As AI rapidly penetrates mathematical research and concerns grow that research culture and core values could be undermined, mathematicians have issued the ‘Leiden Declaration’ setting out principles for the use of AI. Provided by Getty Images Bank
As artificial intelligence (AI) rapidly pushes into mathematical research and concerns grow that core values and research culture could be undermined, mathematicians have issued a joint declaration setting out principles for the use of AI.
On the 2nd (local time), 16 experts, including mathematicians, computer scientists, philosophers, and historians, released the ‘Leiden Declaration on AI and Mathematics’.
The declaration calls for transparent disclosure of whether AI was used in the research process and for stronger verification procedures for AI-generated proofs. It argues that public research funding should be expanded and industry more tightly regulated to correct the imbalance between academia and commercial AI companies. The International Mathematical Union (IMU), the global body representing the world-wide mathematics community, has also endorsed the declaration.
Terence Tao, a 2006 Fields Medalist and professor at the University of California, Los Angeles (UCLA), said in his signature supporting the Leiden Declaration, “This is the outcome of months of community discussion” and noted, “In hindsight, we should have been systematically discussing these issues years ago, but this work has been extremely valuable and has produced an excellent document.”
In recent years, AI’s mathematical capabilities have advanced rapidly. Last month, OpenAI announced that its AI had independently solved the 80-year-old geometric problem known as the ‘unit distance problem’. Mathematicians see AI as moving beyond mere computation and beginning to deeply intervene in actual proof processes.
There is a clear reason why AI researchers have long used mathematics as a primary testing ground. For mathematical problems, computers can automatically determine whether an answer is correct, making it possible to generate virtually unlimited problems and feedback needed for AI training without human supervision. The AI industry regards the ability to prove difficult mathematical theorems as evidence of general reasoning capabilities and therefore uses it as a key benchmark in the development of high-performance AI.
The authors of the declaration warn that the explosion of AI-generated papers and proofs is destabilizing the scholarly ecosystem. The inboxes of journal editors are being filled with AI proofs that are difficult to review. Large language models can recycle existing research ideas without attribution or generate proofs containing subtle but hard-to-detect errors.
The tradition of openness that mathematics has long upheld is also under threat. Most modern mathematical papers are freely available through preprint servers such as arXiv. In contrast, AI companies often choose not to disclose their core methodologies.
When Google DeepMind announced the achievements of ‘AlphaProof’ in 2024, it took more than a year for the methodology to be published in a peer-reviewed journal. AlphaProof is an AI model that solved 4 out of 6 problems at the International Mathematical Olympiad (IMO), achieving a performance comparable to a silver medal.
Jim Portegies, a professor at Eindhoven University of Technology who led the declaration project, said, “As commercial interests have grown, research on AI proofs is increasingly not being made public.”
The declaration criticizes some AI models for using, as training data, databases that organize mathematical papers, theorems, and proofs into machine-readable, machine-verifiable formats, while relying on licenses and access agreements that did not anticipate AI use or infringing copyright protections. It warns that some of the general-purpose AI models developed in this way are being used in areas that raise serious ethical concerns, such as war, repression, large-scale surveillance, and the erosion of democracy.
The declaration defines mathematics not simply as an activity that produces correct answers but as a human-centered research activity that advances understanding, clarity, judgment, and creativity. It also expresses concern that, whereas mathematicians choose research topics based on their potential to generate new ideas and important research questions, AI companies may prioritize problems that are easy to automate or that readily showcase the performance of their AI models.
Peter Scholze, director of the Max Planck Institute for Mathematics and a 2018 Fields Medalist, said in his signature supporting the Leiden Declaration, “Mathematical ideas, like children, need to be nurtured and cared for over a long period of time,” adding, “The goal of mathematical research is for humans to understand mathematics, and just as we do not want children to be educated by AI, I myself prefer to think about mathematical ideas without AI and to avoid reading AI-generated texts as much as possible.”
Ilka Agricola, chair of the IMU Committee on Electronic Information and Communication, said, “If used responsibly, AI can be useful and helpful,” but pointed out that “unfortunately, its positive potential is being overshadowed by the various side effects and problems surrounding AI.”
The declaration sets out specific recommendations for individual mathematicians, mathematical institutions, governments, and commercial AI companies. For mathematicians, it calls for including a ‘Tools and computational resources used’ section in papers and makes clear that even when AI or other automation technologies are used, responsibility for the accuracy of results and the appropriateness of citations lies with the mathematicians.
For institutions and policymakers, it calls for stronger regulation of the AI industry, investment in public computational infrastructure, and the maintenance of peer-review-based publishing principles. For commercial AI companies, it states that they should meet standards comparable to those expected of members of the academic mathematical community and should ensure that employees and external collaborators are free to express their views on company policies and development directions.
The declaration is currently open for signatures from individuals and organizations around the world. It is expected to be a major agenda item at the International Congress of Mathematicians (ICM), to be held in Philadelphia, USA, this summer.
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