Explore the mathematics behind artificial intelligence in this 45-minute lecture by Gitta Kutyniok. Delve into the impact of AI on public life, sciences, and mathematics, focusing on inverse problems and numerical analysis of partial differential equations. Gain insights into the development of a mathematical foundation for AI and novel approaches to solving complex mathematical problems. Examine fundamental limitations of AI methodologies, particularly in terms of computability. Learn about neural networks, generalization capabilities, explainability, and the application of AI to mathematical challenges such as image processing and computed tomography. Discover the potential and limitations of deep neural networks in solving partial differential equations, and consider the implications of computability on digital machines for AI development.