The new wave of artificial intelligence is impacting industry, public life, and the sciences in an unprecedented manner. However, one current major drawback is the lack of reliability. This is also acknowledged by political regularization attempts such as the EU AI Act and the G7 Hiroshima AI Process.
In this lecture we will take a mathematical viewpoint towards this problem. We will first provide an introduction into this vibrant research area. We will then survey recent advances concerning generalization guarantees and explainability, touching also upon the application of reliable AI methods for solving imaging problems and learning physical laws. Finally, we will discuss fundamental limitations and reveal a surprising connection to novel computing approaches such as neuromorphic computing and quantum computing.