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 as well as the enormous energy consumption of AI systems.
In this talk we will take a mathematical viewpoint towards this problem, showing the power of such approaches in the field of AI. We will first provide an introduction into this vibrant research area. We will then discuss key mathematical research directions toward reliability of AI and survey some results on, in particular, performance guarantees as well as explainability. This is followed by a discussion of fundamental limitations also in terms of sustainability. Our mathematical viewpoint will lead us naturally to the necessity of novel (analog) hardware such as neuromorphic computing and the related model of spiking neural networks. We will finish with some very recent mathematical results for spiking neural networks.

We discuss the algebraic geometry of low rank symmetric matrices that have zero blocks along the main diagonal. In theoretical physics, these arise as Gram matrices for kinematic variables in quantum field theories.