翻訳待ち：A Call for Action: The "Leiden Declaration on AI and Math"

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PDFLINK A Call for Action: The “Leiden Declaration on Artificial Intelligence and Mathematics” Siobhan Roberts Introduction The idea for the “Leiden Declaration on Artificial Intelligence and Mathematics”—published on June 2, 2026—first took shape one year before over pints at a pub near Cambridge University. It was during a workshop at the Isaac Newton Institute for Mathematical Sciences on “Big Proof,” addressing complications of bringing automated proof technology into mainstream math research. Dame Ursula Martin, a mathematician and computer scientist at Oxford, was joined at the pub by mathematician Michael Harris of Columbia University, and Rodrigo Ochigame, an historian and anthropologist of computing and artificial intelligence at Leiden University. All three were planning on attending a related meeting that September—a workshop on “Mechanization and Mathematical Research” at Leiden University (Ochigame was an organizer). Ultimately, their pub talk landed on: ‘Hey, why don’t we think of something useful that can come out of the Leiden meeting?’ Harris, author of the Substack newsletter “Silicon Reckoner,” arrived in Leiden with a four-point plan for a declaration. He pitched it to the 60 participants, which included mostly mathematicians, but also computer scientists, engineers, historians, philosophers, social scientists, and policymakers. Part of the workshop program was organized around breakout groups; the two breakout sessions on the declaration were oversubscribed. Subsequently, a working group of 16 authors, in consultation with more than 30 mathematicians independent of the workshop, drafted and redrafted the statement in a process that was at times contentious—the writing and rewriting went on for eight months. Jim Portegies, an applied mathematician at the Eindhoven University of Technology, served as convenor, untangling competing opinions and building consensus. Figure 1. Rodrigo Ochigame and Mateja Jamnik (front row, center), two coauthors of the declaration, and other mathematicians in September 2025 at a workshop at Leiden University, where the “Leiden Declaration on Artificial Intelligence and Mathematics” initially took shape. “Artificial intelligence places core values of the mathematical community under threat,” Portegies said in an interview. “Admittedly, the technological developments could advance mathematics—I hope even to the extent that it benefits much more than the field itself. But if we don’t act and organize ourselves, there’s a large risk that AI will do serious harm to the discipline and beyond. This is why the declaration calls for action, with recommendations for individual mathematicians, mathematical organizations and governments and ends with a request to commercial AI to respect the values outlined in the declaration.” Bryna Kra, a mathematician at Northwestern University and a former president of the American Mathematical Society, was also among the working-group authors. “AI is already transforming our profession: accelerating the pace of research, changing the meaning of authorship, altering the ways students learn, and widening gaps in access to powerful tools,” Kra said in an interview. “Mathematicians must be part of shaping these changes rather than merely reacting to them. This declaration is a call for the mathematics community to engage and develop shared standards and guidelines.” Upon its publication, the Leiden Declaration was endorsed by the International Mathematical Union. It is open for signing and endorsement by individuals and organizations. Two Fields Medalists—with divergent views on AI—were early supporters and endorsers: Peter Scholze, a mathematician at the University of Bonn and 2018 Fields Medal winner commented: “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.” Terence Tao, mathematician at the University of California, Los Angeles, and 2006 Fields Medal winner, commented: “AI is a powerful technology that shows significant promise for being transformatively useful in mathematics in particular (due in large part to our ability to filter out AI’s mistakes to an extent that is not possible in other disciplines), and yet it also carries great risks and harms if used irresponsibly, or if that usage is dictated by external entities not inherently aligned with scientific goals. The apparent contradiction between these two statements requires a lot of nuance to resolve, and I think the declaration has landed in an excellent place that incorporates both.” Figure 2. Robbert Dijkgraaf (moderator), Thomas Hubert, Stephanie Dick, and Akshay Venkatesh at a public symposium held during the September 2025 Leiden workshop. Following is the full text of the declaration, which is also available at https://leidendeclaration.ai. Leiden Declaration on Artificial Intelligence and Mathematics This declaration calls for action to address the challenges posed by the use of artificial intelligence within mathematics research. (June 2026) 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, the San Francisco Declaration on Research Assessment, the UNESCO Recommendation on Open Science, and the UK Universal Ethical Code for Scientists. The International Mathematical Union Committee on Publishing, the Society for Industrial and Applied Mathematics, and the American Mathematical Society 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 g [truncated for AI cost control]