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Twenty-five Fields medalists call the AI industry's goals severely misaligned with mathematics
Their joint statement argues that famous open problems were only ever a proxy for understanding, and that benchmarks miss the years of talks and simplifications that follow a proof.
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What happened
- Twenty-five winners of the Fields Medal signed a joint statement saying the goals of the AI industry and those of mathematics are severely misaligned.
- They argue that mass-producing solved problems with AI undermines conceptual understanding, which the statement calls the discipline's true goal.
- The signatories stop short of asking for a ban, saying AI could enhance and accelerate genuine mathematical study and understanding.
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Why it matters
- constraint Citing a solved open problem as progress in mathematics now requires arguing separately that the absorption process behind it survived, because 25 named senior mathematicians are on record that the score skips it.
- exposure Researchers sitting on partial results in famous problems are working against labs with publicity incentives, so priority and credit are contestable before anything is published.
- contradiction A lab's public account of what it deliberately did not optimize for describes a snapshot, if the-decoder is right that math training followed within weeks.
- precedent Other professions now have a named, on-the-record critique of output-only evaluation to cite, because the signatories framed the problem as a general threat to intellectual work.
Open problems in mathematics were expensive because closing one usually required new machinery, and the machinery was the payoff. The statement says this outright: famous unsolved problems "have often served as landmarks and lighthouses against which one can measure an improved understanding of this landscape" [5]. Solving problems is "only a tool and proxy for achieving the primary goal of conceptual understanding and insight," the signatories wrote [7].
The signatories take the capability as real. According to the-decoder's account, large language models have recently gotten good enough at mathematics to crack "major outstanding problems in many fields of mathematics," and that is what worries the signatories [3]. One of them, Terence Tao, had already warned about an AI-driven foundational crisis in the field [16].
What comes after a proof is slow. The statement describes years of a "long and arduous process of talks, discussions, simplifications" after a result lands [6]. Benchmarks measure none of that. "Without the willing mathematicians who must take care of their development and integration into the mathematical canon, AI-conceived ideas would never become fully alive," the statement reads [11]. Answers at machine speed could "destroy fertile ground instead of breathing life into new ideas" [8].
The signatories describe procedural damage too. AI-generated solutions get announced with "no time for a proper writeup, the isolation of new methods and ideas, and citing relevant previous work of others" [9]. The statement says that raises "severe attribution and plagiarism questions" [10].
The-decoder reports a controversy between two mathematicians and OpenAI, with the accusation that the company caught wind of rumors about a partial solution to a Millennium Prize Problem and tried to beat the researchers to it for the publicity [13]. OpenAI chief researcher Pachocki had said at the Astra announcement that the company deliberately chose not to optimize the model for mathematics [14]. Shortly after, per the same report, OpenAI trained math models anyway, seemingly in direct response to those rumors [15]. The report does not include a response from OpenAI [23].
The signatories widen the claim to a "general threat to intellectual work," arguing that in many fields years of training "served not only to produce a final answer or product, but also to develop understanding and the ability to formulate new questions and ideas" [17]. For that to hold outside mathematics, two things have to be true of the field: the visible artifact has to be a proxy for a capability measured only indirectly, and the training that builds the capability has to be skippable once a machine will emit the artifact. Their own example is schooling, where homework can increasingly be done by AI while exams still ban it, and the distance between the two performance levels, measured in grades, keeps growing [19].
The signatories stop short of asking for a ban. The statement says AI "offers the potential of enhancing and accelerating genuine mathematical study and understanding" [20], and that "whether these changes ultimately benefit the field or have a destructive effect will in large part be determined by the decisions of the humans in control of this new technology" [21]. "These issues must be addressed urgently," the signatories say, calling on the mathematical community [22].
What to watch
- Whether OpenAI answers the two mathematicians' accusation over the Millennium Prize partial solution.
- Whether journals and referees start requiring writeups, method isolation and citations for machine-assisted proofs.
- Whether labs disclose which mathematical capabilities they are optimizing for, after Pachocki's Astra remark.