"We do not know where to look, or what to look for, when something is memorized. We do not know what ..." — Richard P. Feynman

From the point of view of basic physics, the most interesting phenomena are, of course, in the new places, the places where the rules do not work - not the places where they do work! That is the way in which we discover new rules.

The correct statement of the laws of physics involves some very unfamiliar ideas which require advanced mathematics for their description. Therefore, one needs a considerable amount of preparatory training even to learn what the words mean.

The situation in the sciences is this: A concept or an idea which cannot be measured or cannot be referred directly to experiment may or may not be useful. It need not exist in a theory.

If you keep proving stuff that others have done, getting confidence, increasing the complexities of your solutions - for the fun of it - then one day you'll turn around and discover that nobody actually did that one!