School of Social and Political Science

Content

As the rise of artificial intelligence forces mathematicians to rethink what makes their field reliable and valuable, an international group of researchers has warned that AI is putting fundamental values of the discipline under threat. 

The group of mathematicians from 15 international universities has created the new Leiden Declaration on Artificial Intelligence and Mathematics, a call to protect the core values of mathematics in the age of AI.

AI’s challenges for mathematics 

The declaration is a response to questions including: 

• What happens if a mathematical proof is no longer the work of a human, but of a proprietary AI model that academic researchers cannot access?  
• Who is responsible for errors, and who gets credit if it is correct?  
• How can we tell whether an AI-generated proof is truly new, or simply a clever reformulation of existing work without proper attribution? 

These are no longer hypothetical questions, but current dilemmas mathematicians worldwide are grappling with.  

Dr Michael Barany, Senior Lecturer in the History of Science at the University of Edinburgh, is one of the authors of the declaration. Dr Barany works in Science, Technology and Innovation Studies at the School of Social and Political Science.  

A call for action 

The declaration does not ask for AI to be banned, but instead calls for action to ensure the continued flourishing of mathematics. AI is being used to write papers, generate proofs, and assist in peer review. According to the authors, the challenge is to ensure that the technology benefits rather than irreversibly harms the discipline. 

The declaration is officially supported by the International Mathematical Union (IMU)’s Committee on Publishing.  

Its chair, Ilka Agricola, said: “AI is fundamentally transforming the way we do mathematics, and it is doing so at incredible speed. It offers fantastic possibilities when used honestly and competently as a ‘research assistant’. But this seems to be only a small part of what is going on: the by far larger part is a total mess where science itself is under attack.” 

Peter Scholze, director of the Max Planck Institute for Mathematics and a 2018 recipient of the Fields Medal, the discipline’s highest honour, said “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.” 

The declaration outlines: 

• The threats to mathematics 
• What individual mathematicians can do 
• What organisations should do 
• What is needed from governments 
• Requests for commercial use of AI to abide by the same standards expected of academic research 
• Emphasis that similar issues arise in other academic fields and creative industries 
• A clear message that AI offers major opportunities, but without clear choices and shared responsibility, it places the foundations of science under severe pressure. According to the authors, we need to act now. 

Dr Barany said: "One lesson of my historical research is that the conversations mathematicians have about their values and institutions can have as big an impact on their field as conversations about theories and concepts. I was proud to represent Edinburgh's distinguished tradition of social studies of mathematical sciences in the important conversations reflected in the Leiden Declaration." 

The original and full version of this article was published by Leiden University.