As AI models become more capable at cracking high-level math problems, mathematicians have warned that the growing use of AI in the field poses several challenges, including unreliable mathematical proofs, lack of citation, improper disclosure of information, and research bias.
These concerns have been outlined in what may be the first-of-its-kind declaration drafted by a working group of 16 researchers over eight months following a conference held at Leiden University in the Netherlands in September 2025. The document titled ‘Leiden Declaration on Artificial Intelligence and Mathematics’ has drawn hundreds of signatories, and has also been endorsed by the International Mathematical Union.
Essentially, it warns that recent AI developments threaten the characteristic values of mathematical research, “often in ways that disproportionately affect students and early-career mathematicians, and hence the long term future of the discipline.”
The declaration comes just weeks after tech giants such as OpenAI and Google DeepMind made claims about their respective AI models solving decades-old mathematical problems. OpenAI said that its model disproved a famous geometry conjecture first proposed by famous mathematician Paul Erdos in 1946. Days later, Google DeepMind researchers claimed that its model, AlphaProof Nexus, had solved nine out of the 353 open Erdos problems.
While AI models appear to be making progress in mathematical capabilities, an expanding group of mathematicians have questioned the purported milestones.
“Mathematicians should find it quite striking that tech companies are suddenly interested in their work. The Leiden Declaration is a well-thought-through response to what is currently happening, as AI continues to disrupt this space,” Kevin Buzzard, a mathematician at Imperial College London, said in a statement.
“Inaccurate AI-generated drafts are cheap to produce, and there is a risk of cluttering the literature with claimed results that are simply wrong. Once that happens, the errors are likely to propagate as new results are built on faulty foundations,” said Leslie Ann Goldberg, head of computer science at the University of Oxford, in a statement.
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What does the Leiden Declaration say?
Here are the key arguments outlined by mathematicians in the Leiden Declaration:
-Lack of reliable proofs: The declaration argues that AI models “produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs.” This, in turn, puts reviewers under increasing pressure and jeopardizes the ability “to implement traditional standards for the correctness, transparency, and independent verifiability of proof.”
-Lack of citations: “Models trained on published works frequently return outputs that do not properly cite the human works they synthesise,” the declaration read.
-Inequity in access: It adds that the use of AI “may become incentivized for its own sake, disrupting our mechanisms for hiring, funding and recognition” while leaving out researchers who lack access or are “unwilling to use technologies controlled by organizations whose values they do not share.”
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-Lack of proper disclosure channels: Mathematics research “communicated through informal channels such as press releases or blog posts, often without any research paper or other disclosure of information necessary for scientific evaluation,” the declaration warns.
-Threat to autonomy: It further highlights the risk that mathematics research questions amenable to AI-driven techniques may be prioritised with the increasing involvement of technology companies in mathematical research, thereby threatening the autonomy of mathematics at a time university budgets are under pressure and researchers may feel greater professional incentive to collaborate with technology companies
Key recommendations
The Leiden Declaration suggests the following for human mathematicians amid the AI boom:
-Ensure transparency: Individual mathematicians should transparently disclose their use of AI tools, retain responsibility for the correctness of their mathematical work, continue crediting human authors while properly attributing work even if AI tools make that difficult, and consider using only AI tools that align with the values articulated in the declaration.
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-Make ethical decisions: Mathematicians should make ethical decisions when choosing external partnerships with tech companies involved in the development of AI for use in warfare, oppression, mass surveillance, and the undermining of democracy, as per the declaration.
-Develop guidelines for AI use: The declaration urges professional mathematical organisations to develop guidelines for the use of AI and other automated tools in publication and review, protect the rights of researchers as authors through licensing agreements that prevent their work from being used as training data without consent, and support the role of peer-reviewed publications. It further suggests that organisations “actively prepare to become involved if major mathematical results are claimed using unconventional means.”
Standardised partnerships with tech industry: While acknowledging that the tech industry has offered lucrative jobs, monetary rewards, computing resources, and intellectually stimulating opportunities that some mathematicians have found attractive, collaborations between mathematicians and the tech industry have to abide by the standards laid out in the declaration amid the underfunding of higher education and precarious academic employment.
