Mathematicians Against Big AI: Stop Training Models on Our Work Without Consent

At the beginning of the week, the international mathematical community made public the Leiden Declaration on Artificial Intelligence and Mathematics, a document urging researchers to address how AI companies use published mathematical work. The text is approved by the International Mathematical Union (IMU), the body that awards the Fields Medal, and includes signatories such as Peter Scholze, Fields Medalist and director of the Max Planck Institute for Mathematics.

The Declaration challenges the way companies handle material from the discipline: the training of models on published articles without consent, announcements made via press releases instead of peer review, and attributions that are not made.

"Mathematics is, and should always remain, a profoundly human endeavor," stated Ulrike Tillmann, vice president of the IMU.

The document arrives about two weeks after OpenAI claimed a proof of a geometry conjecture formulated by Erdős in 1946, a result we have already covered. The Declaration specifically cites cases where results are communicated "on market timelines, before the normal evaluation processes of the community can take place," and references AlphaProof from Google DeepMind, which solved three problems of the International Mathematical Olympiad in 2024 but took over a year to publish the methods in a peer-reviewed venue.

The Five Identified Risks

The document lists five threats to the values that make mathematics reliable. The first is the generation of plausible but unreliable arguments, difficult to distinguish from correct proofs.

"Inaccurate drafts generated by AI are cheap to produce, and there is a risk of clogging the literature with results that are simply wrong," noted Leslie Ann Goldberg, head of computer science at the University of Oxford. "Once that happens, it is likely that errors will propagate as new results are built on defective foundations."

The second threat is the lack of attribution: models trained on published work often return results without citing the human sources they synthesize, and part of the training data has been obtained by "exploiting licenses and access agreements" or "simply violating copyright protections." This is followed by dependency on proprietary technologies and costly computing resources, which deepens inequality among researchers; the media overexposure of results, announced before any scientific verification; and the loss of autonomy, when technical feasibility or commercial interests dictate research questions.

Recommendations, from Individuals to Governments

The recommendations are structured at multiple levels. The Declaration asks individual researchers to declare the use of AI tools, to maintain accountability for the correctness of their results, to continue attributing work to human authors, and to not recognize the status of authorship for an automatic system. Professional organizations are tasked with developing license agreements that prevent the use of works as training data without consent and defending the role of peer-reviewed publications.

For those in governance, the tone is clear: "do not believe the hype," write the authors, because "there is a strong commercial incentive, from the technology industry, to overestimate the capabilities of their products". Therefore, they call for regulating the sector and investing in public computing infrastructures as an alternative to proprietary systems. The document also reminds that mathematics has applications in the development of technologies for "war, oppression, mass surveillance, and the weakening of democracy," urging a consideration of ethical implications before accepting collaborations with the sector.

The Declaration was drafted over eight months by a working group of 16 authors from fifteen universities, following a workshop hosted by the Lorentz Center in Leiden in September 2025, and is now open for endorsements from the rest of the mathematical community.