Last month many mathematicians were shocked by OpenAI’s announcement that artificial intelligence had solved geometry’s famous “unit distance” problem.
For some, the achievement was exciting. But researchers also worry that AI technology, if left unchecked, will change their field for the worse. To address those fears, a group of mathematicians, computer scientists, and math historians have released guidelines to prevent AI from steamrolling their discipline.
Among their most important prescriptions: disclose the use of AI in research, ensure all papers are peer-reviewed and level the playing field between academia and for-profit companies through, for instance, legal resources and public funding.
On supporting science journalism
If you’re enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.
The mathematicians have been working on the document since last fall, when around 60 researchers and policymakers convened at Leiden University’s Lorentz Center in the Netherlands to discuss how technology will affect mathematics. At the top of many attendees’ minds was the accelerating stream of proofs written partially or entirely by AI.
Used responsibly, AI “can be extremely useful and helpful,” says Ilka Agricola, a mathematician who chairs the Committee on Publishing at the International Mathematical Union (IMU)—the foremost organization for global mathematics. “Unfortunately, this positive aspect is kind of getting small compared to the huge mess around it.”
Journal editors’ inboxes are filling with more AI proofs than they can vet. Large language models regurgitate human ideas, often without attribution. Some fear for the integrity of research itself. They worry that values like transparency and accessibility, which mathematicians have long prioritized, are in danger.
For example, almost every modern paper in math can be read for free on arXiv.org, and the American Mathematical Society hosts its own curated repository of mathematical papers, books and reviews. Commitment to these principles allows anyone on Earth to see and build on new research, says Jim Portegies, a mathematician at the Eindhoven University of Technology in the Netherlands. But tech companies, he says, often keep key details private. For instance, when Google DeepMind announced in 2024 that its AI model AlphaProof 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 proofs, “we retreat behind closed doors because there is now a lot of commercial interest,” Portegies says.
To try to combat these trends, participants at the Leiden workshop decided to work together on a joint statement modeled after similar documents on open science and data management. They called it the “Leiden Declaration on Artificial Intelligence and Mathematics.”
Though all the authors shared some basic concerns, wrangling them into a statement that everyone was happy with was a challenge. “It was a long, arduous process with a lot of lively discussion,” says Rodrigo Ochigame, an anthropologist of AI at Leiden University. “I don’t think I’ve ever been part of a writing process that involved so much debate for such a short text.”
In the final 11-page document, the authors lay out what they value about mathematics research, how those values are threatened by AI and how to address the situation. For instance, one of their concerns was that, whereas a human-written proof can be verified by anyone with the right expertise, AI is given to subtle, hard-to-spot errors; policies that subject AI proofs to extra scrutiny can help catch such errors. And the goals of humans and AI in math aren’t always the same: mathematicians pursue research questions based on the potential for new techniques and ideas to emerge, and tech companies may focus on questions that showcase their AI models but have limited impact in mathematics. Independent funding can help ensure mathematicians still have a say in how their field develops.
Some of the recommendations, such as disclosing AI use and properly attributing previous 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 for Ochigame is the call for commercial AI companies to adhere to the declaration’s principles. “Mathematicians who never intended to contribute to AI development are having their work used for this purpose without their consent,” he says. “I think that’s a deeply concerning situation.”
The IMU plans to endorse the declaration, and Portegies, who led the declaration project, will speak about it at the organization’s upcoming conference this summer.
“They did an immense favor to the whole community, because now we have a starting point for decision making, for discussion,” Agricola says. “I love it.”
It’s Time to Stand Up for Science
If you enjoyed this article, I’d like to ask for your support. Scientific American has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in that two-century history.
I’ve been a Scientific American subscriber since I was 12 years old, and it helped shape the way I look at the world. SciAm always educates and delights me, and inspires a sense of awe for our vast, beautiful universe. I hope it does that for you, too.
If you subscribe to Scientific American, you help ensure that our coverage is centered on meaningful research and discovery; that we have the resources to report on the decisions that threaten labs across the U.S.; and that we support both budding and working scientists at a time when the value of science itself too often goes unrecognized.
In return, you get essential news, captivating podcasts, brilliant infographics, can’t-miss newsletters, must-watch videos, challenging games, and the science world’s best writing and reporting. You can even gift someone a subscription.
There has never been a more important time for us to stand up and show why science matters. I hope you’ll support us in that mission.