Comment by HighFreqAsuka

No, there are many very mathematically inclined deep learning researchers. It's an empirical science because the mathematical tools we possess are not sufficient to describe the phenomena we observe and make predictions under one unified theory. Being an empirical science does not mean that the field is a "wild west". Deep learning models are subjectable to repeatable controlled experiments, from which you can improve your understanding of what will happen in most cases. Good practitioners know this.