In this episode, host Manuel Brenner is joined by Julius Berner. Julius is a PhD Student at University of Vienna, where his research focuses on the mathematical analysis of deep learning at the intersection of approximation theory, statistical learning theory, and optimization. We begin by talking about deep learning and its relationship to machine learning and artificial intelligence. We then delve deeper into the mathematical theory behind deep learning, distinguishing between approximation, generalization and optimization, and discuss some of the most important results and insights of recent years. We talk about scientific machine learning and how mathematics, computer science and physics can come together, Julius' research in partial differential equations, and how neural networks can help solve them. We close by discussing a typical research day, the difference between working theoretically and practically, what motivates research on a daily basis, the importance of not knowing where things are going, how you come up with ideas through geometric intuition, and Julius' favorite books.