# Is there a mathematical theory behind why MLP can classify handwritten digits?

I'm trying to really understand how multi-layer perceptrons work. I want to prove mathematically that MLP's can classify handwritten digits. The only thing I really have is that each perceptron can operate exactly like a logical operand, which obviously can classify things, and, with backpropagation and linear classification, it's obvious that, if a certain pattern exists, it'll activate the correct gates in order to classify correctly, but that is not a mathematical proof.

• This is probably a special case of the universal approximation theorem. Here is a Wikipedia page about the theorem. – senderle Feb 14 '20 at 23:51