I do deep learning research for a living. I've taken graduate classes in probability, stochastic processes, optimization algorithms, and signal analysis (ECE PhD). I almost never completely understand what's going on under the hood of my models as soon as they get larger than a single neuron XOR mapper. That does not prevent me from finding ways to improve the performance of very large models (millions of parameters and dozens of layers). I agree that there are some papers (or the two books you mentioned) that can be quite dense and heavy on math, but I can't say I've ever felt like I needed any math other than basic calculus, linear algebra, and prob/stats 101 to understand almost all ML methods that people actually use in real world. Obviously if you want to make breakthroughs in theoretical ML, then sure, you do need the mathematical maturity (mostly because you will need to be formally proving things), but if you're a regular data scientist? Can you give some example what kind of math is involved in your predictive models?
