"Well said. Advanced math is mostly about working with properties higher up the chain of abstraction, and then seeing what happens when you bring the insights l

"Well said. Advanced math is mostly about working with properties higher up the chain of abstraction, and then seeing what happens when you bring the insights learned up there back down to more concrete examples." I came here to say the same thing. I went through a lesser known engineering discipline, "Mathematics and Enigneering" [0] and found that the type of thinking one learns doing pure math proofs has served me well in my eventual career in aerospace systems engineering. I find that the thought process in considering a proof as a high level whole/black box or being able to drill down to the finest detail while still keeping the big picture in mind has translated quite well to my day to day traversal up and down the abstraction ladder at work. [0] http://www.mast.queensu.ca/meng/undergrad/info.php http://www.mast.queensu.ca/meng/undergrad/info.php