The industrial revolution started with the invention of the steam engine in the 19th century and has made physical work redundant to a large extend. Data Science and Artificial Intelligence (AI) might have the potential to play a similar role for intellectual work.  
There is a huge overlap of Data Science and AI with mathematics, which on one hand comes with unprecedented social responsibility of mathematics and on the other hand with lots of opportunities for application and extension of existing mathematical concepts and results. In this talk, I will give three examples.
First I will present some recent ideas on neural network training by Fredholm integral equations (joint work with P. Gelß and A. Issgali).  Then I will rely on recent work of other authors to discuss the curse of dimensionality in neural network approximation, and to finally sketch a backward error attack on deep learning.