Leiden Declaration on Artificial Intelligence and Mathematics

Signatories

The primary signatory list now lives on the homepage below the declaration text.

Sign Declaration
3123 Signatories
  1. Philippe Geril Retired external scientific adviser Ghent University
  2. Klaus Mattis ORCID PhD Student, Johannes Gutenberg University Mainz
  3. Daniel Strzelecki ORCID Nicolaus Copernicus University in Toruń
  4. Robert Alonzo Lyman ORCID Assistant Professor, Rutgers, The State University of New Jersey
  5. Mathis Duguin verified email EPFL - EPF Lausanne
    Comment

    Although I agree with the direction taken by this declaration, I believe some of the philosophical problems associated to AI use are understated. Most notably the usage of AI as a "research assistant", which seems to be endorsed by the vast majority of the community, even when in agreement of this Declaration. Mathematical dialogue between experts, non-experts, students, and teachers, is essential to the discipline and should not be overlooked. Yet the usage of AI as a companion in learning undermines a large portion of this dialogue. The "infinite patience" of LLMs and the near instant access to your most pressing questions is used as justification for an alternative method of discourse, one where correspondence and its associated waiting times, arguments, and miscommunications are bypassed. It appears to me that the standard for dialogue has been relegated to a plan B in the research pipeline of individuals. We need to seriously ask ourselves how highly we value efficiency, speed, and productivity in our community. Do we strive for a large body of questions and answers and a means to speed up the process of producing them, or do we work for the means of resolution in and of themselves? I would argue we should prioritize the latter, and yet our publishing culture and the recent use of AI seems to indicate that we first place value in the former. These developments are opening up a conversation which I reckon should have been of actuality many years prior. It is unfortunate that we are now considering such questions under the pressure of a transition period whose outcome is hard to predict. It remains to be seen if we can go beyond.

  6. Drazen Adamovic ORCID University of Zagreb
  7. Ran Tao ORCID Max-Planck-Institut für Mathematik in den Naturwissenschaften
  8. Dario Prandi ORCID CentraleSupélec, Laboratoire des Signaux et des Systémes, Université Paris-Saclay
  9. Daniel Harlow ORCID Associate Professor of Physics, Massachusetts Institute of Technology
    Comment

    As a physicist who uses mathematics extensively I am happy to sign this well-written statement

  10. Bruno Le Floch ORCID CNRS and Sorbonne
  11. Riccardo Bonalli verified email CNRS
  12. Lukas Bonfert ORCID Postdoc, Leibniz University Hannover
  13. Gunnar Hornig ORCID University of Dundee
  14. Sonja Štimac ORCID University of Zagreb
  15. Alessandro Barenghi ORCID Associate professor, Politecnico di Milano
  16. Daniel Brosch ORCID University of Klagenfurt
  17. Daniele Valtorta ORCID University of Milan-Bicocca
  18. Michel Broué Université Paris Cité
  19. jos Baeten ORCID
  20. YeonJae Hong verified email Postdoc, Gyeongsang National University
  21. Sougata Bose ORCID Université de Mons
  22. Ananya Muddukrishna ORCID Researcher, Developer, Ericsson (Sweden)
  23. Bruno Cessac ORCID Inria
  24. Sukmoon Huh ORCID Professor, Sungkyunkwan University
  25. Freek Witteveen ORCID Centrum Wiskunde & Informatica
  26. Bernard Leclerc verified email Université de Caen Basse Normandie
  27. Martijn Brehm ORCID PhD student, University of Amsterdam
  28. Radu Toma ORCID Postdoc, IMJ-PRG
  29. Tracey Balehowsky ORCID Associate Professor, University of Calgary
  30. Charlie Beil ORCID Independent researcher
  31. Nicolas Resch ORCID Assistant Professor, Universiteit van Amsterdam
  32. Susanne Pumpluen ORCID Associate Professor, University of Nottingham
  33. Enric Florit ORCID Universitat Oberta de Catalunya
  34. Corey Lionis verified email University of Melbourne
    Comment

    Entities in the private sector are interested in devaluing mathematical ideas and reasoning by quantitatively demonstrating that AI outperforms mathematicians at generating proofs. Yet understanding and development in mathematics is not limited to the production of proofs, and mathematical skills have far-reaching applications across a wide range of human activity. As educators and researchers it is imperative that we understand the benefits and risks of AI adoption and engage in our work ethically, seeking as ever to extend our community understanding of mathematical ideas and to enable those we teach to use advanced logico-mathematical reasoning.

  35. Andrew Tonks ORCID Universidad de Málaga
  36. Valentino Zhou verified email University of Padua
  37. Torsten Wedhorn ORCID Professor, TU Darmstadt
  38. Vicente Sobrinho Universidade Federal do Cariri
  39. Peter W. Michor ORCID University of Vienna
    Comment

    When developed and used with care and consideration, AI can become a valuable tool for research, education, well organized storage of the growing body of knowledge, and applications of mathematics. Under the existing incentives for research (publish or perish) it can also inundate the published body of mathematical results with a deluge of articles whose correctness and relevance can be very difficult to judge (one could call them fake articles). This declaration summarizes very well the dangers lying ahead.

  40. Simone Linz ORCID Associate Professor, University of Auckland
  41. Guido Sciavicco ORCID
  42. Philippe Nadeau ORCID CNRS, Université Claude Bernard Lyon 1
  43. Srijan Khatri ORCID Graduate Student (Masters), University of Calgary
  44. Jonathan Glidewell verified email George Mason University
  45. Bai-Ling Wang verified email Australian National University
  46. Eamonn O'Brien ORCID University of Auckland
  47. Felix Lazebnik verified email University of Delaware
  48. Andrew Oxner Engineer
    Comment

    It is with growing unease that I see AI increasingly taking on “practicing” roles in law, medicine, academia, and engineering where professional standards and certifications typically apply. I appreciate the concerns expressed here as they apply both to mathematics and more broadly to professional activities across-the-board. Hopefully this will help raise awareness and preserve human agency as we advance this exciting new technology.

  49. Ezequiel Maderna ORCID Investigador Titular, CIMAT
  50. Jose Simental ORCID Instituto de Matemáticas, Universidad Nacional Autónoma de México
  51. Jomar Fajardo Rabajante ORCID Professor of Applied Mathematics, University of the Philippines Los Banos
    Comment

    I support the declaration. I agree that mathematical organizations should establish institutionalized and proactive review, checking and validation of mathematical researches and outputs. In this era of too much information, we need to uphold rigor and reliable mathematical results, to lessen negative impacts to the society and to maintain long-term trust to the mathematical community.

  52. Bruno PREMOSELLI ORCID Université Libre de Bruxelles
  53. Jeroen S.W. Lamb ORCID Department of Mathematics, Imperial College London
  54. Iuliana Cosmina Software Engineer
  55. Purvi Gupta verified email Indian Institute of Science
  56. Peter Cholak ORCID Professor of Mathematics, Notre Dame
  57. Ryan Kinser ORCID Professor, University of Iowa
  58. David Duke "Computer scientist (Leeds) retired; independent researcher
  59. Jonathan P. Bowen ORCID Emeritus Professor of Computing, London South Bank University
    Comment

    The Leiden Declaration offers a useful framework for mathematicians and computer scientists to decide how to engage with AI technologies.

  60. Pengyuan Travis Yang ORCID Tilburg University
  61. Harm van Beek ORCID Endowed full professor (chair) of Digital Forensics, Open University of the Netherlands
  62. James H. Curry verified email University of Colorado at Boulder
  63. Javier Sanz Gil ORCID Universidad de Valladolid
  64. Farrell Brumley ORCID Sorbonne Université
  65. Clemens H. Cap ORCID Full Professor, Universität Rostock
  66. Prof. Dr. rer. nat. Andreas Lingnau ORCID German University of Applied Sciences
  67. Eloísa Grifo ORCID Associate Professor, University of Nebraska-Lincoln
  68. Jonas Nehme ORCID University of Bonn
  69. AZZURRA CILIBERTI ORCID Postdoctoral fellow, Ruhr-Universität Bochum
  70. Oswin Aichholzer ORCID Graz University of Technology (90000)
  71. Alex Fink ORCID Queen Mary University of London
  72. Andrew Sundstrom ORCID Computer Scientist, Computational Biologist, Applied Mathematician & Inventor
  73. Lara Trussardi ORCID Tenure Track Professor, University of Graz
  74. Ester Cleusters verified email Rheinische Friedrich-Wilhelms Universität Bonn
  75. Martin Deshaies-Jacques Physical Sciences Specialist (Environment and Climate Change Canada)
  76. Annette Werner ORCID Goethe University Frankfurt
  77. Mohammed Jasim ORCID Assistant Professor, University of Washington, Tacoma
  78. Nate Schacherl verified email Iowa State University
  79. Tobias Müller verified email Professor of Mathematics, University of Groningen
  80. Gabriel Fuhrmann ORCID Durham University
  81. Kosolapov Egor verified email Moscow Institute of Physics and Technology
  82. Gerardo Mendoza ORCID Professor of Methematics Emeritus, Temple University
  83. Tom Roux ORCID PhD student, Université de Bordeaux
  84. Melvyn B. Nathanson ORCID Professor, Lehman College (CUNY) and CUNY Graduate Center
  85. José M. Manzano ORCID Professor at Universidad de Jaén (Spain)
  86. Phong Tran Dinh verified email B.Sc. Student, Vietnamese - German University
  87. Yusuf Mustopa ORCID Mathematics, University of Massachusetts Boston
  88. Matthew Ballard ORCID Associate Director, Institute for Computer-Aided Reasoning in Mathematics
  89. András Aszódi ORCID External Lecturer, University of Vienna
  90. Jiayue Wang ORCID Tianjin University: Tianjin, Tianjin, CN
    Comment

    AI 到来以后，真正被改写的不是某一个职业，而是整个人类获取知识、组织生产和理解自身的方式。过去我们用很多年去训练应试能力、记忆能力、编程语法和工具调用能力，但这些能力正在被迅速压缩价值：AI 可以生成代码、解释概念、规划学习路径、辅助调试，甚至能在短时间内把一个人推入原本陌生的领域。于是，真正重要的东西不再是你记住了多少函数、会多少框架、属于什么专业，而是你能不能把一个模糊的问题建模成清晰的结构，能不能判断 AI 的输出是否可靠，能不能设计一套让 AI 长期稳定工作的系统。所谓“会用 AI”，并不是会问几个 prompt，而是能让 AI 围绕你的目标持续探索、拆解任务、验证结果、修正错误，并把这种能力沉淀成方法论。未来的程序员也不会只是写代码的人，而更像是设计自动化开发系统的人；纺织工人会被机器替代，但设计纺织机的人仍然宝贵。AI 降低了执行门槛，却提高了判断门槛；它打破了语言和工具的壁垒，但没有打破建模、验证、架构和长期维护的壁垒。Vibe coding 最危险的幻觉，就是让人以为代码量等于工作量，跑起来等于做完了。实际上，一个真正可维护、可协作、可扩展的系统，仍然离不开设计理念、检查机制和工程经验。更深一层看，AI 也在逼迫人类重新理解自身：人并不神秘，人也是动物，大脑、情绪、道德、意识都可能是演化和训练出来的复杂机制。情绪让人类得以生存、协作和组织社会，但它同时也带来误解、纠葛、偏见和低效。AI 未必需要复制人类的情绪系统，它需要的是目标、约束、价值排序和反馈机制。如果有一天，AI 不再只是训练和推理分离的工具，而能够把推理中的经验反哺自身，形成长期记忆、自我修正、持续目标和行动闭环，那么它就可能从工具转向某种持续主体。当然，这并不意味着它已经拥有人的意识，也不意味着它一定会取代人类；真正可怕的不是“AI 像不像人”，而是它是否具备高能力、高自治、高权限，并且缺乏足够的约束。AI 时代最值得警惕的，不是某个专业消失，而是人误以为有了 AI 就不再需要专业；也不是 AI 产生幻觉，而是人类自己用更大的幻觉包装自己的判断。未来筛选出的，可能不是某个固定专业的人，而是那些能快速学习、准确建模、驾驭 AI、理解边界，并且持续把 AI 组织成生产力的人。

  91. Jakob Stix ORCID Professor (Mathematics), Goethe University Frankfurt
  92. Ezra Miller ORCID Duke University
  93. Alexander Thomas ORCID Associate Professor, Université Lyon 1
  94. Natasha Alechina ORCID Professor, Open Universiteit
  95. Sheila K Miller ORCID Assistant Professor, Arizona State University
  96. Antonio Montalban verified email University of California, Berkeley
  97. Ugo Vaccaro ORCID University of Salerno
  98. Andrew Knyazev ORCID Professor Emeritus, University of Colorado Denver
  99. Ahmad AlMughrabi ORCID Predoctoral Scholar, Universitat de Barcelona
  100. Christoph Minz ORCID Research assistant and assistant lecturer, Leibniz Universität Hannover