A serious misalignment of AI in mathematics

In recent months, the mathematical capabilities of LLMs (Large Language Models) have improved dramatically, to the point where they can solve complex problems in various areas of mathematics. However, pressure from AI companies to use the ability to solve mathematical problems as an evaluation metric is detrimental to mathematical science and the mathematical community. The goals of AI companies and those of the mathematical community are severely misaligned. We view this as part of a broader issue of alignment that affects other scientific and creative professions, as well as society as a whole.

Research-oriented mathematics deals with understanding the basic structures of shapes, numbers, and natural phenomena. Over generations, it has built up a vast body of sophisticated ideas, methods, abstractions, and other tools for understanding the broader picture of mathematics. In turn, modern technologies and sciences are based on mathematical tools.

Famous problems have often served as milestones and reference points that allow us to assess our understanding of this landscape. Solving one of these problems has been an unmistakable sign of new insights and interesting methods, which would then be studied by a community of mathematicians through a long and arduous process of lectures, discussions, and simplifications. At the end of this process, ideally, we would find the results presented in a textbook suitable for any graduate or even undergraduate student. The journey of some mathematical ideas goes even further, becoming—decades or centuries later—tools understood and used by the general public.

The mathematical community functions, in many ways, as a miniature version of humanity. It is composed of individuals who use a wide variety of different approaches, united by fundamental values. The most precious resources of our profession are the students and the ideas, and we nurture them with great care. We feel a responsibility to allow them to grow to their full potential, until they can take on a life of their own in the world of mathematics. For students, we often propose problems with the primary intention of developing skills that will put them in a favorable position for advances in research and on other fronts. Our ideas are disseminated through lectures, private discussions, and carefully crafted articles, connecting them to the earlier ideas of others. These processes invariably take time and depend on human interaction.

In recent months, AI’s success in solving major mathematical problems has gained attention even outside mathematical circles. But problem-solving is merely a tool and a means to achieve the primary goal of conceptual understanding and insight. Forgetting this in the world of AI can cause the tool to work against its main purpose. In fact, the mass production—at an ever-accelerating pace—of “true/false” statements can destroy fertile ground rather than give life to new ideas.

Often, these solutions are announced in a rush, without time for proper drafting, the refinement of new methods and ideas, or the citation of relevant prior work by other authors. As in all creative professions, this raises serious questions of authorship and plagiarism. Furthermore, without mathematicians willing to take on the task of developing and integrating these ideas into the mathematical canon, the ideas conceived by AI would never come to full life, and the crucial chain of human transmission among mathematicians would be lost.

We are witnessing a widespread threat to intellectual work, with a disconnect between the outcome of AI use and its original purpose. In many fields and activities, years of training have traditionally served not only to produce a response or final product, but also to develop the understanding and ability to formulate new questions and ideas. However, drawing on a vast body of knowledge previously produced by humans, AI systems are becoming increasingly capable of producing the results of this work directly, and these objectives are no longer aligned. The problems the mathematical community now faces are similar to those faced by other scientific and creative professions, and they point to a challenge that all of humanity may eventually face: how can we ensure that, as AI changes the way work is done, we do not lose sight of what that work was meant to achieve in the first place?

AI offers the potential to enhance and accelerate the genuine study and understanding of mathematics. Mathematics, as a profession, will need to adapt to these changes in various ways. However, whether these changes will benefit the field or have a destructive effect will depend, to a large extent, on the decisions of the humans who control this new technology.

These issues must be addressed urgently by the mathematical community, by the companies developing these technologies, and, more broadly, by a society that will face similar problems in many other areas of intellectual work.

Artur Avila (2014 Fields Medal)
Manjul Bhargava (2014 Fields Medal)
Caucher Birkar (2018 Fields Medal)
Pierre Deligne (1978 Fields Medal)
Yu Deng (2026 Fields Medal)
Simon Donaldson (1986 Fields Medal)
Hugo Duminil-Copin (2022 Fields Medal)
Alessio Figalli (2018 Fields Medal)
Martin Hairer (2014 Fields Medal)
June Huh (2022 Fields Medal)
Maxim Kontsevich (1998 Fields Medal)
Elon Lindenstrauss (2010 Fields Medal)
Pierre-Louis Lions (1994 Fields Medal)
James Maynard (2022 Fields Medal)
Curtis McMullen (1998 Fields Medal)
Shigefumi Mori (1990 Fields Medal)
Ngô Bảo Châu (2010 Fields Medal)
Andrei Okounkov (2006 Fields Medal)
Peter Scholze (2018 Fields Medal)
Stanislav Smirnov (2010 Fields Medal)
Terence Tao (2006 Fields Medal)
Maryna Viazovska (2022 Fields Medal)
Cédric Villani (2010 Fields Medal)
Wendelin Werner (2006 Fields Medal)
Efim Zelmanov (1994 Fields Medal)