AI-generated results and connect them to existing knowledge. Without that work, a machine-produced theorem may remain a headline rather than become part of mathematics that students can understand and future researchers can use.
Leiden principles point toward a response
The new declaration follows the Leiden Declaration on Artificial Intelligence and Mathematics, published on June 2 and endorsed by the International Mathematical Union. That document calls for disclosure of AI and computational tools, human responsibility for correctness, complete citations, peer-reviewed publication and independent review of significant results.
Terence Tao, a professor at the University of California, Los Angeles and a 2006 Fields Medalist, endorsed the Leiden document by writing: “The goal of mathematical research is human understanding of mathematics, and so mathematics can only thrive in a community of human mathematicians.”
OpenAI’s withdrawal from the Caltech event adds an institutional dispute to the concerns about individual proofs. The immediate questions are whether the company will explain its decision, whether its Navier–Stokes work will receive independent mathematical scrutiny and how journals and universities will handle results generated through proprietary systems.
The 25 medalists do not call for abandoning AI. They say the technology could accelerate genuine mathematical study if companies and researchers preserve the practices that make mathematics reliable: transparent methods, clear attribution, independent verification and explanations that survive beyond the announcement.