Mathematical Conversations

Artificial intelligence or "deep learning" is becoming ubiquitous in new fields of mathematical applications stemming from the internet economy. This has led to the creation of powerful new tools. We would like to explore how these techniques can be of interest to the working pure mathematician. We'll start by recalling, briefly and in a simple way, what is a neural network and how to train it. Then we'll discuss some recent directions of application in an era starting with "Machine learning (in) the String Landscape". I would like to highlight a couple of recent applications to Gröbner bases and the Gauss-Manin connection, and then discuss my current work on classification of finite semigroups. Our main goal will be to look at the different ways these techniques can be implicated in pure math problems, leading off with the idea of using AI to guide the creation of formalized proofs.