There isnt really any math to deep learning other than the concept of a derivative which is taught in high school calculus. The reason deep learning papers seem mathy is people take network architectures and various elementary operations on them and try to express them symbolically in latex using summations and indexing-hell. For example the easy concept of "updating all the neurons in one layer based on the neurons…
Using matrices to perform the calculations is an optimization over doing a bunch of for loops. This vectorization results in faster code within higher level languages and on certain hardware platforms (SIMD). It's nothing to do with "slicker notation", although having written gradient descent with for loops and matrix operations, the vectorized version is simpler and cleaner to read in my opinion.
Mathematical notation is basically a programming language. A programming language with weird symbols you can't type to search for, single letter variable names for everything, and no comments. And it's written by programmers that are obsessed with fitting everything into a simple line and making it as small as possible, no matter how difficult it is to read. Any programmer understands this is incredibly bad practice. And even if parse every step and perfectly follow what the code is doing, without explanation, it's pretty difficult to figure out why.