About

Mathematics is changing faster than it has in decades. Tools that help write proofs, search the literature, and suggest conjectures are no longer speculative. They sit on mathematicians’ desks alongside chalkboards and papers. What’s uncertain isn’t whether this is happening, but what it means for what counts as a proof and who counts as its author, for how mathematical taste and intuition are formed, for the slow apprenticeship of becoming a mathematician, and for the day-to-day experience of doing mathematics.

These questions are usually discussed in three places: technical papers measuring what a model can or can’t prove; broad, often breathless, public commentary about AI in general; and personal blogs of mathematicians, that are scattered all over the internet. All are useful, but we feel like the third one could be more focused and organized. So this is a blog written by mathematicians, for mathematicians, where people can think aloud about how these tools are changing mathematical practice, without having to justify the premise or dumb down the stakes, without being confined to benchmarks and product announcements, all in a common place to facilitate a fruitful exchange of ideas.

We’re especially interested in voices that don’t usually get a platform for this kind of reflection, that can come here without having to set up and maintain a personal blog. Senior researchers with an established audience are welcome, but so are PhD students still forming an opinion, mathematicians who’ve tried these tools and been unimpressed, and those who haven’t touched them at all and want to say why. We think the range of reactions — enthusiasm, indifference, anxiety, contempt, curiosity — is itself part of the record worth keeping.

Contributions can take any form and any length. A two-paragraph anecdote about a proof a model helped or failed to help with. A longer essay on what mathematical understanding means if a machine can produce correct steps without understanding them. A political or institutional critique of how a lab, a journal, or a department is handling this moment. A personal, maybe uncomfortable, account of how your relationship to your own work has shifted. Or your experience interacting with AI labs.

We’re not looking for a house style or a party line. We’d rather publish something short and true than something polished that doesn’t quite believe itself. We don’t expect consensus either. In fact, we hope not to find it. What we hope to preserve is an honest record of what it felt like to do mathematics while the tools of the discipline were changing.

This is a communal project. It will only be as good, as varied, and as honest as the people who write for it.

Who we are

Raphael Appenzeller

I am a mathematician in geometry and geometric group theory and I have played around with Lean. I am interested in visualization and outreach and I hope to help ensuring that the benefits of AI outweigh the problems. The first step is to have discussions and listen to diverse point of views, for which we created this blog.

Francesco Fournier-Facio

I am a group-theorist working in Cambridge, soon to move at Heriot-Watt for an assistant professorship.

My first involvement in maths and AI was by contributing multiple choice questions to some AI benchmarks. I started integrating AI in my workflow some months ago to search for relevant results in the literature, make diagrams, and transcribe handwritten notes. I have only used the free versions, which do not seem to be very useful beyond this. As OpenAI announced their construction of a non-sofic group, I have engaged with the topic more, trying to understand what the key steps of the proof are, and how much credit should be given to the AI versus the mathematicians whose work was crucially being relied on in the solution. I take every change to learn how people are using and understanding AI in relation to mathematics, and see this blog as an opportunity of learning more from people outside my direct circle.

Simon Machado

I am a mathematician working at ETH Zurich, soon moving to Université Paris-Saclay as a CNRS chargé de recherche. I work in group theory, at the interplay of geometry, dynamics, and combinatorics.

I have closely followed the advancements of AI since GPT-3.5’s breakout in 2023. Already then, I took part in a research project evaluating how well state-of-the-art LLMs could help high school and undergraduate students in their learning. Since then, I’ve kept a close eye on its progress, trying to stay current and stay critical. I’ve watched it go from a decent tool for polishing sloppy writing, to a useful aid for literature review, to an exceptionally powerful proof assistant, now capable of proving and verifying results largely on its own. I’ve tried to keep an open mind towards the range of views on this shift, its impact, and the challenges it brings. Contributing to Proofs and Prompts is my way of staying open to that diversity of opinion.

We subscribe to the Leiden Declaration.