This declaration has its roots in the Lorentz Center workshop Mechanization and Mathematical Research (September 2025), organized by Lenny Taelman, Johan Commelin, Rodrigo Ochigame, Akshay Venkatesh, and Mateja Jamnik.
Jim, which field(s) of research do you work in?
I’m an assistant professor in mathematics in Eindhoven. I initially worked on mathematics for data analysis and then moved to artificial intelligence. My research interests are both theoretical and practical: I’m interested in how people learn mathematics, and in designing algorithms that mimic these learning processes; on a more practical side I also develop software to be used in education, to help students write mathematical proofs.
You are one of the facilitators of the Leiden Declaration for AI in Mathematics. What is this declaration and what are its most important points for you?
The declaration is first and foremost a call to action: we require both individuals and organizations to work towards responsible use of AI within mathematics that is aligned with the principles of Open Science. One important facet of the declaration is being transparent about methodology: if researchers hide their use of AI, it becomes impossible for other scientists to properly use their results, as we need to be able to check what steps have been taken to get to them and reproduce these. There is already an enormous amount of pressure on journals because it has become so easy to produce something that looks like sound mathematics but lacks the commitment that human researchers do have to double-check that their calculations are correct.
There are lots of other things that could go wrong if we don’t coordiante AI use. One example that goes far beyond mathematics is a growing dependency on certain corporations that develop these AI-systems: it is not always clear how the data we feed them are processed and where they end up—in a worst case scenario, your math is used for mass surveillance or other military purposes you never signed up for. Another aspect of this is that using these programs costs money: not everyone has the means to easily access them and those that do end up making mathematics as a field more dependent on the whims of corporations with their own business models. Mathematics has collaborated with industry for a long time, so the problem of how to relate to these corporations responsibly is not new; but the ubiquity of AI programs makes this problem much more urgent for a much larger group of mathematicians. That is one reason why our declaration was initiated as a community-driven document: these problems concern us all.
So, these AI programs can produce what looks like sound mathematics, with all the problems that entails, but are there things it cannot do that humans can?
These programs are very good at providing solutions to very clearly delineated mathematical problems. They have read much more than any human mathematician can be expected to do, and shine in applying techniques from one setting to a problem in a completely different setting. What humans remain much better at is developing theories and new languages to express ourselves. Mathematicians also decide on where to move as a field; which lines of research are worth pursuing and which are not—AI can solve certain problems, but not all of those are interesting. That decision-making process is something we have to do ourselves and want to keep out of tech companies’ hands.
You mentioned the Declaration is a community-driven document. Can you tell us a bit about the process that led to its current iteration?
Much like how opinions on which lines of research to pursue can differ vastly among mathematicians, everyone seems to have a different opinion on the inclusion of AI in mathematical research: getting the Declaration to its current form was thus also a coordinating effort. The idea for a community document on AI sprung from a conversation in a bar in Cambridge among Ursula Martin, Rodrigo Ochigame and Michael Harris, who realized they would all participate in the Mechanization and Mathematical Research workshop at the Lorentz Center—I was not involved yet at that point. During the workshop, we discussed writing the document in several breakout sessions and after the week I was asked to facilitate the writing process. A large part of the workshop participants was involved in developing the document, and it was very helpful that the group included not only mathematicians, but also philosophers and historians of science, for example. The diversity in perspectives also made it very hard to make clear, unified statements as a field. There were times when I thought: “maybe the difference in opinions is just too big, perhaps we should stick to a descriptive document to make people aware of the ins and outs of AI use in mathematics, rather than make recommendations”. Yet we did feel an acute sense of urgency that we had to make a statement as a field, and in the end, we managed to find a lot of common ground. We went through several versions of the document and got extensive feedback from the mathematics community—I’m very glad to say we got there!
The Declaration explicitly highlights students and early-career researchers in mathematics; what was the reason for this?
I talked before about how it is up to us humans to decide where we want mathematics to go as a field, and students are the future of that field. If you just started your career in mathematics and work on certain problems that AI can suddenly ‘solve’, that can be a big blow to your confidence: in the worst-case scenario, you decide not to continue in mathematics research altogether. This is yet another reason why it’s important to make sure that we know what we can and cannot leave up to AI, and to stick to the core values of our field in teaching the next generation of mathematicians.
The logo of the Declaration is a tulip; what sparked that choice?
At the most basic level, tulips represent the fact that this declaration originated from a conference in the Netherlands. We also at one point expressed our hopes that the document might be done before the tulips would bloom—we did not make that deadline. But this suggestion from one of the coauthors did help the process, just like the pictures of tulips that some people signed off their emails with. Because of that, for me the tulips became symbolic of the bottom-up decision making and varied effort that characterizes the Declaration: we took our time to bring together a great variety of perspectives on AI from all corners of mathematics to formulate a call to action that all of us could rally behind. I really hope that it resonates both in and beyond mathematics as a wake-up call not only to individual researchers, but to academic organizations and government bodies as well.
Jim Portegies
Interview written and edited by Glyn Muitjens
