25 Fields Medalists Warn About the Impact of AI

Twenty-five recipients of the Fields Medal believe that the ambitions of the AI industry diverge from the purpose of mathematics. They fear an erosion of conceptual understanding and describe a risk that extends beyond their discipline. They call for urgent attention to the issue, without banning AI, reminding that the outcome will depend on human choices.

A Warning Beyond Mathematics and an Urgent Call

The signatories present the situation as a general threat to intellectual work, beyond their discipline. They believe that the difficulties faced by mathematicians resemble those of other scientific and creative professions and could herald challenges for all of humanity. They urge for urgent action on the subject and address the mathematical community, the companies developing these tools, and society as a whole. NATO's Special Operations University describes a similar mechanism, termed the "tragedy of cognitive goods": each company that replaces entry-level jobs with AI gains efficiency, but the erosion of expertise is distributed across the entire talent pool. Mathematicians claim to observe this phenomenon in their own field. They add that the outcome, whether beneficial or destructive, will largely depend on the decisions made by those who control the technology.

Misalignment with AI and Highlighted Drifts

The collective of 25 Fields Medalists warns of a misalignment between the goals of the AI industry and those of mathematics. According to them, the massive reliance on automated systems to generate solutions jeopardizes conceptual understanding, which is essential to the discipline. They believe that reducing mathematical problems to mere steps to be completed harms the science and those who sustain it. They criticize the fact that solutions produced by AI are announced without allowing sufficient time for proper writing, the identification of new methods, and the mention of relevant prior work, which raises significant issues of attribution and plagiarism. Without the engagement of mathematicians to develop and integrate these ideas into the corpus, the chain of human transmission would be lost, and the ideas conceived by AI would never fully come to life. Flooding the field with machine-speed answers risks, in their view, destroying fertile ground instead of bringing new ideas to life.

In Research, the Process Matters More Than the Answer

Reference problems often serve as benchmarks for measuring the progression of mathematical understanding. Once a problem is solved, the new thinking it required matters more than the solution itself. The community then spends years clarifying and simplifying the ideas that enabled this advancement. For the signatories, solving a problem is merely a tool to achieve conceptual understanding and insight. They believe that AI threatens to shortcut this essential process of knowledge maturation.

No Ban, but Human-Guided Adaptation

The group does not call for a ban on AI. They assert that these tools have the potential to enhance and accelerate the study and authentic understanding of mathematics, provided that practices are adapted. The signatories emphasize that the final effects will depend on the choices of the humans who control this technology. Among the 25 signatories are Terence Tao, Pierre Deligne (1978), Peter Scholze (2018), Maryna Viazovska (2022), Martin Hairer (2014), Cédric Villani (2010), Manjul Bhargava (2014), and Yu Deng (2026). Terence Tao had already warned of a fundamental crisis in the mathematical discipline caused by AI, and the signatories believe that language models are now capable of solving major open problems in many areas of mathematics.