Twenty-five Fields Medal winners have signed a declaration warning that AI solving famous math problems risks destroying the slow, human-centered process of mathematical discovery. The document, titled “A Misalignment of AI in Mathematics,” urges urgent action from companies, mathematicians and society alike.
This statement emerged from talks held among its signers over the past week. Its shape follows the pattern of the Leiden declaration, which opened itself up for additional signatures. The authors express regret, however, that a more consultative approach was not possible this time because of how urgent the circumstances were.
What the Declaration Says
Mathematicians claim that the objectives of AI firms and those of the mathematical field are badly out of line with each other. The drive to resolve issues as a standard, they contend, does real damage to the science of mathematics and to the community of mathematicians.
The study of mathematics is presented as a discipline that constructs a vast body of refined concepts, approaches, abstract models and resources for grasping the mathematical terrain. These mathematical resources underpin current technologies and scientific fields.
Throughout history, well-known problems have acted as signposts marking advances in comprehension. Their resolution has frequently indicated fresh insight and novel approaches, which were then examined through a prolonged course of lectures, conversations and simplifications, ultimately resulting in textbook presentations fit for graduate or undergraduate instruction.
Decades or even centuries after they first appear, certain mathematical ideas travel far enough to become familiar tools used across a whole population.
The Threat to Intellectual Work
A warning is issued about a general danger facing intellectual labor, arising from a mismatch between what using AI produces and what it was meant for. Training has long been understood to do more than simply yield a finished answer or item; it also builds comprehension and the capacity to raise fresh questions and concepts.
As AI systems grow ever more able to produce the results of such work on their own, the aims behind that work no longer match up with what they deliver. Similar troubles are arising within other fields of scientific and creative labor, and the same difficulties could reach into wider society: ensuring that, as AI alters the way work gets done, we do not forget what that work was supposed to accomplish in the first place.
The declaration cites several concerns:
- The mass production at faster and faster pace of “true/false” statements could destroy fertile ground instead of breathing life into new ideas.
- Solutions are often announced in a rush, leaving no time for a proper writeup, the isolation of new methods and ideas, or citing relevant previous work of others.
- This raises severe attribution and plagiarism questions.
- Without willing mathematicians taking care of the development and integration of AI-conceived ideas, the crucial human transmission chain between mathematicians would be lost.
Who Signed It
Among the signatories are Artur Avila, Manjul Bhargava, Caucher Birkar, Pierre Deligne, Yu Deng, Simon Donaldson, Hugo Duminil-Copin, Alessio Figalli, Martin Hairer, June Huh, Maxim Kontsevich, Elon Lindenstrauss, Pierre-Louis Lions, James Maynard, Curt McMullen, Shigefumi Mori, and Ngô Bảo Châu.
The Path Forward
The document recognizes that AI holds the promise of strengthening and speeding up true mathematical research and comprehension. The field of mathematics must adjust to these shifts in multiple respects.
The outcome of these changes — whether they ultimately benefit the field or have a destructive effect — will depend largely on the choices made by the people who control this new technology.
The urgent need to address these issues exists across all three spheres: within the mathematical community, among the companies building these technologies, and, more broadly, throughout a society that will face comparable challenges in many other kinds of intellectual work.
Some of the most accomplished minds in mathematics are raising an alarm about the direction AI is taking. Their concern is not that AI can solve problems, but that the manner in which it arrives at solutions could undermine the very discipline they have spent their lives building.