New Declaration Warns AI Could Threaten Math’s Foundations

Mathematicians are drawing a line in the sand. Today, a group of 16 mathematicians, working alongside peers and relevant organizations, released the Leiden Declaration on Artificial Intelligence and Mathematics. This document aims to address the growing influence of AI on the field.

By the time of its publication, the declaration had already garnered over 130 signatures. It outlines the key challenges posed by the widespread adoption of AI in mathematical research, and offers a set of recommendations for individual researchers, institutions, governments, and commercial entities.

“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 endorsing the text. “It asks the mathematical community to respond in a way that is transparent and guided by the values of our discipline.”

The process of crafting the declaration was far from simple. “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 helped shape 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 out the concerns

The 11-page document grew out of a workshop held last September. It is not a blanket condemnation of AI in mathematics. Instead, it questions what it truly means to use AI “responsibly,” especially when weighed against values like accuracy, transparency, and the irreplaceable role of human judgment and creativity in mathematical discovery.

Left unchecked, the declaration warns, the rise of AI threatens the autonomy of mathematics. One key issue is that AI-generated proofs do not easily fit into established procedures for developing, presenting, and validating both formal and informal arguments. The declaration also cautions that when AI results are promoted through press releases or blog posts without rigorous validation, it becomes difficult for mathematicians to correct significant errors once the information is in the wild.

“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 was not 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 worry is that AI systems scrape the literature, including repositories like arXiv, to generate answers, but rarely cite the human work they build on. While arXiv is meant to be open, tech companies often withhold key details about how their AI reached its conclusions, Jim Portegies, a mathematician at the Eindhoven University of Technology in the Netherlands, told Scientific American.

A call to action

The declaration offers several key recommendations. These include requiring disclosure of AI use in research, tightening peer-review processes, and investing in public computational infrastructure to level the playing field against big tech firms. The document repeatedly stresses that the focus should remain on humans, whether or not they use AI in their mathematical work.

“Mathematics is, and should always remain, a profoundly human endeavor,” Ulrike Tillmann, IMU’s vice president, said in her endorsement.

Ochigame told Gizmodo that the easiest recommendation to implement might be requiring tool use disclosure and developing clearer guidelines for that in mathematics. He added that regulations on the AI industry “affect so much more than mathematics,” making that a priority as well.

Litt, who was also among the experts consulted for OpenAI’s recent disproof of a longstanding mathematical conjecture, called the declaration “certainly timely, and a lot of what’s on there echoes my own thoughts.” He added, “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 noted that 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.”

The declaration’s primary goal is to spark serious conversations about AI’s impact on mathematics, a field that underpins virtually every area of science. Those discussions will continue next month when top mathematicians gather in Philadelphia for the International Congress of Mathematicians, hosted by the IMU.