The Leiden Declaration on Artificial Intelligence and Mathematics is a recommendations document addressed to the mathematical community and to the institutions and companies around it. It sets out five values it takes to be characteristic of mathematical research, five ways recent AI developments threaten them, and four separate sets of recommendations — for individual mathematicians, for mathematical organizations and not-for-profit funders, for policymakers, and for commercial AI developers. It is published at leidendeclaration.ai with a deposited copy at Zenodo record 20302944, and has been endorsed by the International Mathematical Union.
The document carries no publication date on its face. It states that it "reflects artificial intelligence technologies and mathematical practice as of May 2026," which is a currency statement about its content rather than a date of issue. The IMU endorsement letter and press accounts place publication in June 2026.
Origin
In September 2025 the Lorentz Center at Leiden University hosted a conference titled Mechanization and Mathematical Research. Around 60 participants from 10 countries attended — "mathematicians, computer scientists, philosophers, historians and social scientists, including those with experience in industry and in government." Over the eight months that followed, a working group of sixteen drafted the Declaration with what it describes as extensive feedback from the mathematical community. The group was convened by Jim Portegies of Eindhoven University of Technology.
The working group members are Jarod Alper (University of Washington), Michael Barany (University of Edinburgh), Alain Chavarri Villarello (Vrije Universiteit Amsterdam), Sander Dahmen (Vrije Universiteit Amsterdam), Walter Dean (University of Warwick), Karthik Ganapathy (University of California, San Diego), Michael Harris (Columbia University), David Holmes (Leiden University), Mateja Jamnik (University of Cambridge), Steven Kelk (Maastricht University), Bryna Kra (Northwestern University), Ursula Martin (University of Oxford), Bartosz Naskręcki (Adam Mickiewicz University and Warsaw University of Technology), Rodrigo Ochigame (Leiden University), Jim Portegies, and Johannes Schmitt (ETH Zurich). Not all sixteen are mathematicians: Barany is a historian of science and Jamnik works in computer science.
The Declaration positions itself alongside the Uppsala Code of Ethics for Scientists, the San Francisco Declaration on Research Assessment, the UNESCO Recommendation on Open Science, and the UK Universal Ethical Code for Scientists, and is written "in solidarity with other research endeavors and creative professions facing similar challenges."
The five values
The recommendations rest on values the authors state as held in common:
- 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."
- Attribution and responsibility. "Results are attributable to specific authors who take credit for their discovery and assume responsibility for their correctness."
- Transparency and independent verification. Arguments "may be extremely long or difficult, but in principle no proprietary knowledge or equipment should be required to understand them."
- Shared standards of evaluation — of "depth, difficulty, and significance."
- Autonomy of the discipline. Mathematics produces "understanding, clarity, and judgment" as well as results, and "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."
The five threats
The Declaration states that recent AI developments threaten each value, "often in ways that disproportionately affect students and early-career mathematicians."
Unreliable arguments. Automated techniques "can produce plausible but unreliable (or even incorrect) arguments which are difficult to distinguish from correct mathematical proofs," including in formalizations, where the difficulty lies in translating between computer-encoded and human presentations. The authors state this puts the review system "under increasing pressure."
Attribution and the commons. Models trained on published work "frequently return outputs that do not properly cite the human works they synthesize," and many are "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." See AI Copyright.
Incentives. AI use "may become incentivized for its own sake, disrupting our mechanisms for hiring, funding, and recognition," disadvantaging researchers without access to the technologies or "who are unwilling to use technologies controlled by organizations whose values they do not share."
Evaluation by press release. Results "communicated through informal channels such as press releases or blog posts, often without any research paper," seek "publicity for new results on market timelines before the accepted processes of community evaluation in mathematics can take place." The authors add that this leads to "overemphasizing the significance of automated tools and undervaluing the prior human contributions," and "misleadingly uses specific mathematical tasks as metrics for the general reasoning capacities of commercial products." See AI Benchmarks and Evaluation.
Autonomy. Increasing corporate involvement "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," and "broader understanding of the field may be permanently lost in the process of automation." With university budgets under pressure, the authors argue, incentives shift toward collaboration with technology companies "on asymmetric terms."
The threats section closes by placing the discipline's position inside a wider set of concerns — "warfare, mass surveillance, political disruption, and environmental damage" — and states that "[b]y failing to act, we run the risk of becoming complicit in the support of technologies which threaten much more than the practice of mathematics."
Recommendations
The four sets of recommendations are addressed to different audiences and differ in kind. Which audience a given provision speaks to matters for reading the document: the provision most often quoted against AI developers is in fact addressed to individual mathematicians.
To individual mathematicians
Eleven recommendations, each a bolded imperative. They cover disclosure of tool use (including a "Tool and computational resource disclosure" section in papers); making peers' reviewing easier; adherence to open-science principles; retention by human authors of "the responsibility for the correctness and adequacy of the arguments and results, as well as for the completeness and accuracy of citations"; and affirming 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."
Others ask mathematicians to put proactive effort into attribution where tools fail at it and to say so explicitly where attribution is not possible; to participate in public discourse and support science journalism; to stay informed about the tools; and to welcome new contributors from adjacent disciplines while asking entrants "to approach it with respect for our values."
Two are choices about participation rather than practice. "Consider carefully which tools to use" asks readers to weigh whether "non-proprietary, energy-efficient, or small-scale systems suffice," and whether "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" asks readers to withdraw from harmful work, naming "warfare, oppression, mass surveillance, and the undermining of democracy," and to "[o]nly enter into external partnerships which respect the values articulated in this Declaration."
To mathematical organizations and not-for-profit funders
Eight recommendations: build technical expertise and prepare "to become involved if major mathematical results are claimed using unconventional means"; lead on publishing and reviewing guidelines; maintain standards of rigor, potentially "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 authors' rights, with material "not to be used as training data without consent" and publishing agreements allowing opt-out; insist results continue to appear in peer-reviewed venues; support public research laboratories "administratively and financially independent from industry"; provide legal representation and codes of practice to researchers negotiating with industry, given asymmetries in bargaining position; and take alignment with the Declaration into account when funding academic–industry collaborations.
To policymakers
Four recommendations, and the section reaches beyond mathematics. It asks governments to strengthen legal protections for authors; to "[c]onsult with experts, including mathematicians, in forming policy decisions rather than relying on press releases or popular reporting," under the heading "Don't believe the hype," which states that "[t]here is currently a strong commercial incentive on the part of the technology industry to overstate the capabilities of their products"; to regulate the AI industry, citing "involvement in military and mass surveillance programs, development of technologies which promote misinformation and undermine democracy, and environmental costs," and calling for "significantly increased public oversight"; and to invest in public computational infrastructure — "public alternatives to proprietary technologies, from basic services for online collaboration, to computer clusters for mathematical modeling and machine learning applications" — funded "at university, national, and international levels." See Compute Governance.
To commercial AI developers
This section opens by noting the asymmetry it operates under: "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."
It describes two routes by which mathematics has been drawn into industrial AI work: the use of mathematics "to advertise the capabilities of commercial artificial intelligence systems in public communications and public relations campaigns," and the use of mathematical publications and formal libraries as training data "not only for specialized models for mathematics, but for more general-purpose artificial intelligence." On why mathematics is attractive for the latter, the Declaration states that the automatic checkability of formalized proofs 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," and that the strategy "often rests on a further assumption: that capabilities developed through mathematical theorem proving will extend to broader general reasoning."
The authors acknowledge what industry has offered — "lucrative jobs, monetary rewards, computing resources, and intellectually stimulating opportunities" — "in an era of underfunding of higher education and precarious academic employment."
The section's operative asks are two, and they are narrower than the individual-mathematician section's: that collaborations between mathematicians and industry "abide, at minimum, by the standards we expect of our colleagues and that are described throughout this Declaration," and that "[s]uch collaborations must respect the freedom of conscience of employees or contributors to speak openly about corporate policies and priorities."
Endorsements and reception
The International Mathematical Union is the sole institutional endorser named. Its statement reads in part: "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." The Declaration separately notes that the IMU Committee on Publishing, the Society for Industrial and Applied Mathematics, and the American Mathematical Society "have also produced related material" — which it distinguishes from endorsement.
Eight individual endorsements are featured. Terence Tao (UCLA) writes that the document "has been the result of months of community input about the fundamental values and goals of the mathematical community," that "these were questions we should have been systematically discussing years ago," and that he "wholeheartedly endorse[s] the statements and recommendations." Peter Scholze (Max Planck Institute for Mathematics) states that he ponders "mathematical ideas without use of AI, and generally avoid[s] reading AI-generated text as best as I can." Ilka Agricola, chair of the IMU Committee on Publishing, writes that AI "offers fantastic possibilities when used honestly and competently as a 'research assistant'" but that "the by far larger part is a total mess where science itself is under attack," citing fake research articles "whose sole purpose is to be counted as 'published' and cited, rather than actually read." Leslie Ann Goldberg (Oxford) picks out the unreliable-argument threat and the risk of "cluttering the literature with claimed results that are simply wrong," where "the errors are likely to propagate as new results are built on faulty foundations" — see AI-Fabricated Citations. Robbert Dijkgraaf, Jeremy Avigad, Kevin Buzzard and Steven Strogatz also endorse. Buzzard observes that "[m]athematicians should find it quite striking that tech companies are suddenly interested in their work."
The site displays a live signature counter, which stood at 3,964 on 13 September 2026.
OpenAI cited "the signers of the Leiden declaration on AI and Mathematics" in the authorship statement accompanying its September 2026 mathematics results, expressing "deep respect and understanding" for their concerns (Ten Advances in Mathematics and Theoretical Computer Science). The provision OpenAI's statement answers — that credit for an AI-generated proof should not be claimed as human authorship — sits in the Declaration's individual-mathematician section and is addressed to mathematicians rather than to developers; the asks the Declaration makes of commercial developers are the collegial-standards and freedom-of-conscience provisions above. Anthropic linked the Declaration in its account of formalizing Fermat's Last Theorem as evidence that mathematicians are contesting AI's role, while stating that "[f]ormalization, however, is a place where we feel unambiguously good about the role of AI" (Formalizing Fermat's Last Theorem (Anthropic, September 2026)).
Relation to the Fields Medallists' declaration
The Declaration is distinct from "A Severe Misalignment of AI in Mathematics," the September 2026 statement signed by 25 Fields Medal recipients (A Severe Misalignment of AI in Mathematics (Fields Medallists' declaration, 2026)), which coverage describes as following it (Source: techcrunch.com). The two differ in form as much as in content: Leiden is a long recommendations document produced over eight months with community consultation and endorsed by the discipline's international union, while the Fields statement is a short declaration whose signatories, according to Tao's account of it, deliberately forwent a comparable consultative process. Tao endorsed Leiden and signed the Fields statement. Both are covered in Machine-produced mathematics: claims, verification and credit.
Provenance
Captured 13 September 2026 from leidendeclaration.ai — preamble, values, threats, all four recommendation sections, working-group membership, the "About the declaration" note, the IMU endorsement and the eight featured endorsements. The signature list itself is not in the capture; the site renders only the most recent 24 names inline. Corroborated by the IMU endorsement letter hosted on mathunion.org and the Zenodo deposit record. Seven divergences from the secondary accounts that previously stood in for this document are recorded in the raw file's ## Source-fidelity notes.
Relationships
- depends-on: AI for Science — the Declaration is the mathematical community's most developed institutional response to AI in research practice
- instance-of: AI Research Authorship and Attribution — the concept the Declaration's authorship, disclosure and attribution provisions anchor
- related: A Severe Misalignment of AI in Mathematics (Fields Medallists' declaration, 2026) — a separate, shorter statement by 25 Fields Medallists three months later, produced without the consultative process
- contradicts: Ten Advances in Mathematics and Theoretical Computer Science — on evaluation by press release and on the use of mathematical tasks as general-reasoning metrics, though OpenAI cites the Declaration approvingly on authorship
- supports: AI Benchmarks and Evaluation — the "misleadingly uses specific mathematical tasks as metrics for the general reasoning capacities of commercial products" objection
- supports: AI-Fabricated Citations — the unreliable-argument and attribution threats, and Agricola's and Goldberg's endorsements
- related: AI Copyright — the training-data provisions on consent, opt-out and licence exploitation
- related: Compute Governance — the call for publicly funded computational infrastructure
- endorsed-by: the International Mathematical Union (sole institutional endorser); Terence Tao among eight featured individual endorsers
- related: Machine-produced mathematics: claims, verification and credit, Astra, OpenAI, Anthropic
Sources
- Declaration text (Source: leidendeclaration.ai); deposited copy (Source: zenodo.org)
- International Mathematical Union endorsement letter, IMU_AO_CL_8_2026 (Source: mathunion.org)
- TechCrunch — "OpenAI's feud with mathematicians is only escalating", 2026-09-11, which places the Declaration in June 2026 (Source: techcrunch.com)