Abstract

I grew up fascinated by computers. However, as I trained as a mathematician, I was consistently surprised by how little use I could get out of computers. Most examples I cared about were simply intractable. In some examples, I could compute too much, and I had no idea where to look in the output. Often visualizing the output in any reasonable way was impossible, or would involve many weeks of careful programming. In collaboration with DeepMind, I worked on some of the first applications of neural networks to problems in pure mathematics. Here the potential is obvious, but the engineering difficulties are real, necessitating collaboration between mathematicians and engineers.   Modern tools (particularly coding agents, and the *Evolve algorithms) provide a genuine paradigm shift. Suddenly, it has become much easier to run experiments, visualize data, and connect powerful systems. I will give an overview of some of the work I’ve been involved recently. The emphasis will be on three aspects: a) the essential role played by specialized software (LP solvers, SageMath, Magma, GAP , …); b) the skillset needed to do this work is significantly different to that of the typical working pure mathematician, which presents challenges for our educational programs at all levels, c) the emerging challenges around access to models and compute, which threaten the fundamental democracy of mathematics.