Mathematicians warned against rising tech industry influence in a declaration describing the many challenges that AI poses to mathematics research. The timing of the declaration comes two weeks after OpenAI publicized one of its AI models as having disproved an 80-year-old mathematical conjecture in geometry.
The declaration was developed by a working group of 16 researchers over eight months following a conference held at Leiden University in the Netherlands in September 2025. Published on June 2, 2026, the resulting Leiden Declaration on Artificial Intelligence and Mathematics has been endorsed by the International Mathematical Union—the international non-governmental organization that hosts conferences and oversees the most prestigious prizes in mathematics such as the Fields Medal.
“Mathematicians should find it quite striking that tech companies are suddenly interested in their work,” said Kevin Buzzard, a mathematician at Imperial College London, in a statement. “The Leiden Declaration is a well-thought-through response to what is currently happening, as AI continues to disrupt this space.”
The Leiden Declaration, which has already drawn hundreds of signatories, warns that recent AI developments are threatening “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.”
First, it points out how AI models can “produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs.” Such developments put reviewers under increasing pressure and are “jeopardizing our ability to implement traditional standards for the correctness, transparency, and independent verifiability of proof,” the declaration warns.
“Inaccurate AI-generated drafts are cheap to produce, and there is a risk of cluttering the literature with claimed results that are simply wrong,” said Leslie Ann Goldberg, head of computer science at the University of Oxford, in a statement. “Once that happens, the errors are likely to propagate as new results are built on faulty foundations.”
Second, the declaration highlights how “models trained on published works frequently return outputs that do not properly cite the human works they synthesize,” while also pointing out that many current AI models were trained on data obtained through “exploiting licenses and access arrangements” or “simply violating copyright protections.”
Third, the declaration describes how 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.”
Fourth, the declaration warns against 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.” Such communication strategies can lead to “oversimplification” in media reporting that overemphasizes AI tools’ significance at the expense of prior human contributions, and “misleadingly uses specific mathematical tasks as metrics for the general reasoning capacities of commercial products.”
Fifth, the declaration describes “increasing involvement of technology companies in mathematical research” as threatening the “autonomy of mathematics,” especially as university budgets are under pressure and researchers may feel greater professional incentive to collaborate with technology companies on “asymmetric terms.” This also raises the risk that mathematics research questions amenable to AI-driven techniques may be prioritized.
The OpenAI example
Many of the Leiden Declaration’s warnings seem especially relevant to how OpenAI announced its model’s mathematical achievement on the same day that news publications reported the company was preparing to offer stock shares to the general public. The declaration pointedly described corporate press releases highlighting AI mathematical achievements as operating on “market timelines before the accepted processes of community evaluation in mathematics can take place.”
“The tech industry proceeds in accordance with commercial logic, which is antithetical to the values of mathematics,” said Michael Harris, a mathematician at Columbia University and an author of the declaration, in a New York Times interview. He also spoke of the declaration attempting to “recover control of the narrative about the values and goals of mathematics from the AI industry.”
OpenAI uploaded a research paper describing its AI model’s mathematical proof along with commentary from independent mathematicians. But the company did not disclose information about prompts, AI training data, and the amount of computational resources used to solve the mathematics problems in question, said Rodrigo Ochigame, a historian and anthropologist of computing and artificial intelligence at Leiden University and another author of the declaration.
“The AI model is proprietary and unavailable to anyone outside the company,” Ochigame told The New York Times. “We get a flashy promotional video, while basic information needed to assess the scientific meaning of the result is kept secret.”
The OpenAI achievement was “remarkable” but likely involved substantial compute resources, said Ursula Martin, a mathematician and computer scientist at Oxford University and an author of the declaration, in The New York Times interview. She suggested that similar quantities of equivalent effort from human mathematicians would have probably solved the problems in the same way—and she cautioned that mathematics is also about the “cultivation of ideas, understanding, judgment and human insight” beyond solving problems.
Similar expressions of support for human intellectual efforts in mathematics appear in endorsements published on the Leiden Declaration website.
“In my experience, mathematical ideas, like children, must be nurtured and grow over the years,” said Peter Scholze, director of the Max Planck Institute for Mathematics, in a statement. “Just like I do not want my children to be educated by AI, I am pondering my mathematical ideas without use of AI, and generally avoid reading AI-generated text as best as I can.”
Recommendations for humans
So what is a human mathematician to do during the AI boom? The Leiden Declaration recommends that individual mathematicians 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
The declaration also reminds mathematicians that mathematics has “applications in the development of technology for use in warfare, oppression, mass surveillance, and the undermining of democracy,” and so mathematicians should make ethical decisions accordingly when choosing external partnerships with tech companies.
Professional mathematical organizations can 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. The declaration also suggests such organizations “actively prepare to become involved if major mathematical results are claimed using unconventional means.”
The authors of the declaration also offer straightforward recommendations for policymakers, including “protect the rights of authors,” “regulate the artificial intelligence industry,” and “invest in public computational infrastructure.” Under “don’t believe the hype,” the declaration warns about how “there is currently a strong commercial incentive on the part of the technology industry to overstate the capabilities of their products.”
Lastly, the declaration acknowledges that the tech industry “has offered lucrative jobs, monetary rewards, computing resources, and intellectually stimulating opportunities that some mathematicians have found attractive… in an era of underfunding of higher education and precarious academic employment.” It calls on such collaborations between mathematicians and the tech industry to abide by the standards laid out in the declaration.
“By endorsing the declaration, the IMU affirms that the future of mathematical research must be guided by human judgment, fair and transparent practices, and the shared values of the global mathematical community,” said Ulrike Tillmann, vice president of the International Mathematical Union, in a statement. “Mathematics is, and should always remain, a profoundly human endeavor.”
