Mathematicians sign declaration to curb the use of AI

Last month, many mathematicians were shocked by OpenAI’s announcement that artificial intelligence had solved the famous problem of the geometry of the “unit of distance”.

For some, the realization was exciting. But researchers also fear that AI technology, if left unchecked, will change their field for the worse. To address these fears, a group of mathematicians, computer scientists and mathematics historians have published guidelines aimed at preventing AI from straining their discipline.

Among their most important requirements: disclose the use of AI in researchensure that all articles are peer-reviewed, and level the playing field between academia and for-profit companies through, for example, legal resources and public funding.

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Mathematicians have been working on this document since last fall, when around 60 researchers and policymakers gathered at the Lorentz Center of the University of Leiden in the Netherlands to discuss how technology will affect mathematics. At the forefront of many participants’ concerns was the growing flow of evidence written partially or entirely by AI.

Used responsibly, AI ‘can be extremely useful and helpful,’ says Ilka Agricolaa mathematician who chairs the Publishing Committee of the International Mathematical Union (IMU), the leading organization for world mathematics. “Unfortunately, this positive aspect is somehow small compared to the enormous mess surrounding it.”

The newspaper editors’ inboxes are filling up with more evidence of AI than they can verify. Large linguistic models regurgitate human ideas, often without attribution. Some fear for the integrity of the research itself. They fear that values ​​such as transparency and accessibility, which mathematicians have long prioritized, are at risk.

For example, almost all modern papers in mathematics can be read for free on arXiv.org, and the American Mathematical Society hosts its own paper. organized repository of articles, books and mathematical reviews. Commitment to these principles allows anyone on Earth to see and rely on new research, says Jim Portugalmathematician at Eindhoven University of Technology in the Netherlands. But tech companies, he says, often keep key details confidential. For example, when Google DeepMind announced In 2024, after its AlphaProof AI model had solved three difficult math competition problems, it took more than a year before the methods were published in a peer-reviewed journal. Often when it comes to AI evidence, “we retreat behind closed doors because there is now a lot of commercial interest,” says Portegies.

To try to combat these trends, participants at the Leiden workshop decided to work together on a joint declaration modeled on similar documents. on open science And data management. They called it the “Leiden Declaration on Artificial Intelligence and Mathematics.”

Although all the authors shared some fundamental concerns, putting them together into a statement that appealed to everyone was a challenge. “It was a long and arduous process, with many lively discussions,” says Rodrigo OchigameAI anthropologist at Leiden University. “I don’t think I’ve ever been involved in a writing process involving so much debate for such a short text.”

In the final 11-page paper, the authors outline what they value in mathematical research, how these values ​​are threatened by AI, and how to deal with the situation. For example, one of their concerns was that while a proof written by a human can be verified by anyone with the appropriate expertise, AI is prone to subtle, hard-to-spot errors; Policies that subject AI evidence to greater scrutiny can help detect such errors. And the goals of humans and AI in mathematics are not always the same: mathematicians pursue research questions based on the potential for new techniques and ideas to emerge, and technology companies may focus on questions that highlight their AI models but have limited impact in mathematics. Independent funding can help ensure that mathematicians always have a say in the development of their field.

Some of the recommendations, such as disclosing AI use and properly attributing prior research, are up to individuals or AI companies. Others, like the recommendation to regulate the AI ​​industry, require large-scale organization or government intervention.

Most crucial to Ochigame is the call for commercial AI companies to adhere to the principles of the declaration. “Mathematicians who never intended to contribute to the development of AI are seeing their work used for this purpose without their consent,” he says. “I think it’s a deeply concerning situation.”

The IOM plans to approve the declaration, and Portegies, who led the draft declaration, will speak to the organization’s next conference this summer.

“They have done a huge service to the whole community, because now we have a starting point to make decisions and discuss,” Agricola says. “I love it.”