Leiden Declaration on Artificial Intelligence and Mathematics

The Leiden Declaration on Artificial Intelligence and Mathematics is a statement on the use of artificial intelligence in mathematical research, published on 2 June 2026 at leidendeclaration.ai and deposited on Zenodo under DOI 10.5281/zenodo.20302944. It was written by a 16-member working group drawn from a September 2025 workshop at the Lorentz Center in Leiden, the Netherlands, and was endorsed the day it appeared by the International Mathematical Union (IMU).^[1][2][3]

The declaration sets out five values it takes to be characteristic of mathematical research, five ways in which recent AI developments threaten those values, and 23 named recommendations addressed to individual mathematicians, to mathematical organizations and not-for-profit funders, and to policymakers, followed by a fourth section addressed to commercial AI developers. Its principal recommendations are that tool use be disclosed, that responsibility for correctness and attribution stay with human authors, that results continue to be published in peer-reviewed venues rather than announced by press release, and that published mathematics not be used as training data without consent.^[1]

The declaration is open for individual signature through a public form. The site reported 4,013 signatories when checked on 13 September 2026.^[4] Both sides of the dispute it describes have pointed to it: OpenAI named its signers in the August 2026 announcement of the results credited to GPT-6 Astra, and Terence Tao cited the declaration's consultative process as the model that a much shorter September 2026 statement by 25 Fields Medallists had no time to follow.^[5][6]

Origins

From 15 to 19 September 2025 the Lorentz Center at Leiden University hosted a workshop called "Mechanization and Mathematical Research", organized by Lenny Taelman (University of Amsterdam), Johan Commelin (Utrecht University), Rodrigo Ochigame (Leiden University), Akshay Venkatesh (Institute for Advanced Study) and Mateja Jamnik (University of Cambridge). The files the Lorentz Center posted for the workshop include presentations by Tim Gowers ("Will mathematics exist in 2035"), Kevin Buzzard ("Problematic proofs"), Jeremy Avigad ("Is Mathematics Obsolete"), Emily Riehl, Heather Macbeth and Thomas Hubert (on AlphaProof), along with a scientific report. The workshop page lists the Leiden Declaration under its workshop links.^[7] The organizers also published a separate report, "Shaping the Future of Mathematics in the Age of AI", on arXiv in March 2026.^[8]

The declaration's about section describes the workshop as bringing together around 60 participants from 10 countries, including mathematicians, computer scientists, philosophers, historians and social scientists, some with experience in industry and government; the IMU editorial gives the same participant figures. A smaller working group then developed the declaration with feedback from the mathematical community over what the site calls "the eight months following the conference" (the IMU editorial says six months), and the site states that the text reflects AI technologies and mathematical practice as of May 2026. The working group was convened by Jim Portegies of Eindhoven University of Technology, who is also the contact point for institutional endorsements.^[1][3]

It is named after the city where that workshop took place. A Nature editorial pointed out that the Leiden Manifesto on research metrics, published in Nature in 2015 after a 2014 conference at Leiden University, came out of the same place, and read the new declaration as part of the same tradition of community-written guardrails.^[9]

Working group

The same 16 names are recorded as the authors of the Zenodo deposit, each with an ORCID identifier. The deposit is licensed CC BY-NC 4.0 and carries a publication date of 2 June 2026; as of 13 September 2026 DataCite listed one version of the record under the concept DOI 10.5281/zenodo.20302943.^[2] Johannes Schmitt and Bartosz Naskręcki are listed on the site as its current convenors and administrators, with a note that their institutional addresses are given for legal-contact purposes only and do not imply institutional endorsement.^[10]

IMU endorsement

The IMU endorsement is documented in the union's own records rather than only in the declaration's self-description. On 2 June 2026, IMU Secretary General Christoph Sorger sent Circular Letter 8/2026 to the IMU's Adhering Organizations under the heading "The IMU endorses the Leiden Declaration on Artificial Intelligence and Mathematics". It states that "The IMU Executive Committee and its Committee on Publishing (CoP), chaired by Ilka Agricola, have followed the development of the declaration closely. With its publication, I can now announce that the IMU endorses the Leiden Declaration on Artificial Intelligence and Mathematics."^[3]

Sorger also wrote a longer editorial in IMU News 137 that summarizes the declaration section by section and explains the endorsement. He allows for dissent within the membership: "I do not expect every colleague to agree with every sentence of the declaration. In fact, some of the reactions we have seen already show exactly why the declaration is useful, prompting consideration and discussion of what we want to protect, what we are willing to change, and where we need more clarity." The editorial singles out two risks as especially important, the asymmetry between individual mathematicians and companies, and the prospect that areas of mathematics become fashionable because AI tools happen to work well in them rather than because the community judges them significant, and concludes that "The IMU endorses the Leiden Declaration because it is a timely, serious and balanced contribution to a discussion that is only just beginning." It adds that "Yet endorsement does not mean an end to the debate."^[11]

The declaration's site carries the IMU as its only institutional endorsement, quoted through IMU Vice President Ulrike Tillmann: "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."^[1]

The declaration itself asks for more of this: it closes its threats section by encouraging "professional organizations to endorse this Declaration, and to add provisions according to their own values, priorities, and governance."^[1]

Structure

On the web page the text runs as a preamble with two subsections, on values and on potential threats, then four blocks of recommendations, and ends with the working-group list. It is published both as a web page and as a PDF deposited on Zenodo.^[1][2]

Preamble

The preamble places current AI in a long history of technologies that have changed mathematical practice, and reports a range of reactions among researchers: "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." Its framing claim is one of agency: "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."^[1]

The preamble also states the scope. Although written from the perspective of mathematical research, the authors say much of it applies to the broader mathematical sciences, education, mentoring, publishing, funding, science policy and applied use, and that the declaration is "conceived in solidarity with other research endeavors and creative professions facing similar challenges, both within and beyond academia."^[1]

Values

Five values are listed as the basis for the recommendations:^[1]

1. Proof and scientific integrity. "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."
2. Attribution and responsibility. Results are attributable to specific authors, who take credit for the discovery and assume responsibility for its correctness.
3. 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."
4. Shared standards of evaluation. Work is judged against community standards of depth, difficulty and significance.
5. Understanding and autonomy. Mathematics produces not only results but understanding, clarity and judgment within a community, and the discipline has long drawn strength from autonomously shaping its own research directions and methods.

The section closes by noting that these characteristics are compatible with mathematics as a human practice, and that mathematicians have "a duty to care for other people and our environment."^[1]

Potential threats

The corresponding five threats, which the declaration says fall disproportionately on students and early-career mathematicians, are:^[1]

The section ends by tying these to wider concerns about warfare, mass surveillance, political disruption and environmental damage, and states: "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."^[1]

Recommendations

The declaration gives 23 headed recommendations across three audiences, plus a fourth section addressed to commercial AI developers that is written as prose rather than as headed items. Each heading in the original is followed by a short paragraph of explanation.

Several of the individual recommendations are specific. "Disclose tool use" asks authors to include a "Tool and computational resource disclosure" section in their papers, covering large language models, machine learning systems, proof assistants and other mathematical software. "Retain the responsibility for correctness" states that when automated techniques are used, responsibility for the correctness and adequacy of arguments and results, and for the completeness and accuracy of citations, "remains exclusively with the human authors". "Affirm the humanity of authorship" says credit and responsibility "continue to belong to humans within the mathematical community and should not be given to automated systems", adding that AI "may obscure, but does not replace, the collective human labor behind a result". "Consider carefully which tools to use" suggests weighing whether non-proprietary, energy-efficient or small-scale systems suffice, and asks readers to 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" asks researchers to withdraw from harmful work if necessary and to enter only external partnerships that respect the declaration's values.^[1]

Two of the organizational recommendations bear directly on publishing and on training data. "Protect the rights of authors" asks societies to develop sample licensing agreements, holds that material "should not be used as training data without consent", and says publishing agreements should let authors opt out. "Insist on appropriate publication outlets" demands that results continue to appear in peer-reviewed 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." Others ask for university-based, national or international laboratories for automated mathematics that are "administratively and financially independent from industry", for legal representation for researchers negotiating with industry, and for alignment with the declaration's values to count in funding decisions.^[1]

The recommendations to policymakers are short. "Don't believe the hype" notes "a strong commercial incentive on the part of the technology industry to overstate the capabilities of their products" and asks governments to consult mathematicians rather than relying on press releases or popular reporting. The other three ask for stronger legal protections for authors, "significantly increased public oversight" of the AI industry, and public funding of computational infrastructure at university, national and international levels.^[1]

Section addressed to commercial AI

The final block is addressed to companies rather than to mathematicians, and it opens by conceding the limits of that address: "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 identifies two routes by which mathematics has been drawn into industrial AI: as advertising for system capabilities in public communications, and as training data, both mathematical publications and formal mathematical libraries, "not only for specialized models for mathematics, but for more general-purpose artificial intelligence."^[1]

The section then states the mechanism it thinks explains the interest: "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." It notes that the strategy usually rests on the further assumption that capabilities developed through automated theorem proving will extend to broader general reasoning, a premise also central to how vendors present mathematical reasoning benchmarks.^[1]

It acknowledges that 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", and that many mathematicians did not expect their work to be pulled into systems used for purposes they may find troubling. It calls on collaborations between mathematicians and industry to abide at minimum by the standards the declaration describes for colleagues, and states that "Such collaborations must respect the freedom of conscience of employees or contributors to speak openly about corporate policies and priorities."^[1]

Signatories and endorsements

Signing is open to individuals, not institutions. The site offers two verification paths: an ORCID login, which pre-fills affiliation from the signer's most recent public employment or education record and attaches an ORCID badge to the signature, or a single-use email link valid for 20 minutes, which yields a "verified email" badge for academic domains. Signers must accept the terms of participation and confirm they have read the privacy notice. Organizations, departments and institutions cannot use the form; institutional endorsements are handled separately through the convener and are not counted as signatures. Affiliations shown next to a signature identify the signer and do not imply institutional endorsement, and the site provides a withdrawal route.^[10][12]

Signature counts move, so each figure below carries the moment it was read. The first four rows come from Internet Archive snapshots of the site's own counter; the last is a direct read.

Signers may attach a public comment, and the list shows names, optional affiliations, badges and signing dates. The signatory list appears on the home page below the declaration text, with a search box on a separate page.^[1][4]

Separately from the signature list, the site displays eight curated named endorsements, which the operators say are published only where they have permission to do so. As of 13 September 2026 they were, in the order shown: Peter Scholze (Director, Max Planck Institute for Mathematics), Terence Tao (UCLA), Robbert Dijkgraaf (University of Amsterdam, President-Elect of the International Science Council and former Dutch Minister of Education, Culture and Science), Ilka Agricola (Chair of the IMU Committee on Publishing, Philipps-Universität Marburg), Jeremy Avigad (Carnegie Mellon University), Kevin Buzzard (Imperial College London), Leslie Ann Goldberg (Head of Computer Science, University of Oxford) and Steven Strogatz (Cornell University).^[1]

Tao's endorsement describes the process: "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." Scholze's is a personal statement of practice, saying that he ponders his mathematical ideas without use of AI and generally avoids reading AI-generated text as best he can. Agricola, writing as chair of the IMU publishing committee, warns that language models have 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". Buzzard's runs to two sentences: "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."^[1]

Relation to other codes and declarations

The declaration positions itself as complementing four existing documents, which it links directly: the Uppsala Code of Ethics for Scientists, the San Francisco Declaration on Research Assessment (DORA), the UNESCO Recommendation on Open Science, and the UK Universal Ethical Code for Scientists. It also points to related material from the IMU Committee on Publishing, the Society for Industrial and Applied Mathematics, and the American Mathematical Society. The SIAM item is the AI Task Force report "The Role of Applied Mathematics in a New Era of Artificial Intelligence", published in February 2026.^[1][14]

The companion documents line up with different parts of the declaration's argument. DORA addresses research assessment, which is the subject of the incentives and evaluation threats; the UNESCO Recommendation on Open Science is cited twice more inside the recommendations, alongside the FAIR data principles; and the two ethics codes cover the warfare, surveillance and environmental questions the declaration raises without developing. Nature's editorial grouped the Leiden Manifesto and DORA together as precedents that were "adopted around the world".^[1][9]

Reception

Nature published an editorial on the declaration dated 16 June 2026 (Nature 654, 571) under the headline "Mathematicians are developing rules for AI use, other fields should follow". It stated that "Nature wholeheartedly endorses both the declaration process and its conclusions", noted that the declaration had drawn endorsements from researchers both sceptical of and optimistic about AI, and argued that other disciplines should copy the approach. The same editorial used the unit-distance result OpenAI had announced the previous month as its worked example of the transparency problem, observing that OpenAI had posted the proof publicly and that independent mathematicians had verified it, but that the company had not disclosed which software produced it and, like other AI companies, had not fully disclosed its training data.^[9]

The declaration was presented and discussed at the International Congress of Mathematicians in Philadelphia on 26 July 2026, where Portegies spoke on it as part of an IMU panel on challenges for mathematical research and publishing.^[12][11]

Several mathematical bodies and universities published announcements on the day of release. The London Mathematical Society's summary describes the declaration as developed after the 2025 Lorentz Center workshop "and in consultation with an international group of researchers", lists the identified problems as the reliability of automatically generated results, attribution of results produced with trained proprietary models, and the effect of new tools on publication and peer review, and notes that the document also discusses the role of commercial organisations. The declaration's news page additionally collects announcements from the Academy for the Mathematical Sciences, the Isaac Newton Institute, Oxford, Edinburgh, Eindhoven, Vrije Universiteit Amsterdam, Northwestern, Columbia and Leiden University, and lists press coverage from 2 June 2026 onward in The New York Times, Scientific American, Science, NRC and Le Monde.^[15][12]

OpenAI's response

On 1 August 2026 OpenAI published "Ten advances in mathematics and theoretical computer science", the post that also disclosed the existence of the model later named GPT-6 Astra. Its section "Responsibility to the mathematical community" names the declaration:

The emergence of systems capable of contributing to mathematical research raises questions that cannot be answered by a technology company alone. There are many views as to the role of AI in mathematics, and we have deep respect and understanding for those concerned with its impact, including the signers of the Leiden declaration on AI and Mathematics.

The same paragraph sets out OpenAI's attribution position, which accepts part of what the declaration asks and rejects part of it. OpenAI writes that claiming human authorship for a proof generated entirely by an AI system would misrepresent both the system's contribution and the nature of genuine human intellectual work, that its researchers prepared the manuscripts and formalized the proofs in Lean and take responsibility for their correctness, and that "the mathematical arguments themselves were generated by our system". That is close to the declaration's demand that humans retain responsibility for correctness, and opposite to its recommendation that credit "should not be given to automated systems". The wording is present in the earliest successful Internet Archive capture of the post, taken on 1 August 2026, and unchanged in the capture of 7 September 2026.^[5]

The announcement was made by blog post and preprint rather than through a journal, which is the practice the declaration's "Insist on appropriate publication outlets" recommendation targets. The Next Web, reporting the announcement the same day, summarized the declaration as warning that AI companies are "using published research without consent, bypassing peer review, and threatening the integrity of proof and attribution", said it "specifically cited companies that announce results through press releases rather than peer-reviewed journals", and closed by describing whether the community will accept results announced through a blog post rather than a peer-reviewed journal as "an open question, one the Leiden Declaration was written to answer". The declaration's text does not name individual companies.^[6][1]

The September 2026 Fields Medallists' statement

On 11 September 2026 a second and much shorter document, A Severe Misalignment of AI in Mathematics, was published at mathandai.org with 25 initial signatories, all Fields Medallists. It argues that the goals of AI companies and of the mathematical community are severely misaligned, and that announcing solutions in a rush leaves no time for proper writeups, isolation of new methods or citation of prior work.^[16]

Tao, who is one of the Leiden Declaration's featured endorsers and one of the September statement's 25 initial signatories, drew the comparison himself when he posted the September text on his blog. He wrote that it "grew out of discussions between ourselves over the last week" and that the group invited further signatures "similarly to the Leiden declaration", adding: "It is unfortunate that we did not have the time to have a more consultative process, as with Leiden; but we decided that the urgency of the situation was such that we needed to release a statement sooner rather than later."^[17]

The two therefore differ in kind, on their authors' own account. The Leiden Declaration took, by its own account, eight months of consultation after a week-long workshop, carries an institutional endorsement from the IMU, and is built around named recommendations addressed to four audiences. The September statement came out of about a week of discussion among its signatories, is signed by individuals rather than endorsed by a body, and states a diagnosis and an urgency rather than a list of actions. Both invite open signature, and both name attribution, the pace of announcement, and the loss of human understanding as the core problems.^[1][16][17]

References

1. ^1 ^2 ^3 ^4 ^5 ^6 ^7 ^8 ^9 ^10 ^11 ^12 ^13 ^14 ^15 ^16 ^17 ^18 ^19 ^20 ^21 ^22 ^23 ^24 ^25Leiden Declaration on Artificial Intelligence and Mathematics - leidendeclaration.ai, dated 2 June 2026; full declaration text, working group list, about section and endorsements as read 13 September 2026.
2. ^1 ^2 ^3Leiden Declaration on Artificial Intelligence and Mathematics - Zenodo deposit, DOI 10.5281/zenodo.20302944, issued 2 June 2026, CC BY-NC 4.0; author list, ORCIDs and version metadata read via the DataCite API record for the DOI, 13 September 2026.
3. ^1 ^2 ^3The IMU endorses the Leiden Declaration on Artificial Intelligence and Mathematics - IMU AO Circular Letter 8/2026, Christoph Sorger, International Mathematical Union, 2 June 2026 (PDF).
4. ^1 ^2 ^3Signatories - leidendeclaration.ai, read 13 September 2026.
5. ^1 ^2Ten advances in mathematics and theoretical computer science - OpenAI, 1 August 2026; read via Internet Archive snapshots of 1 August 2026 and 7 September 2026.
6. ^1 ^2OpenAI says its next model, Astra, has solved ten open problems in mathematics - The Next Web (Ana Maria Constantin), 1 August 2026.
7. ^Mechanization and Mathematical Research - Lorentz Center, workshop held 15-19 September 2025.
8. ^Shaping the Future of Mathematics in the Age of AI - Johan Commelin, Mateja Jamnik, Rodrigo Ochigame, Lenny Taelman, Akshay Venkatesh, arXiv:2603.24914, 26 March 2026.
9. ^1 ^2 ^3Mathematicians are developing rules for AI use, other fields should follow - Nature editorial, 16 June 2026, Nature 654, 571 (2026).
10. ^1 ^2About this website - leidendeclaration.ai, read 13 September 2026.
11. ^1 ^2IMU News 137: May 2026 - editorial by Christoph Sorger, Secretary General of the IMU.
12. ^1 ^2 ^3Sign the Declaration and News - leidendeclaration.ai, read 13 September 2026.
13. ^1 ^2 ^3 ^4Internet Archive snapshots of leidendeclaration.ai showing the site's signatory counter: 2 June 2026 12:51 UTC, 2 July 2026 21:42 UTC, 1 August 2026 22:44 UTC, 4 September 2026 10:55 UTC.
14. ^The Role of Applied Mathematics in a New Era of Artificial Intelligence - SIAM AI Task Force Report, Society for Industrial and Applied Mathematics, February 2026, DOI 10.1137/26M1860195.
15. ^Leiden Declaration on Artificial Intelligence and Mathematics - London Mathematical Society, last updated 2 June 2026.
16. ^1 ^2A Severe Misalignment of AI in Mathematics - mathandai.org, read 13 September 2026.
17. ^1 ^2A Severe Misalignment of AI in Mathematics - Terence Tao, What's new, 11 September 2026.