Connections between Neural Networks and Pure Mathematics

Nowadays, artificial intelligence is present in almost every part of our lives. Smartphones, social media feeds, recommendation engines, online ad networks, and navigation tools are examples of AI-based applications that affect us on a daily basis. Deep learning has been systematically improving the state of the art in areas such as speech recognition, autonomous driving, machine translation, and visual object recognition. However, the reasons why deep learning works so spectacularly well are not yet fully understood. Paul Dirac, one of the fathers of quantum mechanics and arguably the greatest English physicist since Sir Isaac Newton, once remarked that progress in physics using the "method of mathematical reason" would There are many examples in history where purely abstract mathematical concepts eventually led to powerful applications way beyond the context in which they were developed.