25 Fields Medalists Warn of Severe AI Misalignment with Mathematical Research

IT Home, September 12 news: On September 11 local time, 25 Fields Medalists—including Terence Tao, Yu Deng, and Peter Scholze—as initial signatories, jointly issued a statement titled "A Severe Misalignment of AI in Mathematics," warning of a "severe misalignment" emerging between AI companies and the mathematical community.

The statement noted that over the past few months, the mathematical capabilities of large language models have improved significantly, enabling them to solve major open problems across many mathematical fields. However, the push by AI companies to solve math problems as benchmarks is harmful to both mathematical science and the mathematics community. The goals of AI companies are severely misaligned with those of the mathematical community, which are part of broader alignment issues affecting other scientific and creative professions, as well as society as a whole.

The study of mathematics is the understanding of the fundamental structures of shapes, numbers, and natural phenomena. Developed over generations, it has accumulated a vast array of sophisticated ideas, methods, abstractions, and other tools to comprehend the mathematical realm. In turn, modern technology and science are built upon mathematical tools.

The mathematical community is in many ways a microcosm of humanity. It consists of individuals employing a wide variety of approaches, centered around core values. For students, mathematicians often pose problems primarily to foster skills that will give them a strong foundation in research and other areas. Mathematicians seek to connect these with prior ideas of others through lectures, private discussions, and careful written dissemination. These processes generally take time and are based on human-to-human interaction.

The statement mentioned that in recent months, AI's success in solving major mathematical problems has even made headlines. But problem-solving is merely a tool and a vehicle toward the primary goal of achieving conceptual understanding and insight. Forgetting this in the AI realm risks turning the tool against its primary purpose. Indeed, the mass production of increasingly rapid "true-or-false" statements may poison the fertile ground rather than bring new ideas to life.

These solutions are often rushed out without time for formal writing, without isolating new methods and ideas, or without citing relevant work by others. As with all creative professions, this raises serious questions of attribution and plagiarism. Furthermore, without mathematicians willing to take responsibility for developing them and integrating them into the mathematical canon, ideas conceived by AI can never be fully realized, and the crucial human chain of transmission among mathematicians will be lost.

The statement pointed out that we are witnessing a widespread threat to intellectual work: an inconsistency between the results of AI usage and its original purpose. Across many fields and activities, years of training have traditionally served not only to produce final answers or outputs, but also to cultivate understanding and the ability to ask new questions and generate new ideas. However, as AI systems increasingly generate these outputs directly based on vast amounts of earlier human achievements, these goals are no longer aligned. The issues currently facing the mathematical community are similar to those faced by other scientific and creative professions, reflecting a question that all humanity may confront: how to ensure that as AI transforms the way work is done, we do not forget why the work was undertaken in the first place.

AI has the potential to enhance and accelerate genuine mathematical learning and understanding. As a profession, mathematics will need to adapt to these changes in multiple ways. However, whether these changes ultimately benefit the field or have a disruptive impact depends largely on the decisions of the humans in control of this new technology. The statement urged that this must be addressed urgently within the mathematical community, by the companies developing these technologies, and in broader society, as similar issues are faced across many other forms of intellectual work.

IT Home附: List of the 25 signing Fields Medalists: 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 (Korean-American, 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 (Japanese mathematician, 1990 Fields Medal) Ngô Bảo Châu (Vietnamese mathematician, 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)

According to a separate report by the South China Morning Post, Fields Medalist Yu Deng recently posted on WeChat Moments that the mathematics community he has interacted with lately is permeated by an atmosphere of restlessness and anxiety.

Deng expressed that he is genuinely curious about where the ceiling of AI lies. If AGI can solve widespread problems across mathematical fields, witnessing a miracle in one's lifetime wouldn't be a loss; after that, it would simply be a matter of going home and writing yuri (girls' love) novels.

In a response to the South China Morning Post, Deng clarified: "I am not currently writing yuri novels. That remark was entirely a joke." "I don't think AI can develop to the point of solving all math problems—at least not the ones I mentioned in the post."