Protecting the Values of Mathematics as It Adapts to AI

Mathematicians are watching the rapid development of AI technologies, and the announcement of new milestones reached by their applications to theoretical mathematics, with fascination as well as foreboding. Optimists and pessimists alike worry that claims about these developments, amplified by industry PR and repeated uncritically by mass media and some scientific publications, promote a distorted image of the purposes and priorities of mathematics, whose primary goal is to expand human understanding.

In September 2025, the Lorentz Center at Leiden University in the Netherlands hosted a conference titled Mechanization and Mathematical Research. The 60 participants from 10 countries, mathematicians and computer scientists as well as philosophers and social scientists, spent a week in Leiden taking stock of these developments. At the end of the week, 16 participants, myself among them, began to work on drafting a Declaration of principles for the future relations between the mathematical community and the new technologies. Eight months later, after extensive consultation with colleagues, the Leiden Declaration on Artificial Intelligence and Mathematics was released on June 2. That same day, articles about the Declaration were published in the New York Times, Scientific American, and Science, and it has since been covered by news media around the world. 

In addition to proposing guidelines for the appropriate use of the new technologies, the Declaration concisely reaffirms some of the discipline’s values that are at special risk of being overlooked in the maelstrom of money and activity around AI, and lists specific threats to these. The body of the Declaration is devoted to a series of recommendations, addressed to individual mathematicians, to mathematical societies, to policymakers, and to the industry, all aimed at preserving the autonomy and the integrity of the discipline as it adapts.

By any measure the Declaration has been a success. As of today, it has been signed by more than 2,100 mathematicians from around the world, with more on the way; it has been endorsed by such prominent mathematicians as Peter Scholze and Terence Tao, as well as by the International Mathematical Union, the only organization that represents mathematicians from all countries. Mathematicians have rallied in a way that is unprecedented behind the values expressed in the Declaration. Now the work begins to ensure these principles are respected.

The AI industry has been committing extraordinary resources to the idea that mechanizing the process of establishing theorems, on the basis of rigorous rules of deduction, is key to a more general capability for reasoning. Theoretical mathematics has come to be regarded as an essential step toward the industry’s goal of Artificial General Intelligence. We want to affirm that our field flourishes independently of the imperatives of the commercial AI market, and supports broader values of honesty, transparency, access, and furthering human insight.

Michael Harris has just published “Knowledge Collapse,” an essay that explores the implications of AI for mathematics, in Boston Review.

This column is editorially independent of Columbia News.