> do we see the same trends in that there is a high-level in Mathematics where new theories are being created but a lower level where a large amount of people u

> do we see the same trends in that there is a high-level in Mathematics where new theories are being created but a lower level where a large amount of people use tools to apply these new theories? Definitely. If you allow more longer-running examples, this is exactly the situation of calculus. The Calc I-III that many use regularly is the application; Real Analysis is the theory. Ditto for any "applied" sort of math you can think of (stats, crypto, machine learning, etc. -- all basically just use theorems which are the "abstract interfaces" to pure mathematics.) > we never fully mastered teaching how to come up with abstractions and new models And we never will, as long as the human race continues progressing :-)