I bet I know much more on the topic than you, but please enlighten me on which part of this is complex?

The core concepts of DNNs are taught in high-school, and putting them together can done by a Bachelor student. Shit, people often advise writing a NN libraries as a good learning exercise when picking up a new programming language.

I think mathematically illiterate people assume that incredible results necessarily imply complexity, but that's simply not the case here. Or the idea that unknown things are necessarily complex, maybe.

The main reason DNNs are popping up is because we finally have the hardware for it. And the second reason is that tech companies have the resources (both financial and in terms of available data) to throw at it.