Talking about AI & Math

How can we have a productive discussion about AI and mathematics, a topic that’s become so polarizing and that carries existential consequences for our profession? Sounds cliché, I know, but it’s something we need to figure out. At a workshop last week, I ran such a discussion and have since received multiple requests for the questions, so I’m sharing them here in the hope that others will find the format useful.

The workshop, “Homology and homotopy in the world of graphs,” was organized by Luigi Caputi and Henri Riihimäki at the EPFL Bernoulli Center. My only complaint was that the talks and informal discussions were so engaging that I didn’t have a chance to go hiking, the main reason to visit Switzerland in the first place. I gave a talk, “Introduction to discrete homotopy theory,” reporting on the work of my fantastic current and former students: Daniel Carranza, Sterling Ebel, Jacob Ender, and Nathan Kershaw. Daniel and Nathan also spoke at the workshop.

I devoted the final slide of my talk to a topic close to my heart: artificial intelligence. My question for the audience was how we, as an area, should respond to AI, and what senior people can do to create jobs and opportunities for the next generation of discrete homotopy theorists. What might change about the work we do, and how should we prepare? The slide generated enough discussion that the organizers asked me to lead an evening conversation on AI & Math later in the week. I’m grateful to them for making space for it.

The mathematics community is failing to have this discussion in a reasonable format. Established events and publications continue to approach top mathematicians for their views on the subject, but mathematical distinction alone, measured, say, in the number of Annals papers, does not establish expertise about AI. For comparison, in his March 1996 essay for Time, Garry Kasparov described Deep Blue’s intelligence as weird, inefficient, and inflexible, concluding that he had a few years left. He lost the rematch the following year. In February 1995, Clifford Stoll wrote a piece for Newsweek, “The Internet? Bah!”, dismissing the prospects of online shopping and buying books and newspapers over the Internet. It’s hard to shake off the feeling that the mathematical community looks to these examples now and says “hold my beer.”

In my experience, the most insightful and thoughtful discussions on this topic occur on X (formerly Twitter). Crazy, I know, but that’s where I keep finding experts familiar both with mathematics and artificial intelligence. As someone critical of social media, I find this state of affairs frustrating, which is why I’m happy to help create spaces for such discussions. Young people in particular want to talk about AI and mathematics, and it is our responsibility to provide them with an opportunity to do so.

In preparing the discussion, I wanted to hear from as much of the room as possible. Simply asking “So what do y’all think about AI?” can leave two or three people doing most of the talking and sucking the oxygen out of the room. It can also be easy to mistake agreement within one’s own circle for a wider consensus. My goal was to give everyone a chance to contribute and showcase the range of opinions in the room.

I ran four anonymous polls consisting of three or four questions each. Participants scanned a QR code on the screen and answered on their phones. After each poll, I displayed the results and invited comments. The sequence moved from personal experience to expectations, acceptable uses, and broader questions about the future. The questions were deliberately broad, leaving room for participants to interpret terms differently; those differences were part of what I hoped the discussion would bring out. The results are snapshots of the views of a small, self-selected workshop audience, rather than estimates for the mathematical community as a whole.

The first poll asked about participants’ use of large language models:

I asked whether anyone was surprised, inviting comments both from those who were and from those who were not. Broadly, they agreed with my expectations. This was a room full of grad students and postdocs, mostly European. I’d be curious to see the same polls in a room full of senior faculty, or at a workshop in the US.

The second poll asked what problems participants thought LLMs could solve, now and in the near future. Each question began “How many of your current research projects can be solved by large language models …” and named one of the categories below.

One striking result was that nobody selected “None,” even for models already available to the public. Everyone who answered thought that current LLMs could solve at least some of their research projects. These are participants’ assessments, rather than a record of projects completed by AI, but they say something about expectations in this group.

My follow-up focused on those who answered “Some” to the last question: what made them expect that some of their projects would remain beyond AI’s reach? There was a variety of responses. One particularly interesting response concerned applied problems that might require collecting data or conducting experiments. Neither of these can be done by a large language model alone. Perhaps this answer foreshadows the direction mathematical research will take in the next couple of years. Others argued that pure mathematics was a safer career choice than applied mathematics. The disagreement gave us more to discuss than the percentages alone could convey.

The third poll asked about acceptable limits on AI use in research. Each question began “What is the acceptable limit of use of AI in …” and named one of the activities below.

Two things stood out to me. First, nobody who answered selected “Exclusively human” for literature review or publication preparation. Second, except for conceptualization, majorities accepted AI doing most or all of the work. Respondents appeared to place particular value on human involvement in deciding what research to pursue. I asked what stood out to the audience, and my impression was that they noticed a similar distinction.

The fourth poll was about ethical judgements and the future – in light of the discussion so far, how do people feel about the future? I had four statements with possible answers: Strongly agree (SA), Agree (A), Disagree (D), and Strongly disagree (SD).

I invited participants who strongly agreed that AI was both an opportunity and a threat to share their reasons. Both statements received 88% agreement, suggesting that many respondents saw opportunity and threat together. That was the point I wanted to explore: how can we, as a community, make use of the opportunities and respond to the threats? The audience, I felt, generally agreed that both deserved attention.

At this point, I displayed one more QR code, asking: “What topic would you be most interested in discussing in a group?” I offered teaching, supervision, publication standards, and job applications as suggestions, but participants had to type their answers, rather than merely select from the list. The purpose of these groups was to make actionable recommendations for individuals.

Teaching, publication standards, and job applications were popular choices; supervision received no votes (younger crowd, remember?). Participants also suggested “What’s the purpose of math?”, “Why should mathematics exist?”, and “What defines a good mathematician?” Those interested in these questions formed the largest group. With so many graduate students and postdocs in the room, I found that especially worth attending to: a conversation about the future of research had become a conversation about the purpose of the profession they were entering.

I had hoped the groups would help people think about some concrete suggestions, but the interest in these broader questions was itself a valuable part of the evening. I mostly left the groups to their discussions. Junior participants need space to explore ideas freely, without feeling judged by senior colleagues.

I want to end with a question one member of that largest group asked: “What is the service that mathematicians provide to non-mathematicians (scientists, engineers, general public, etcetera)?” I think we will all be well served by thinking more about it in the weeks and months to come.

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