Advanced Topics in Deep Learning: AI for Mathematics

AI is rapidly changing how mathematics is explored, computed, and verified. In this course, we examine the methods behind this development and their implications for mathematical research. How can neural networks help discover constructions, accelerate algorithms, or search for proofs? How can we verify the correctness of their outputs? And how might these tools change the way mathematicians work?

The course is split into two parts:

Part I · Foundations of modern deep learning

In the first part, we build the foundations of modern deep learning, from neural networks and optimization to transformers, language models, and agents that use computational tools. Practical examples in PyTorch connect the mathematical ideas to working implementations.

Part II · Applications to mathematical research

In the second part, we explore applications to mathematical research: discovering patterns and constructions, accelerating algebraic algorithms, solving differential equations, and proving theorems with proof assistants. Throughout, we examine how to verify results and where human mathematical judgment remains essential.

Audience and prerequisites

The course is taught in English and is aimed at mathematics MSc students. Familiarity with Python is expected, experience in PyTorch is recommended, but could also be developed along the way.