Leiden Declaration on Artificial Intelligence and Mathematics

# Leiden Declaration on Artificial Intelligence and Mathematics Source: [https://leidendeclaration.ai/](https://leidendeclaration.ai/) This declaration calls for action to address the challenges posed by the use of artificial intelligence within mathematics research\. It is the result of a community initiative and is endorsed by the International Mathematical Union \(IMU\)\. ### Preamble Technological developments have repeatedly transformed the practice of mathematics\. Recent artificial intelligence technologies, including symbolic and neural methods for the generation and formalization of mathematics, may already have initiated a significant chapter in this long history\. Among researchers, artificial intelligence has produced a wide range of reactions: enthusiasm for its potential to yield new discoveries; intimidation by the pace of developments; indifference to these rapid changes; and concern for the implications, both for mathematics and in wider society\. Mathematicians have a choice about whether and how to adopt artificial intelligence in the conduct of their research\. They also have a responsibility to ensure the continued flourishing of the discipline\. This Declaration calls upon mathematicians to exercise this responsibility, and provides recommendations for individuals, institutions, government, and industry\. Although we adopt the perspective of mathematical research, much of what we write applies equally to other aspects of mathematics\. This includes work in the broader mathematical sciences, education, mentoring, publishing, funding, science policy, and use of mathematics in the wider world\. The Declaration is conceived in solidarity with other research endeavors and creative professions facing similar challenges, both within and beyond academia\. It complements other calls for action such as the[Uppsala Code of Ethics for Scientists](https://phsj.org/wp-content/uploads/2007/10/Uppsala-Code-of-Ethics-for-Scientists.pdf), the[San Francisco Declaration on Research Assessment](https://sfdora.org/read/), the[UNESCO Recommendation on Open Science](https://www.unesco-floods.eu/wp-content/uploads/2022/04/379949eng.pdf), and the[UK Universal Ethical Code for Scientists](https://www.gov.uk/government/publications/universal-ethical-code-for-scientists)\. The[International Mathematical Union Committee on Publishing](https://www.mathunion.org/cop), the[Society for Industrial and Applied Mathematics](https://www.siam.org/media/b03hwuwe/siam-report-ai-task-force.pdf), and the[American Mathematical Society](https://www.ams.org/about-us/ai-summary)have also produced related material\. #### About our values We base our recommendations on what we take to be characteristic values of mathematical research that we have a joint interest in preserving\. Among these are the following: 1. There are many reasons to pursue mathematical research, ranging from intellectual curiosity to a desire to solve practical and societal problems\. Underlying much of mathematics is the activity of proof\. Mathematical proofs are regarded as conferring the highest degree of certainty to their conclusions, as well as imparting understanding of why their conclusions are true\. These characteristics of proof support the scientific integrity of mathematics\. 2. Results are attributable to specific authors who take credit for their discovery and assume responsibility for their correctness\. These principles ground the merit\-based standards to which we aspire in mathematical research\. 3. Mathematical arguments are regarded as transparent and subject to independent verification\. They may be extremely long or difficult, but in principle no proprietary knowledge or equipment should be required to understand them\. 4. Mathematicians share a concern for proper evaluation of mathematical work relative to shared standards of depth, difficulty, and significance\. 5. Mathematics produces not only a body of results, but also understanding, clarity, and judgment among the communities of mathematicians who have shaped them, often in the context of their own autonomously guided research\. This expert knowledge is essential, both to effectively use mathematics, and to continue to articulate new and significant research questions\. A key source of strength of the discipline has long been the autonomous shaping of the direction of research and the methods used to pursue it\. These characteristics of mathematics as a subject matter are also compatible with understanding mathematics as a human practice, and its place in the world\. As mathematicians, and also as inhabitants of a shared world, we have a duty to care for other people and our environment\. #### Potential threats Recent developments in artificial intelligence threaten each of these values, often in ways that disproportionately affect students and early\-career mathematicians, and hence the long term future of the discipline\. 1. Current automated techniques can produce plausible but unreliable \(or even incorrect\) arguments which are difficult to distinguish from correct mathematical proofs\. This applies not only to informal arguments, but also to formalizations, where the difficulty lies in the translation between computer\-encoded and human presentations of concepts\. These fast\-moving developments put our present system of review under increasing pressure, jeopardizing our ability to implement traditional standards for the correctness, transparency, and independent verifiability of proof\. 2. Technologies that draw extensively on the published mathematical commons undermine the traditional system of attribution\. Models trained on published works frequently return outputs that do not properly cite the human works they synthesize\. Many current models are also built on data obtained by systematically exploiting licenses and access arrangements that were not made with artificial intelligence in mind, or indeed by simply violating copyright protections\. 3. Technologies which affect the way in which mathematics is practiced may disturb the current system of incentives\. The use of artificial intelligence — and thus also the sort of problems which it can address — may become incentivized for its own sake, disrupting our mechanisms for hiring, funding, and recognition\. This disadvantages researchers who do not have access to the technologies or decision\-making related to them, or who are unwilling to use technologies controlled by organizations whose values they do not share\. 4. Proper evaluation is endangered if results are 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\. This practice seeks publicity for new results on market timelines before the accepted processes of community evaluation in mathematics can take place\. In many cases this leads to simplifications in reporting, such as overemphasizing the significance of automated tools and undervaluing the prior human contributions which have made those tools possible\. Such oversimplification risks influencing public opinion in a way that not only damages perceptions of mathematics, but also misleadingly uses specific mathematical tasks as metrics for the general reasoning capacities of commercial products\. 5. These developments put the autonomy of mathematics under threat\. The increasing involvement of technology companies in mathematical research raises the risk that research questions may come to be prioritized because of their amenability to automated mathematics, rather than expert judgment of their deeper significance\. Indeed, broader understanding of the field may be permanently lost in the process of automation\. With university budgets under pressure, this reshaping also changes professional incentives in a manner which encourages the collaboration of researchers with technology companies on asymmetric terms\. If left unchecked, these trends go beyond threatening researchers’ autonomy, affecting the scope and depth of mathematical research itself\. All of these challenges arise at a moment when the consequences of large\-scale investment in artificial intelligence are being widely discussed in regard to warfare, mass surveillance, political disruption, and environmental damage\. These raise grave ethical concerns\. By failing to act, we run the risk of becoming complicit in the support of technologies which threaten much more than the practice of mathematics\. We thus feel that there is an urgent need for a considered response from the mathematical community\. The following constitute brief descriptions of actionable recommendations\. We encourage professional organizations to endorse this Declaration, and to add provisions according to their own values, priorities, and governance\. ### Recommendations for individual mathematicians #### Disclose tool use Transparently disclose the use of automated tools, including large language models, machine learning systems, proof assistants, and other mathematical software\. Include a “Tool and computational resource disclosure” section in your papers; many journals, publishers, and professional organizations have already developed guidelines for this, and though the precise form of such a section will necessarily evolve, we encourage authors to live up to the spirit reflected in the[UNESCO Recommendation on Open Science](https://www.unesco-floods.eu/wp-content/uploads/2022/04/379949eng.pdf)and the[FAIR principles](https://www.nature.com/articles/sdata201618)\. When acting as a reviewer, abide by publisher guidelines\. If the use of artificial intelligence is allowed, be transparent about how you used it, and take responsibility for any significant recommendations you make\. #### Support the needs of reviewing The use of artificial intelligence in preparing papers can introduce material that makes reviewing more demanding\. Make it easier for your peers to review your work by disclosing tool use, giving precise and complete references to previous results, and providing formal proofs where feasible and appropriate\. #### Adhere to principles of open science The international open science movement aims to make scientific research transparent and accessible to all\. As mathematical research becomes more reliant on data and software, adhere to principles of open science\. See also the[UNESCO Recommendation on Open Science](https://www.unesco-floods.eu/wp-content/uploads/2022/04/379949eng.pdf)\. #### Retain the responsibility for correctness When automated techniques are employed in published mathematical research, the responsibility for the correctness and adequacy of the arguments and results, as well as for the completeness and accuracy of citations to relevant prior work, remains exclusively with the human authors\. #### Affirm the humanity of authorship Credit and responsibility continue to belong to humans within the mathematical community and should not be given to automated systems\. Artificial intelligence may obscure, but does not replace, the collective human labor behind a result\. #### Put effort into proper attribution The known limitations of automated tools in properly attributing ideas create a corresponding obligation for proactive effort to find and credit the sources that made a new result possible\. Where a satisfactory attribution is not possible, state this explicitly in the publication\. #### Participate in public discourse Mathematicians have a responsibility to support serious science journalism and to engage in public discourse to explain and contextualize artificial intelligence\-assisted methods and results\. This is particularly important for work within our own subfields, where specialized knowledge is required to assess claims about the depth, difficulty, and significance of results\. Moreover, we encourage mathematicians to seek opportunities to cooperate with and support other researchers and creative professionals facing similar challenges\. #### Stay informed about the emerging technologies As appropriate to your interests and research, stay informed about the capability of computer\-aided mathematical tools\. Such understanding is important for informing how our discipline adapts to new technologies and for participating in governance and public discourse\. #### Welcome new contributors The growing intersection of artificial intelligence and mathematics continues to attract researchers from other disciplines\. We welcome this broadening of our community and the range of skills and perspectives these contributors bring\. We encourage the mathematical community to actively engage with the broader community, to make our standards and practices explicit and accessible, and to create pathways for meaningful participation\. In turn, we ask those entering our field to approach it with respect for our values, while also helping us to adapt and develop them\. #### Consider carefully which tools to use Some automated tools and their developers will align with the provisions of this Declaration, while others will not\. Consider this when deciding which tools to use, or whether to use them at all\. Also consider whether non\-proprietary, energy\-efficient, or small\-scale systems suffice for your task\. If not, consider how preservation of the values articulated in this Declaration may be worth a delay in obtaining results\. #### Evaluate the ethical consequences of your work, and take action accordingly Mathematics has led to technology which greatly improves everyday life for many people, yet it also has applications in the development of technology for use in warfare, oppression, mass surveillance, and the undermining of democracy\. Evaluate the ethical consequences of your research to the best of your abilities, and if necessary withdraw from harmful work\. Only enter into external partnerships which respect the values articulated in this Declaration\. ### Recommendations for mathematical organizations and not\-for\-profit research funders #### Build expertise and plan strategically Professional organizations should keep abreast of technical developments and be proactive in making informed recommendations to members and to the broader community\. They should work together to guide the development of policy within academic publishing, funding bodies, and government\. They should also actively prepare to become involved if major mathematical results are claimed using unconventional means\. #### Take the lead on policies for publishing and reviewing Professional organizations within mathematics should take a leadership role in developing guidelines in regard to the use of automated techniques in publication and in reviewing\. These would include, for example, tool and computational resource disclosure, attribution, rules pertaining to authorship, and codes of conduct consistent with the values of mathematics\. These would supplement and support guidelines already being developed by publishers and journals\. #### Maintain standards of rigor When establishing policies, demand that results obtained by automated techniques be held to standards that address the risks raised by those techniques\. These might include requiring human descriptions of central arguments obtained by automated tools, insisting on formal verification when appropriate, cross\-checking theoretical and computational results, or external pre\-submission review\. #### Protect the rights of authors Automated mathematics presents new challenges to the rights of authors, and societies should be proactive in the development of sample licensing agreements to protect these rights\. In particular, material should not be used as training data without consent, and publishing agreements should allow authors to opt\-out of the use of their work in this way\. #### Insist on appropriate publication outlets Demand that mathematical results continue to be published in peer\-reviewed venues such as journals, proceedings, and books\. Informal mechanisms such as press releases or blog posts can provide a valuable supporting role, but they cannot replace peer\-review or community scrutiny\. #### Support public research laboratories Support the formation of university\-based, national, or international research laboratories devoted to studying automated mathematics which are administratively and financially independent from industry\. Support the use of less resource\-intensive technologies accessible to individual researchers\. #### Provide frameworks for collaboration Mathematicians and academic organizations collaborating with industry often face asymmetries in their bargaining positions, as well as in access to professional support such as legal resources, or advice on intellectual property\. Support researchers in such collaborations by providing access to legal representation, and by facilitating the development of codes of professional practice\. #### Align funding with values Alignment with the values of this declaration should be taken into account in the evaluation and funding of projects which involve collaboration between academics and industrial partners\. ### Recommendations for policymakers in government and elsewhere #### Protect the rights of authors Strengthen legal protections for authors, in line with this declaration\. #### Don’t believe the hype There is currently a strong commercial incentive on the part of the technology industry to overstate the capabilities of their products\. Consult with experts, including mathematicians, in forming policy decisions rather than relying on press releases or popular reporting of mathematical results\. #### Regulate the artificial intelligence industry Recent developments continue to highlight the strong public interest in regulating the technology industry, for example in regard to involvement in military and mass surveillance programs, development of technologies which promote misinformation and undermine democracy, and environmental costs\. We stand with others in calling for significantly increased public oversight\. #### Invest in public computational infrastructure Current events illustrate the need for public alternatives to proprietary technologies, from basic services for online collaboration, to computer clusters for mathematical modeling and machine learning applications\. We support the funding of public infrastructure at university, national, and international levels\. ### Recommendations for commercial artificial intelligence While the mathematical community has recognized standing in academic and public policymaking, it has no comparable role in the corporate decision\-making that is playing an increasing role in our discipline\. Nonetheless, recent developments have drawn mathematical work into industrial artificial intelligence efforts in multiple ways\. One is through the use of mathematics to advertise the capabilities of commercial artificial intelligence systems in public communications and public relations campaigns\. Another is that artificial intelligence developers have increasingly used mathematical publications and formal mathematical libraries as sources of training data — not only for specialized models for mathematics, but for more general\-purpose artificial intelligence\. What currently makes mathematics attractive for general\-purpose artificial intelligence development is that the correctness of formalized proofs can be checked automatically, without the need for human oversight\. This makes it possible to generate and check vast numbers of problems, both human\-authored and computer\-generated, to produce an effectively unlimited source of feedback for training artificial intelligence models\. The rationale for this strategy often rests on a further assumption: that capabilities developed through mathematical theorem proving will extend to broader general reasoning\. Some of the resulting general\-purpose models are being commercialized for applications that raise grave ethical concerns, including those named earlier: warfare, oppression, mass surveillance, and the undermining of democracy\. We recognize that industry has offered lucrative jobs, monetary rewards, computing resources, and intellectually stimulating opportunities that some mathematicians have found attractive\. This has taken place in an era of underfunding of higher education and precarious academic employment\. We also recognize that many mathematicians did not expect their work to become entangled with social and ethical implications of such magnitude, nor to be incorporated into systems used for purposes they may find deeply troubling\. We call on collaborations between mathematicians and industry to abide, at minimum, by the standards we expect of our colleagues and that are described throughout this Declaration\. Such collaborations must respect the freedom of conscience of employees or contributors to speak openly about corporate policies and priorities\. ### Members of the working group Jarod AlperUniversity of WashingtonMichael BaranyUniversity of EdinburghAlain Chavarri VillarelloVrije Universiteit AmsterdamSander DahmenVrije Universiteit AmsterdamWalter DeanUniversity of WarwickKarthik GanapathyUniversity of California, San DiegoMichael HarrisColumbia UniversityDavid HolmesLeiden UniversityMateja JamnikUniversity of CambridgeSteven KelkMaastricht UniversityBryna KraNorthwestern UniversityUrsula MartinUniversity of OxfordBartosz NaskręckiAdam Mickiewicz University Warsaw University of TechnologyRodrigo OchigameLeiden UniversityJim PortegiesEindhoven University of TechnologyJohannes SchmittETH Zurich ## About the declaration In September 2025 the Lorentz Center at Leiden University in the Netherlands hosted a conference entitled[Mechanization and Mathematical Research](https://www.lorentzcenter.nl/mechanization-and-mathematical-research.html)\. The around 60 participants from 10 countries comprised mathematicians, computer scientists, philosophers, historians and social scientists, including those with experience in industry and in government\. During the eight months following the conference, a smaller working group developed this Declaration, with extensive feedback from the mathematical community\. The Declaration reflects artificial intelligence technologies and mathematical practice as of May 2026\. The working group was convened by[Jim Portegies](mailto:[email protected]), who can be contacted for any further information\. ## Acknowledgment The authors of the Leiden Declaration would like to thank the many members of the mathematical community who gave valuable feedback on an early draft of the Declaration\. ## Updates and announcements We will share curated updates about the Declaration, including press releases, media coverage, talks, institutional endorsements, and launch announcements\. [Open News](https://leidendeclaration.ai/news) ## Institutional Endorsements 1. **International Mathematical Union \(IMU\)** > We take the rapid development and impact of Artificial Intelligence on our discipline very seriously: It opens new and exciting opportunities, but it also raises questions that cannot be left unexamined\. 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\. Mathematics is, and should always remain, a profoundly human endeavour\. ## Featured Endorsements 1. **Peter Scholze**verifiedDirector, Max Planck Institute for Mathematics > This is a wonderful declaration, coming at the right time\. The goal of mathematical research is human understanding of mathematics, and so mathematics can only thrive in a community of human mathematicians\. It is crucial to preserve this communal spirit\. In my experience, mathematical ideas, like children, must be nurtured and grow over the years\. 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\. 2. **Terence Tao**verifiedProfessor, University of California, Los Angeles > This has been the result of months of community input about the fundamental values and goals of the mathematical community\. In retrospect, these were questions we should have been systematically discussing years ago, but in any event the exercise was extremely valuable, and the end result is excellent\. I wholeheartedly endorse the statements and recommendations in this declaration\. 3. **Robbert Dijkgraaf**verifiedDistinguished University Professor, University of Amsterdam; President\-Elect, International Science Council; Former Minister of Education, Culture and Science, The Netherlands > Scientific research is in the midst of a major transformation through the impact of AI, and mathematics is one of the disciplines most fundamentally affected through automated proof generation and machine\-generated reasoning\. It is therefore more important than ever that the mathematical community comes together to establish clear guidelines and shared standards, to safeguard not only the practice of mathematics but its deeper purpose: the cultivation of understanding, judgment, and human insight\. 4. **Ilka Agricola**verifiedChair of the Committee on Publishing, International Mathematical Union > AI is fundamentally transforming the way we do mathematics, and it is doing so at incredible speed\. It offers fantastic possibilities when used honestly and competently as a ‘research assistant’\. But this seems to be only a small part of what is going on: the by far larger part is a total mess where science itself is under attack\. In this situation, it is essential—and courageous—to take a step back and ask ourselves: What does it mean for us as a community to conduct mathematical research in this context? What principles should guide us, and what dangers do we see? For the dangers are real: The advent of sophisticated AI language models has made it cheaper and easier than ever to produce fake research articles whose sole purpose is to be counted as ‘published’ and cited, rather than actually read, and the peer review process as we used to know it is endangered\. The IMU Committee on Publishing is deeply worried by the current situation, and hence we strongly welcome and support the community effort that led to the Leiden Declaration\. Mathematics as we know and love it is at stake\! 5. **Jeremy Avigad**verifiedProfessor of Philosophy and Mathematical Sciences, Carnegie Mellon University > As AI plays an increasing role in our decision\-making processes, it’s as important as ever to keep mathematical reasoning and justification in the loop\. The Leiden Declaration offers a helpful framework for mathematicians to decide how, when, and whether to engage with the new technologies\. 6. **Kevin Buzzard**verifiedProfessor of Pure Mathematics, Imperial College London > 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\. 7. **Leslie Ann Goldberg**verifiedHead of Computer Science, University of Oxford > The Leiden Declaration identifies an important way in which the incorrect use of AI may harm the progress of mathematical research: ‘Current automated techniques can produce plausible but unreliable \(or even incorrect\) arguments which are difficult to distinguish from correct mathematical proofs\.’ This is a serious problem: research in mathematics \(and in mathematical disciplines like theoretical Computer Science\) almost always builds on previous research, so it is essential for researchers to know that the results in the literature are correct\. 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\. I welcome the recommendations of the Leiden Declaration, particularly the disclosure of tool use, and continued publication through peer\-reviewed journals\. 8. **Steven Strogatz**verifiedDistinguished Professor for the Public Understanding of Science and Mathematics, Cornell University > AI has the potential to become a powerful partner in mathematical discovery\. That power brings new responsibilities\. The Leiden Declaration calls on mathematicians to protect what makes our subject trustworthy and illuminating: proof, attribution, and the quest for insight\. ## Signatories 1. **Stein Meereboer**[ORCID](https://orcid.org/0009-0008-0185-0767)IMAP, Radboud University Nijmegen 2026\-06\-03 2. **Marco Bertola**[ORCID](https://orcid.org/0000-0001-7945-925X)Professor, Concordia University 2026\-06\-03 3. **Michael Eichmair**[ORCID](https://orcid.org/0000-0001-7993-9536)Professor, University of Vienna 2026\-06\-03 4. **Yoav Len**[ORCID](https://orcid.org/0000-0002-4997-6659)Senior Lecturer, University of St Andrews 2026\-06\-03 5. **KEROBOTO BENJAMIN ZA'NGOTI OGUTU**[ORCID](https://orcid.org/0000-0001-9340-1193)Lecturer/Researcher, Dedan Kimathi University of Technology 2026\-06\-03 6. **Colin J Cotter**[ORCID](https://orcid.org/0000-0001-7962-8324)Mathematics, Imperial College London 2026\-06\-03 7. **Steven Khan**[ORCID](https://orcid.org/0000-0002-7614-3257)Associate Professor, Brock University 2026\-06\-03 8. **Amira Tlemsani**[ORCID](https://orcid.org/0009-0003-1068-2842)PhD Candidate, Leiden University 2026\-06\-03 9. **Mickael Randour**[ORCID](https://orcid.org/0000-0001-8777-2385)F\.R\.S\.\-FNRS & UMONS \- Université de Mons, Belgium 2026\-06\-03 10. **Christopher Sangwin**[ORCID](https://orcid.org/0000-0002-3725-8625)University of Edinburgh 2026\-06\-03 11. **Justin Uhlemann**[ORCID](https://orcid.org/0009-0000-6422-8221)PhD student, Utrecht University 2026\-06\-03 12. **Benjamin Gammage**[ORCID](https://orcid.org/0000-0002-2154-7190)Assistant Professor, University of Toronto 2026\-06\-03 13. **Isobel Falconer**[ORCID](https://orcid.org/0000-0002-7076-9136)Professor, History of Mathematics, University of St Andrews 2026\-06\-03 14. **John Klein**[ORCID](https://orcid.org/0000-0002-2132-4982)Professor, Wayne State University 2026\-06\-03 15. **Florian Spicher**verified emailUniversität Bern 2026\-06\-03 16. **Ilkka Törmä**[ORCID](https://orcid.org/0000-0001-5541-8517)University of Turku 2026\-06\-03 17. **Hannah Markwig**verified emailEberhard\-Karls\-Universität Tübingen 2026\-06\-03 18. **Ignacio Barros**[ORCID](https://orcid.org/0000-0002-7729-9413)Professor, Universiteit Antwerpen 2026\-06\-03 19. **Jiaben Zhang**[ORCID](https://orcid.org/0009-0005-1971-9853)Xi'an Eurasia University 2026\-06\-03 20. **Gunther Leobacher**[ORCID](https://orcid.org/0000-0002-7837-784X)University of Graz 2026\-06\-03 21. **Daniel Turaev**verified emailTechnische Universität Berlin 2026\-06\-03 22. **Leon Menger**[ORCID](https://orcid.org/0000-0003-0621-4977)PhD Student, University of Notre Dame 2026\-06\-03 23. **Christopher Pirie**[ORCID](https://orcid.org/0009-0004-0340-928X)Mathematics, Radboud University Nijmegen 2026\-06\-03 24. **Andrea Conti**[ORCID](https://orcid.org/0000-0001-9279-9451)Postdoctoral fellow, Heidelberg University 2026\-06\-03 Showing the latest 24 signatories\.[View the complete signatory list](https://leidendeclaration.ai/signatories)\.