Mathematicians, students of mathematics at all levels, and the general public are currently confronted with almost daily news on mathematical achievements by AI companies and individuals using AI tools in research, teaching, and dissemination. Many initiatives are forming to address these developments, and many of us have strong feelings about them. Without having fully digested the flood of press releases, opinion statements, blog entries, preprints, websites, etc. on the development, I am getting the impression that some aspects I highly care about receive too little attention, and I would therefore like to draw some of your attention to these aspects.
Human-to-human interaction is a priority — and has almost no environmental footprint
When we learned mathematics at university (and before), we learned it from more experienced humans (e.g. instructors, text book authors) and in interaction with fellow students. I don’t know what this meant to you; to me, it meant that somebody was there to guide me to the mathematics that was most interesting and yet within reach for me based on their longterm experience. Which worked because I trusted them. It meant that I got feedback for my work from somebody I could rely on (most of the time, in the case of teaching assistants). It meant I was given time and guidance to develop my own mathematical voice and taste. Also, I wasn’t alone feeling overwhelmed at times, and I learned to handle frustration from and with my peers, friends, and mentors. I had role models for giving good talks and lectures, for writing good papers, and for having productive mathematical discussions. I regularly hear about similar observations from current students and junior researchers.
For me personally, all these aspects have continued to be relevant throughout my academic career, for research, for teaching, and for outreach. I expect this to apply to most if not to all of you as well, and similarly to the undergraduate and graduate students, postdocs, and junior colleagues we mentor. In my view, it also applies to students in schools at all levels and generally to people who care about mathematics.
I am not willing to give up on the next generation sharing this experience nor to accept that we might lose it. I want all of us to be able to become and/or continue to be members of a mathematical community. It makes me cringe to think of first year students learning mostly from AI-written lecture notes or of PhD students learning about a field from AI-written papers. Or of the uniformity of written mathematics if students learn to write mostly from AI output. Or of school teachers having to teach by preparing their classes relying mostly on AI because they have no idea how to do it differently (and the uniformity in the outcome).
In addition, first empirical research on humans and AI seems to indicate that we might emotionally suffer from too much conversation with AI systems, in particular if we use them alone. Many of us might develop feelings of inferiority, taking frustration to levels which stop being conducive for learning and researching. Based on my experiences described above, I expect that space and time for human-to-human interactions between students as well as between students and educated mathematicians, between junior and senior researchers, researchers, practitioners, and teachers, etc. will help us remain aware that humans can understand mathematics in a way AI systems cannot and that the process of understanding and connecting to previous knowledge needs time. This will reduce frustration and thereby enable us to continue being productive. I expect it to also help not to succumb to the illusion of understanding.
I would thus like to encourage and urge you to use the power you have to create time and space for human-to-human interaction in mathematics, in particular in learning and teaching. This could take many different forms: We could decide to have students defend their homework in front of a teaching assistant1 instead of or in addition to having the teaching assistant (or an AI system) look at the written homework. We could offer ” no AI use” or ” ask a human first” classrooms (i.e., a room + a more experienced person) where students can come to work on their homework alone or in small groups or to study for exams, protected from the temptation to immediately resort to asking AI by the sheer presence of others they can ask and who watch them. We can offer more interactive classes, e.g. with hands on activities (more on this in a future article in the Mitteilungen). We could have local writing competitions, panel discussions, … with our students and junior researchers where we discuss when and how using AI is conducive for learning mathematics or for (learning to) doing good mathematical research, allowing for interpersonal and cultural differences, financial situations, environmental concerns, ….
Last but not least, taking action to preserve and increase human-to-human interaction in mathematics learning and research will help us remain sane, pro-active, and genuinely in charge of our field as a community. No matter how things develop in general at the AI front. Moreover, us focusing on and enhancing the human aspects of learning and research will hopefully help preventing political decisions to further cut our funding for teaching (including for teaching assistants, PhD and postdoc positions, and teaching reductions for developing new courses and approaches) and for research. And it will help us in making hiring and funding decisions wisely choosing the people who will design the future of our field with us.
Let’s communicate the benefits of mathematics
Looking at the media coverage on Math & AI, I miss seeing enough mathematical societies and individual mathematicians inviting the ” general public” to understand why we care about mathematics, what mathematics is good for, what mathematicians are good for, and what learning mathematics properly is good for. I hope many of us will participate in human-to-human outreach activities or get involved with ” the media”, making a case for mathematics as a field, for learning mathematics, and for mathematicians as a profession. After all, we will need more, not fewer, mathematically well trained people to develop, use, and oversee AI systems in all aspects of our society. I strongly believe that pursuing mathematics is a central component for developing judgement. And judgement will only become more important in the future.
I look forward to hearing and reading about many interesting ideas, opinions, and initiatives at meetings, in the Mitteilungen2 and in other media.
- An idea that I learned about from colleagues who pursue it at the University of Potsdam ↩︎
- This article also appeared in the quarterly “Mitteilungen” of the German Mathematical Society DMV ↩︎
Received 13 October 2026.
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