At the same time, I find it amazing how many programmers never make the cognitive jump from the "playing with legos" mental model to "software is math".

They're both useful, but to never understand the latter is a bit worrying. It's not about using math, it's about thinking about code and data in terms of mapping arbitrary data domains. It's a much more powerful abstraction than the legos and enables you to do a lot more with it.

For anybody who finds themselves in this situation I recommend an absolute classic: Defmacro's "The nature of Lisp". You don't have to make it through the whole thing and you don't have to know Lisp, hopefully it will click before the end.