Editorial Team
6 min read
Twenty-five Fields Medal recipients say the race to announce AI solutions to famous problems risks rewarding priority over explanation, attribution and the work that makes a result usable. Their warning follows OpenAI's unverified claim that an internal system solved the Navier–Stokes existence and smoothness problem.
Twenty-five Fields Medal recipients have warned that turning famous unsolved problems into an AI benchmark could damage the mathematical work that follows a proof: identifying its ideas, locating prior work, explaining it and teaching it. In their declaration, they call the incentives of AI companies and the mathematical community “severely misaligned.”
The warning lands as OpenAI, the AI developer, says an internal system produced a proof that three-dimensional Navier–Stokes flow can develop a finite-time singularity—the outcome that would resolve the existence-and-smoothness problem. The company has released a writeup and a Lean formalization, but an independent report described the proof as unverified. That distinction matters: a formal artifact makes a claim inspectable; it is not, by itself, independent scholarly acceptance.
OpenAI’s diagram of the vortex in its company-reported Navier–Stokes claim; orange marks faster angular rotation and teal slower rotation. Source: openai.com.
Terence Tao, a mathematician, 2006 Fields Medal recipient and one of the 25 initial signatories, published the statement after a week of discussion among the group. The Fields Medal is mathematics’ highest-profile award; the signatories range from Pierre Deligne, honored in 1978, to Yu Deng, honored in 2026. Their shared standing gives the declaration weight as an argument about how the field recognizes a contribution, rather than as a finding that OpenAI’s claimed proof is wrong.
The group’s premise is that a celebrated problem has historically been valuable not only because it yields a true-or-false answer, but because attempts to solve it generate methods and explanations that other researchers can use. Their statement says a rushed announcement can leave too little time for a proper writeup, isolation of new ideas and citation of prior work. Without mathematicians who develop and integrate an AI-conceived result, it says, the result cannot fully enter the mathematical canon.
“Solving problems is only a tool and proxy for achieving the primary goal of conceptual understanding and insight.”
That is a narrower claim than “AI has no role in mathematics.” The declaration explicitly says AI could enhance and accelerate genuine mathematical study and understanding. Its warning is that the eventual effect depends on the choices of people controlling the systems—especially whether they optimize for a fast announcement or for a result that can be understood, scrutinized and built upon.
OpenAI’s paper depicts the vortex core at successive times in its company-reported Navier–Stokes claim. Source: openai.com.
Navier–Stokes equations describe fluid motion; the question at issue is whether a smooth, three-dimensional incompressible flow can break down into an infinite-speed singularity in finite time despite viscosity. The problem, one of the seven Millennium Prize Problems named by the Clay Mathematics Institute in 2000, has been unresolved for roughly 90 years, according to OpenAI’s account.
OpenAI says its system found an analytical proof and Lean formalization of a finite-time singularity from an initially smooth fluid at rest under a smooth applied force, with finite energy throughout. It says the agent group that produced the claimed resolution involved on the order of 10,000 concurrent agents. The company says agents reached the result about 88 hours after the first were launched, used about 130 billion output tokens on the Navier–Stokes effort, and that Lean formalization and verification took another 17 hours.
Those are company-reported measures of a particular multi-agent run, not a price, an independently measured efficiency figure or a measure of mathematical importance. They do, however, show the asymmetry at the center of the declaration: a lab can concentrate an unusually large automated search effort on a public landmark, while checking exposition, novelty and intellectual lineage remains work for the broader research community.
Lean formalization can check that a conclusion follows from specified formal assumptions. It does not establish that the formal statement captures the intended problem, that the work is original, that relevant predecessors have been credited, or that researchers can explain and generalize the underlying idea. Those are the separate tasks the signatories say need to be treated as part of a completed contribution.
OpenAI’s own framing is also more limited than a prize claim: it says it does not intend to claim the Millennium Prize and describes the release as a snapshot of model progress. The key evidentiary question therefore remains mathematical: whether independent specialists validate the proof and its correspondence to the official problem formulation.
The announcement followed a separate AI-assisted result by Tristan Buckmaster, an NYU mathematics professor, and Levent Alpöge, an Anthropic employee, on a forced Euler problem. A contemporaneous account reported Buckmaster’s accusation that OpenAI had seized on the problem after word of the pair’s work spread and copied their unusual approach.
Another report said Buckmaster accused OpenAI of pressuring him not to credit Alpöge and questioned whether the company had used their work with Codex. OpenAI says it had no access to the researchers’ work before its public release, that its investigation found Buckmaster’s Codex prompts could not have influenced the system or its training, and that the two projects differ: Buckmaster and Alpöge’s result concerned forced Euler, while OpenAI’s concerned unforced Euler as a related effort. It recognizes their priority on the forced-Euler work.
The allegations are not proof that OpenAI used the pair’s work. But the competing accounts demonstrate why the signatories put attribution alongside correctness. In a field where being first can confer status, an announcement can settle attention and credit before a community has had time to establish what was actually new and whose work it extends.
The immediate next step is independent review of OpenAI’s Navier–Stokes proof, including whether its formalization and paper establish the claimed result. That will address correctness, not every issue in the declaration.
The broader decision belongs to research institutions, mathematicians and AI developers: whether an AI-generated result is treated as complete at announcement, or only after it comes with a readable account, a record of dependencies and attribution, and enough human scrutiny for others to reuse it. The signatories are not asking the field to ignore faster discovery. They are asking it to decide that a benchmark win is not the same thing as shared mathematical knowledge.
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