Leiden Declaration on Artificial Intelligence and Mathematics is an AI declaration addressed to the mathematical research community. It was published on 2026-06-02. Its focus is not simply whether AI can help people do mathematics, but how AI is changing verification, authorship, attribution, publishing, incentives, and autonomy in mathematical research.
The declaration was developed by researchers from mathematics, computer science, philosophy, history, the social sciences, and related fields, and it has been endorsed by the International Mathematical Union (IMU). Its starting point is clear: mathematics can use new automated tools, but it should not give up the verifiability of proof, the responsibility of human authors, the judgment of the academic community, or the autonomy to set research directions without being steered by commercial platforms.
What the declaration is worried about
The declaration looks at AI’s impact on mathematical research through several basic values.
The first is the reliability of proof. Mathematical proof is not only about reaching a correct conclusion; it is also about understanding why that conclusion is correct. Current automated tools can generate arguments that look like proofs but may be unreliable. This puts pressure on reviewing, peer verification, and subsequent research. Even formalized proof still involves the difficult translation between machine representations and human understanding.
The second is attribution and author rights. Many models absorb existing mathematical literature, formal libraries, and shared knowledge, but their outputs may not cite sources accurately. The declaration argues that this weakens traditional mechanisms of academic credit and sharpens questions around unauthorized data use, copyright, and publishing agreements.
The third is the reshaping of research incentives. If being suitable for automated AI processing becomes an advantage in itself, the choice of problems, hiring, funding, and recognition in mathematics may all be distorted. The declaration is especially concerned about early-career researchers, people without access to advanced tools, and researchers unwilling to rely on commercial systems whose values they do not share.
The fourth is the way results are communicated. The declaration criticizes a trend in which major mathematical advances are first announced through press releases, blog posts, or product marketing, without papers, detailed disclosure, or peer review. This can exaggerate the role of tools, undervalue long-term human contributions, and turn specific mathematical tasks into marketing metrics for general reasoning ability.
The fifth is the autonomy of the mathematical community. Large technology companies are increasingly entering mathematical research. They provide jobs, funding, and compute, but they may also influence research directions. The declaration worries that the importance of a problem may become determined by its amenability to automation, product narratives, or commercial objectives rather than by expert mathematical judgment.
Recommendations for individual mathematicians
For individual researchers, the declaration emphasizes transparency, responsibility, and careful tool use.
The most direct recommendation is to disclose tool use. Papers should state whether large language models, machine learning systems, proof assistants, or other mathematical software were used, and should explain the way they were used and the computational resources involved where possible. Disclosure is not a formality. It helps reviewers and readers understand how a result was produced and which parts require additional checking.
The declaration also stresses that human authors must remain responsible for correctness. Even when automated techniques are used, the adequacy of the argument, the completeness of citations, and the reliability of the result remain the responsibility of the authors, not the model or software system.
On authorship, the declaration takes a clear position: credit and responsibility should belong to humans in the mathematical community, and automated systems should not be authors. AI may participate in generation, search, formalization, or auxiliary verification, but it cannot replace human understanding, judgment, or responsibility.
For citation and attribution, the declaration asks researchers to make a more active effort. Because automated tools can easily miss sources, authors should proactively look for and credit prior work. If satisfactory attribution is not possible, that should be stated in the publication.
The declaration also encourages mathematicians to participate in public discourse. AI-assisted mathematical results are often placed in popular media and company marketing. Researchers in the relevant fields have a responsibility to explain the real difficulty, depth, and significance of these results, so the public does not understand mathematics and AI only through promotional material.
Recommendations for institutions and funders
For mathematical organizations, journals, publishers, and nonprofit funders, the declaration calls for proactive rulemaking instead of waiting for commercial platforms to define the facts.
First, organizations need to build expertise. Mathematical societies and research organizations should keep up with the development of automated mathematics tools and provide community-oriented guidance in publishing, funding, and policy discussions. When a major mathematical result is announced through unconventional channels, professional organizations should be able to help assess it.
Second, they should develop policies for publishing and reviewing. The declaration recommends that mathematical organizations take the lead on disclosure of tool use, authorship, attribution, review rules, and codes of conduct. AI-generated content can make peer review more demanding, so review processes also need new disclosure and verification mechanisms.
Third, they should maintain rigorous standards. For results involving automated techniques, authors may be required to provide human-readable accounts of the central arguments, formal verification where appropriate, cross-checks between theoretical and computational results, or external assessment before submission.
Fourth, they should protect authors’ rights. The declaration explicitly says that mathematical material should not be used as training data without consent. Publishing agreements should also allow authors to opt out of such use of their work.
Fifth, they should support public research infrastructure. The declaration supports university-based, national, or international laboratories independent from industry companies, both to study automated mathematics itself and to support less resource-intensive technologies that individual researchers can use.
Recommendations for policymakers and AI companies
For governments and policymakers, the declaration’s advice is direct: do not rely only on commercial publicity, and consult experts who genuinely understand mathematical research. AI companies have incentives to overstate product capabilities, especially when they use mathematical tasks to demonstrate general reasoning, so professional judgment is needed to unpack the limitations.
The declaration also calls for stronger public oversight of the AI industry, including risks around military use, surveillance, misinformation, democratic harm, and environmental costs. Mathematical research may look abstract, but it can be pulled into the training, evaluation, and promotion of these technical systems.
On public investment, the declaration supports public computational infrastructure, including compute resources, collaboration services, and research platforms at university, national, and international levels. The point is that mathematical research should not have to depend entirely on the compute and tools offered by a small number of commercial platforms.
For commercial AI companies, the declaration asks them to meet at least the standards expected inside the mathematical community: respect for authorship, attribution, transparency, peer review, and researchers’ freedom of conscience. When companies collaborate with mathematicians, employees and contributors should be allowed to speak openly about corporate policies and priorities, rather than being forced into asymmetric arrangements around resources and legal support.
Why this matters
The importance of the declaration is not that it opposes AI. On the contrary, it recognizes that AI, proof assistants, and automated tools may become part of the development of mathematics. What it opposes is the mathematical community handing its standards of verification, authorship, and research direction to external systems as tool capabilities, commercial incentives, and communication speeds change rapidly.
Mathematics is distinctive because it has long depended on verifiable proof, traceable attribution, peer judgment, and human understanding of concepts and structures. AI can accelerate some parts of the work, but if it makes incorrect arguments cheaper, sources more opaque, and research evaluation more dependent on corporate messaging, efficiency gains may end up damaging the discipline itself.
For the wider AI industry, the Leiden Declaration also offers a useful lens: the more a field appears to be automatically verifiable, the more it needs to discuss who defines verification standards, who bears responsibility for errors, who has rights over training data, and who decides whether a research problem is worth pursuing.
Conclusion
The core of the Leiden Declaration is not a request for mathematicians to stay away from AI. It is a request for the mathematical community to actively define the boundaries under which AI enters research.
Tools can be used, but their use should be disclosed. Results can be produced with automation, but human authors must remain responsible. Mathematical advances can be communicated publicly, but marketing timelines cannot replace peer review. Industry can participate in research, but commercial goals should not rewrite the values of the mathematical community.
In the broader AI discussion, the declaration points to the same lesson: AI governance does not happen only in laws and model safety evaluations. It also happens whenever a professional community redefines its own rules, responsibilities, and bottom lines.
References: Leiden Declaration on Artificial Intelligence and Mathematics, Zenodo DOI: 10.5281/zenodo.20302944, International Mathematical Union