Rodrigo co-organized the workshop with Lenny Taelman (University of Amsterdam), Johan Commelin (Utrecht University), Mateja Jamnik (University of Cambridge), and Akshay Venkatesh (Institute for Advanced Study, Princeton).
Welcome, Rodrigo! What is your field of research?
I'm an anthropologist and historian of science and technology, and I mainly work on issues related to computing and artificial intelligence. For the past few years, I have been documenting how mathematical research is changing at a time when automated systems can discover and prove theorems in increasingly sophisticated ways. I am interested in questions like: How do mathematicians assess a purported proof in practice? How do they judge the originality and creativity of a result? How will mathematical careers and collaborations change when much of the work gets automated? These questions were also at the core of many discussions we’ve had during the workshop.
How did you get into this specific line of research?
In 2022, I was invited to speak at the Fields Medal Symposium, held at the Fields Institute in Toronto. I was asked to respond to an essay by Akshay Venkatesh on the automation of mathematical research. He had won the Fields Medal a few years earlier and requested that the workshop to be held in his honor focus not on his own work, but on broader debates about automation and its implications for the field. I was surprised to receive the invitation, since until that point I had written about the history and anthropology of AI but not specifically in relation to mathematics. I assumed I would just give this one talk about the topic, then go back to work on my other projects. But I got unexpectedly engrossed by the debates, which raised fundamental doubts about mathematics and its future. I would meet people who had spent their whole lives in mathematical research careers, and who would sit around the coffee table and ask, “What is it that we do?” These mathematicians were deeply reflexive, asking existential questions about their field. I was really taken by that.
How did you decide to organize this workshop at the Lorentz Center?
As organizers, we thought there was a lot to be gained by an interdisciplinary reflection on questions of mechanization and mathematical research – a conversation we felt was missing. We wanted mathematicians, computer scientists, historians, philosophers, educators, and policymakers in the same room. At the same time, this was an unusual type of event that we are not used to organizing, not only for its diverse mix of disciplines but also for the broad scope of its questions. There are only a handful of spaces where this sort of interdisciplinary meeting would have been possible. The Lorentz Center was our first option because it was the most clearly suitable.
One of the things you discussed in the workshop is the role of the mathematician: how have mathematicians’ skills changed in the past, and how do you think they will change in the future?
The introduction of every major technology used in research reconfigures the kinds of skills that are considered most valuable. Take handheld calculators: the ability to perform complex calculations manually is no longer a valued skill for researchers or students. With new AI systems, the valuation of different kinds of skills is again in flux. In the workshop, there was no consensus about how such values will or should change. Some people were eager to have computers automate what they see as the tedious tasks of proof writing. But others thought that, in these very tasks, there were vital and creative aspects of the craft of mathematics. Since these values are being actively contested, there is not yet an obvious outcome.
Did you discuss also future scenarios about AI and the generation of mathematical knowledge?
The most popular narratives about the future of AI and mathematics are either utopian or dystopian. Some people imagine that you can let AI loose, and it will simply discover new mathematical truths on its own, rapidly generating conjectures and proofs without any human guidance. Others present such scenarios as the end of mathematics departments, whose research and education would be rendered obsolete. I think it was very difficult to come out of this workshop believing in these simplistic narratives. Although the participants did not reach a consensus, they came out with more nuanced and plausible views.
Was there something that surprised you about the workshop organization?
We decided on a format of discussion where people could just submit questions on post-it notes, which the organizers would then cluster into topics for breakout rooms each day. We were initially apprehensive, because none of us had ever organized an academic event in this organic format, but we were surprised by how well this worked.
Since I have followed the discussions about AI and mathematics for years, I was surprised that I left the workshop with a different understanding of the topic than I did going in. For example, I learned a lot about recent commercial interests behind the development of AI models for mathematical reasoning. One of our aims was to expose all participants to perspectives they hadn’t encountered before.
I think that changing your opinion on what you think you know is one of the most powerful things that can happen in a workshop. Did other things happen during the workshop that you think will benefit the community?
There has been a lot of interest in the workshop discussions, so we are preparing a short report with the key takeaways from the workshop. Slides and notes from the lectures are freely available online, and so are the videos of the public symposium on the last day. The number of people who have viewed those materials already far exceeds the number who attended in person. The workshop also sparked various collaborations among the participants. We saw the beginning of some important initiatives, for example the development of a declaration of ethical principles regarding the use of AI in mathematics.
How was your overall experience of organizing a workshop here?
We were delighted by the positive response to the event. Some participants even told us that this was the best scientific meeting they had ever attended. For myself, this was also the smoothest experience I’ve ever had organizing a workshop. The way that you have the infrastructure and logistical processes all set up here in the Lorentz Center made the experience quite easy for us. We really appreciated that.
One last question: do you use large language models (LLMs) for your work?
Anthropologists are good at exactly the things that AI cannot do. LLMs reproduce the most common patterns of discourse on the web and in other training data, and much of what anthropologists do is diametrically opposite to that. You have to go into the world, spend a long time with people, and find stories you could not have easily found on the internet. You try to ask questions that are not already part of an established discourse, to observe things that people don't articulate too explicitly, and to speak with people who aren’t necessarily the most vocal. At least for now, all of this work is not something that AI systems can do. When it’s no longer necessary to do all that, perhaps we should have another workshop on Mechanization and Anthropological Research. But I think we will have to wait for quite some time.
