In my experience, K-12 and 4-year college were all about "useful abstractions and assumptions" to help people understand concepts, and grad material was about s

In my experience, K-12 and 4-year college were all about "useful abstractions and assumptions" to help people understand concepts, and grad material was about slowly peeling away those assumptions and abstractions that made it convenient to learn and teach but were never really there (at least not guaranteed to be there). One of the best teachers I had forced us to write or assumptions down every time for every problem on the test. If you didn't write any, you got zero credit. "What's the point in learning equations if you don't know when they stop applying?" You also got _negative_ credit if you applied the wrong assumptions because you were just guessing or going on habit.