After OpenAI’s announcement of an AI breakthrough in geometry shocked the field, mathematicians, computer scientists, and math historians are responding with the 11-page “Leiden Declaration on Artificial Intelligence and Mathematics.” The document urges resear
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 sounded like a door cracking open to new possibilities. For others. it felt like the beginning of a different story—one in which proofs start arriving faster than they can be checked. and the culture of mathematics starts shifting under their feet.
The concern isn’t abstract. In inboxes across the field, journal editors are seeing more AI proofs than they can adequately vet. Large language models can also repeat ideas drawn from people’s work without attribution. Some researchers worry that the integrity of research itself is at risk as values mathematicians have long treated as non-negotiable—transparency and accessibility—are strained.
That pressure is now crystallizing in a formal response: guidelines released by a group of mathematicians. computer scientists. and math historians designed to rein in how AI is used in mathematics research. The recommendations culminate in a joint statement called the “Leiden Declaration on Artificial Intelligence and Mathematics. ” a 11-page document built to be a shared starting point for decision-making.
The group began assembling the statement 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. By then, the accelerating stream of proofs written partially or entirely by AI was already top of mind. The meeting was also shaped by a broader tension: AI’s usefulness is real. but the speed and incentives around it can distort what mathematics is supposed to do.
Ilka Agricola, a mathematician who chairs the Committee on Publishing at the International Mathematical Union (IMU), framed that contradiction plainly. “Used responsibly, AI ‘can be extremely useful and helpful,’” she said. “Unfortunately, this positive aspect is kind of getting small compared to the huge mess around it.”.
Part of that “mess” is practical. Journal editors’ inboxes are filling with AI proofs. Some fear that AI-generated arguments contain subtle, hard-to-spot errors. The declaration addresses that risk directly by arguing that AI proofs should face extra scrutiny—because. unlike a human-written proof that can be verified by anyone with the right expertise. AI can carry mistakes that are harder to catch.
The statement also pushes on the culture that allows mathematical work to travel freely. 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 means anyone on Earth can see new research and build on it. says Jim Portegies. a mathematician at the Eindhoven University of Technology in the Netherlands.
But Portegies points to a different pattern tied to commercial power. When tech companies work with AI proofs, he says, they often keep key details private. He cites an example from 2024: when Google DeepMind announced 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. Portegies describes a recurring dynamic—“we retreat behind closed doors because there is now a lot of commercial interest.”.
The Leiden workshop participants decided to respond to those trends by building their statement on models from open science and data management. Yet turning shared worries into a document that everyone could live with wasn’t simple. Rodrigo Ochigame. an anthropologist of AI at Leiden University. described the process as exhausting and intensely disputatious: “It was a long. arduous process with a lot of lively discussion. ” he said. “I don’t think I’ve ever been part of a writing process that involved so much debate for such a short text.”.
The final declaration lays out what its authors say mathematics research should value. how AI threatens those values. and what could be done in response. It also distinguishes between actions that individuals and companies can take and those that require larger intervention. Disclosing AI use and properly attributing previous research, for example, are framed as responsibilities for individuals and for AI companies. Other recommendations—like regulating the AI industry—would need large-scale organization or government intervention.
The declaration also tries to map incentives. The goals of humans and AI in math aren’t always aligned: mathematicians pursue research questions based on the potential for new techniques and ideas to emerge. while tech companies may focus on questions that showcase their AI models but have limited impact in mathematics. The statement argues that independent funding can help ensure mathematicians still have a say in how the field develops.
For Ochigame, though, the sharpest worry is about consent. He says, “Mathematicians who never intended to contribute to AI development are having their work used for this purpose without their consent.” He calls the situation “deeply concerning.”
Even with agreement on basic concerns. the declaration still has to live in a world where commercial AI is already moving quickly. Some recommendations are aimed at changing behavior; others are meant to set expectations—especially for companies whose research priorities can diverge from the community’s.
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. Agricola described the immediate value in concrete terms. saying the declaration does “an immense favor to the whole community. ” because it offers “a starting point for decision making. for discussion.” “I love it. ” she added.
In mathematics, a proof isn’t supposed to be a performance. It’s supposed to be something others can pick up, check, and extend. The Leiden Declaration is a bid to make sure that—even as AI accelerates—those fundamentals don’t disappear behind speed, secrecy, or profit.
Leiden Declaration on Artificial Intelligence and Mathematics IMU mathematicians AI proofs unit distance problem OpenAI arXiv peer review Google DeepMind AlphaProof AlphaProof methods published commercial AI transparency accessibility Lorentz Center
So basically AI is doing math now, cool I guess.
I don’t get why they’re upset, if it can solve unit distance then that’s progress. But also like… can it actually prove it or is it just guessing and spitting out something that sounds right? Seems like editors are just overwhelmed, not like the sky is falling.
Wait unit distance problem solved?? Isn’t that the one from like geometry class? If AI did it, then shouldn’t teachers be happy instead of making “declarations.” Sounds like they want control over who gets credit for math, not “proof quality.”
This is why I don’t trust anything AI says. They’re like “we’re worried proofs arrive faster than we can check” which is basically “we don’t want people to catch mistakes.” Also the part about repeating ideas without attribution—doesn’t that already happen with regular papers too? Like citation problems have been around forever. If they need 11 pages of guidelines maybe just slow down submissions? Not sure what Leiden has to do with any of it though.