Mathematicians are setting some boundaries. Today, 16 mathematicians in consultation with peers and relevant organizations published the Leiden Declaration on Artificial Intelligence and Mathematics.
The declaration, which had attracted more than 130 signatories by the time of publication, outlines key challenges that widespread AI use poses to mathematics research, as well as recommendations for individual researchers, organizations, governments, and commercial enterprises.
“I do not expect every colleague to agree with every sentence of the declaration,” Christoph Sorger, secretary general of the International Mathematical Union (IMU), wrote in a column in IMU’s endorsement of the declaration. “It asks the mathematical community to respond in a way that is transparent and guided by the values of our discipline.”
“It was not easy to reach consensus on a complete text, and the process tested everyone’s patience,” Rodrigo Ochigame, an anthropologist of AI at Leiden University in the Netherlands, who was involved in the declaration, told Gizmodo. “We did this the hard way: we decided to publish the text only when we reached full consensus, after gathering extensive feedback from a wide range of people and debating every point in detail.”
Laying things out
The 11-page document emerged from a workshop held in September of last year. To be clear, the declaration isn’t denouncing the use of AI in mathematical research. Rather, it questions what it really means to use AI “responsibly,” in the context of values such as accuracy, transparency, and the weight of human judgment and creativity behind mathematical breakthroughs.
Unchecked, the advance of AI on mathematics puts the “autonomy of mathematics under threat,” reads the declaration. For instance, the declaration argues that AI-generated proofs are difficult to incorporate into established procedures for ideating, presenting, and validating both formal and informal arguments in mathematics. It also warns that, when such results are promoted through informal press releases or blog posts without rigorous validation, it’s difficult for mathematicians to rectify information that’s already out there, should there be significant errors in the AI’s work.
“There’s a rush to announce results that aren’t often checked or contextualized correctly from a number of AI math startups,” Daniel Litt, a mathematician at the University of Toronto who wasn’t involved in the declaration, told Gizmodo. “By and large, those are mostly correct and also not very interesting. Of course, companies also have financial incentives to overstate how interesting they are.”
Another major concern is that AI agents scrape the literature—arXiv, for example—to concoct their answers, but rarely while properly citing the human work they build on. While repositories like arXiv are meant to be accessible, tech companies often abstain from sharing key details on how the AI reached its conclusions, Jim Portegies, a mathematician at the Eindhoven University of Technology in the Netherlands, told Scientific American.
An action plan
Some key recommendations of the declaration include the disclosure of AI use in research, stricter peer-review processes, and investments in public computational infrastructure to level the playing field against big tech firms. Again, the declaration stresses that greater focus should be placed on humans—whether or not they use AI in the way they engage with mathematics.
“Mathematics is, and should always remain, a profoundly human endeavor,” Ulrike Tillmann, IMU’s vice president, said in her endorsement comments.
Among the recommendations, Ochigame told Gizmodo that the easiest item to implement might be to disclose tool use and, by extension, develop clearer instructions for AI disclosure in math. In addition, regulations on the AI industry “affect so much more than mathematics,” so that should also be prioritized, he added.
The declaration “certainly looks timely, and a lot of what’s on there echoes my own thoughts,” said Litt, who was also among the experts consulted for OpenAI’s recent disproof of a longstanding mathematical conjecture. “I do think [AI] is a very important and powerful technology that has the potential to help us with a lot of interesting math… [but] I don’t think the tools will do that on their own.”
Sorger added that the reactions from the mathematical community “already show exactly why the declaration is useful, prompting consideration and discussion of what we want to protect, what we are willing to change, and where we need more clarity.”
Indeed, the primary goal of the declaration is to initiate serious discussions on AI’s influence on mathematics—an area of fundamental research that has supported virtually every aspect of science, if you really think about it. And that’s due to continue next month, as top mathematicians will convene in Philadelphia for the International Congress of Mathematicians hosted by the IMU.
