AI and the Future of Mathematics

Rapid advances in AI are changing how we do mathematics, how we teach it, and how we see ourselves as mathematicians. This talk explores the consequences for mathematical culture, education, research infrastructure, and the recognition of contributions. It invites to further discussions and exchange of positions.

Mathematics is entering a period of remarkable promise and significant unease. AI systems are beginning to contribute to mathematical discovery, research-level reasoning, and formal verification, while also raising serious questions about reliability, attribution, access, education, and the future role of mathematicians. This talk surveys these developments through recent examples, including AI-guided search, advances in longstanding problems, and Lean formalization. The central theme is that AI is most powerful when it complements rather than replaces mathematical judgment: broadening discovery, accelerating exploration, and strengthening trust through machine-checkable proof.

Doing research changes the researcher. In this talk I will try to document my personal story with AI. I love computers and have been an early adopter of AI with a mostly positive outlook onto the future. Recently the picture has become a lot more grim.

This has two reasons. The first is that it is becoming clearer every day how we simply cannot extend the trust that we naturally have between mathematicians also to big tech. The second reason is that I observe changes in myself that I don't like.

I used to say that writing is thinking and I still believe it is true. But I also outsourced a lot of writing to the machine, feeding it notes and unfinished thoughts and then editing the result to sound more like me. For certain texts (like bureaucratic letters) this is certainly an efficient and acceptable way to proceed, but for my core thinking I want to learn to accept that this is a slow and messy human process.

I trace how AI entered my research workflow and how I refined the tools surrounding it. I focus on two comparatively mature aspects: manuscript review and infrastructure. For review, AI has become a useful component of my toolchain, while mathematical judgment remains with me as the researcher.

I also describe a workflow for human-guided, AI-generated research, focusing on joint work with Olav Richter and Matt Ortiz. This project served as a case study. Rather than relying on costly, opaque, specialized models, we used standard subscription-based AI tools to develop a workflow that can be adapted to other research projects in mathematics. The case study invites reflection on the need to increase the level of acceptable good to mid-level research and on a potential future for top-level research in mathematics.