The Universal Approximation Theorem for neural networks
Channel: Michael Nielsen
Date: 2017-11-03

For an introduction to artificial neural networks, see Chapter 1 of my
free online book: http://neuralnetworksanddeeplearning.com/chap1.html 

A good series of videos on neural networks is by 3Blue1Brown.  Start
here: https://www.youtube.com/watch?v=aircAruvnKk

This video just shows the (very simple!) basic idea of the proof.  For the full proof of the universal approximation theorem, including caveats that didn't make it into this video, see Chapter 4 of my book:
http://neuralnetworksanddeeplearning.com/chap4.html

This video was made as part of a larger project, on media for mathematics: http://cognitivemedium.com/magic_paper/