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
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.
I am a group theorist working in Cambridge, soon moving to Heriot-Watt for an assistant professorship. My first involvement with maths and AI was through contributing multiple-choice questions to AI benchmarks. I started using AI in my workflow some months ago to search the literature, make diagrams, and transcribe handwritten notes. After OpenAI’s announcement of their construction of a non-sofic group, I engaged more with the topic, trying to understand the key steps of the proof and how much credit should be given to AI versus the mathematicians whose work was crucial to the solution.
I am a third-year PhD student in ETH Zurich working on dynamics. I have been tracking the progress of AI generally since AlphaGo; but admittedly only with a sense of urgency since the launch of OpenAI’s o1 model, the first with enhanced reasoning. Back then I thought that Mathematics would be relatively immune to the changes (barring widespread economic and societal ones); as evidence mounts to the contrary I believe this platform (as initially launched by the other four) can become a valuable way to help us navigate the changes together.
I am a mathematician working at ETH Zurich, soon moving to CNRS. 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. Since then, I’ve kept a close eye on its progress, trying to stay current and critical. I’ve watched it go from a tool for polishing writing, to a useful aid for literature review, to a powerful proof assistant capable of proving and verifying results largely on its own.
I am a third-year PhD student at the University of Cambridge working on automatic theorem proving, and I’ve been an enthusiastic user of Lean for formalization and tactic writing for the past several years. I’m an avid reader of mathematics blogs and have been following recent discussions surrounding mathematics and AI, the philosophy of mathematical practice and speculations on how the subject may evolve. I hope that this blog will serve as a forum for fostering conversations around these topics within the broader mathematical community.
I am a mathematician at the University of Oxford, and will soon join Carnegie Mellon University as an Assistant Professor. I see Proofs and Prompts as a valuable space for us to share our thoughts, concerns, and hopes.
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Logo by Radhika Gupta