Mathematicians are developing rules for AI use — other fields should followDownload PDF EDITORIAL16 June 2026The mathematics community is right to call for transparency, integrity and fairness to be protected when AI tools are used. Researchers in other disciplines could learn from this approach.You have full access to this article via your institution.Download PDF The city of Leiden in the Netherlands is gaining a reputation for hosting meetings on integrity in science.Credit: GettyA little more than a decade ago, after a 2014 conference at Leiden University in the Netherlands, researchers published the Leiden Manifesto in Nature. It called for the responsible use of metrics in research and included a set of ten principles to help to ensure rigour and fairness in the evaluation of research1. Along with the San Francisco Declaration on Research Assessment (DORA), the Leiden principles have been adopted around the world.How AI is reshaping discovery in maths and physicsThe principles came about in response to a suite of metrics data and innovative computational tools in universities and science that required guardrails for their use. Last September, the city of Leiden and its university reprised their part as a meeting point for scholars concerned about new technologies and the integrity of science — this time, about the role of artificial intelligence in mathematics.The resulting Leiden Declaration on Artificial Intelligence and Mathematics, published earlier this month2, shares some of the concerns of its namesake. It recognizes the power and potential of a transformative technology while urging researchers and institutions to ensure that human judgement, transparency and fairness are protected — principles that are foundational to science and must remain so. The declaration has been gaining endorsements from researchers across the discipline, which includes those who are deeply sceptical of AI and those who are much more optimistic. Nature wholeheartedly endorses both the declaration process and its conclusions.The Leiden declaration and the preceding workshop brought together researchers from maths, computer science, philosophy and history. AI is transforming learning and research in the field, as a group of London-based mathematicians wrote in a Nature Comment last week3. Applications range from automating the checking and verification of mathematical proofs to helping to solve — or even autonomously solving — open problems in particular areas of maths. Only last month, an 80-year-old challenge in geometry, known as the unit-distance problem, was solved by mathematicians at the US technology firm OpenAI using only a single prompt to a chatbot.Why we have nothing to fear from the decolonization of mathematicsIn the words of Fields medallist Terence Tao at the University of California, Los Angeles, AI is rapidly changing mathematicians’ job descriptions. But it is arguably doing more than that. As AI and commercial AI software become integrated into maths research, they “will change the kinds of problems that are pursued and the forms of proof that are valued”, according to a report from the workshop4. The Leiden declaration warns of the risks this poses to the autonomy of the field. Indeed, evidence is starting to emerge that, across science, the use of AI correlates with a narrower breadth of research topics5. As the declaration states, this will disadvantage both researchers who lack access to the technology and those who do not wish to use proprietary AI tools.The Leiden declaration holds that mathematical results should continue to be published in peer-reviewed venues subject to the principles of open science, and that “no proprietary knowledge or equipment should be required to understand them”. Moreover, any material used as training data should have the required attributions and should not be used without consent.AI cracks 80-year-old mathematics challenge — researchers are astonishedThose recommendations reflect real concerns raised by the breakneck pace of developments, as highlighted in the workshop. To take the example of the unit-distance problem, OpenAI researchers have posted the proof on the publicly accessible company website (see go.nature.com/4epjtkd) and the findings have been verified by a group of mathematicians who are independent of the firm. But OpenAI has so far not disclosed the name or details of the software used to solve the conjecture, which was first proposed by Hungarian mathematician Paul Erdős (1913–1996). Furthermore, and despite several requests, OpenAI, in common with other tech companies, has not fully disclosed which data sets its models are trained on.The maths knowledge that has fed AI models has come from all parts of the world, with people and institutions from different regions contributing at various points in history. As the mathematician and historian Dirk Jan Struik — a Leiden alumnus — wrote in his A Concise History of Mathematics6, first published in 1948: “Mathematics is a vast adventure in ideas; its history reflects some of the noblest thoughts of countless generations.”‘The job description is changing’: mathematician Terence Tao on the rise of AIThe same can be said for AI. The ability of machine-learning tools to perform accurately rests on centuries of knowledge that has been catalogued and codified, verified and attributed. The AI research community needs this diversity and integrity in maths to be retained and strengthened. It means that transparency is non-negotiable.The working group behind the Leiden declaration and the mathematics community have initiated an important conversation about AI in the discipline. Now it’s time for the discussion to become wider and stretch to other fields.Nature 654, 571 (2026)doi: https://doi.org/10.1038/d41586-026-01881-2ReferencesHicks, D., Wouters, P., Waltman, L., de Rijcke, S. & Rafols, I. Nature 520, 429–431 (2015).Article Google Scholar Alper, J. et al. Preprint at Zenodo https://doi.org/10.5281/zenodo.20302944 (2026).Burtsev, M., He, Y.-H., Sobko, E., Bhattacharya, A. & Graepel, T. Nature 654, 324–326 (2026).Article PubMed Google Scholar Commelin, J., Jamnik, M., Ochigame, R., Taelman, L. & Venkatesh, A. Preprint at arXiv https://doi.org/10.48550/arXiv.2603.24914 (2026).Hao, Q., Xu, F., Li, Y. & Evans, J. Nature 649, 1237–1243 (2026).Article PubMed Google Scholar Rowe, D. E. Hist. Math. 21, 245–273 (1994).Article PubMed Google Scholar Download references How AI is reshaping discovery in maths and physics AI cracks 80-year-old mathematics challenge — researchers are astonished ‘The job description is changing’: mathematician Terence Tao on the rise of AI The Leiden Manifesto for research metrics Why we have nothing to fear from the decolonization of mathematicsSubjectsMachine learningMathematics and computingLatest on:Machine learningMathematics and computingJobs Associate or Senior Editor (Nature Geoscience – Biogeochemistry)Job Title: Associate or Senior Editor (Nature Geoscience - Biogeochemistry) Organisation: Nature Portfolio Location: Shanghai, Beijing, Milan and P...Shanghai, Beijing, Milan and PuneSpringer Nature LtdAssociate or Senior Editor (Nature Geoscience - Solid Earth)Job Title: Associate or Senior Editor (Nature Geoscience - Solid Earth) Organisation: Nature Portfolio Location: Shanghai, Beijing, Milan and Pune ...Shanghai, Beijing, Milan and PuneSpringer Nature LtdAssociate or Senior Editor, Nature Reviews PhysicsJob Title: Associate or Senior Editor, Nature Reviews Physics Location: Shanghai, Beijing or Madrid – Hybrid working model Applications Deadline: 8...Shanghai, Beijing or Madrid – Hybrid working modelSpringer Nature LtdPostdoctoral Research Fellow in Semiconductor Devices at NIMSNIMS invites applications for a Postdoctoral Research Fellow in Semiconductor Devices (approx. 4M-6M JPY per annum, at Tsukuba, Japan).Tsukuba, Japan (JP)National Institute for Materials Science (NIMS)Permanent Researcher in Next-Generation Semiconductor Devices at NIMSNIMS invites applications for a Permanent Researcher in Next-Generation Semiconductor Devices (approx. 6M-10M JPY per annum, at Tsukuba, Japan).Tsukuba, Japan (JP)National Institute for Materials Science (NIMS)