The Leiden Declaration on Artificial Intelligence and Mathematics—as the declaration is formally known—takes its name from a workshop held during a conference in Leiden in September.

But the idea originated earlier, says Jim Portegies, assistant professor in TU/e’s Department of Mathematics and Computer Science.“In a pub, during a conference in Cambridge.”

Mathematicians Ursula Martin (Oxford), Michael Harris (Columbia), and Rodrigo Ochigame (Leiden) decided there to organize a workshop at the next conference where they would all meet—in Leiden—and work with the broader community to draft a document.

In addition to mathematicians, computer scientists, philosophers, historians, and social scientists also attended the workshop in Leiden. “Although opinions varied widely, everyone felt a sense of urgency about the topic,” says Portegies, who was asked by the initiators to guide the drafting process of the Leiden Declaration.

In that role, he focused on finding common ground. “I tried to identify as much overlap as possible among the different viewpoints within the writing group.”

Declining autonomy

And it turned out that those shared concerns were indeed there—no fewer than five. They include unreliable results, inadequate source attribution, a lack of transparency about methods, dependence on commercial AI, and the resulting increase in inequality among mathematicians. Researchers are also facing a loss of autonomy, as commercial interests gain greater influence over the scientific agenda.

“On top of these five threats, many mathematicians are suddenly finding themselves confronted with ethical questions because of AI,” Portegies adds. “Their work can help improve AI models, but those models may then be used for warfare, to disrupt political systems, for mass surveillance ... And they have an enormous environmental impact.”

A blessing

Yet AI is solving mathematical problems that brilliant minds have struggled with for decades. Isn’t AI actually a blessing for mathematics? “From a scientific perspective, it is incredibly interesting that more and more mathematical problems can be solved using AI,” Portegies acknowledges. 

But, he adds: “It’s important to put that into perspective: AI systems are very good at certain things within mathematics, such as solving problems by applying ideas from one area of the field to another. They have much more difficulty with other tasks though, such as developing new theories.”

“And if we look at how AI performs on non-mathematical problems, those limitations are even greater.” Which is not the story AI companies tell, says Portegies.

“They like to suggest that if their model can solve mathematical problems, then it can solve everything, and that AGI (Artificial General Intelligence, ed.) is just around the corner. That’s exaggerated and creates misplaced confidence in what AI is currently capable of.”

Resonating

What do the authors hope to achieve with the Leiden Declaration? “We encourage mathematicians, governments, and commercial actors alike to take action, in solidarity with other academic disciplines and societal institutions. Ultimately, this goes far beyond mathematics itself, and we will need to work together to ensure AI develops in a responsible direction.”

“The International Mathematical Union has endorsed the Declaration, and more than 1,500 scientists from around the world have signed it. The text appears to be resonating within the community, and we’re seeing tremendous international support,” Portegies concludes.

This article was translated using AI-assisted tools and reviewed by an editor.