How is AI changing mathematical discovery? I will begin with our work on discovering integrable systems - exactly solvable models central to theoretical physics and a rich source of new mathematical structures. Despite their importance, finding new integrable systems remains a major challenge. Combining neural networks with analytical insights into the Yang–Baxter equation, we developed a closed-loop framework that has discovered thousands of new models. This unexpected abundance raises qualitatively new questions and calls for new methods of analysis. It also provides a concrete setting for exploring the global structure of the space of integrable theories and already suggests novel connections with algebraic geometry.

In the second half, I will place this work in the broader context of AI-assisted mathematical discovery. I will briefly introduce the main ideas behind modern AI, discussing what we do - and do not - understand about how it works and where its limitations lie. I will then give an overview of approaches ranging from large-scale analysis of mathematical data and reinforcement learning for counterexample search to large language models, (auto)formalisation, automated theorem proving and agentic systems that combine reasoning with computational and other tools. Finally, I will briefly comment on the epistemological and social implications of these rapid developments.