Theorems... record more complex patterns of thinking that once shown to be valid need not be repeated every time they are needed. - Richard Hamming

When you know something cannot be done, also remember the essential reason why, so later, when the circumstances have changed, you will not say 'It can't be done.

We intend to teach the doing of mathematics. The applications of these methods produce the results of mathematics (which usually is only what is taught)... There is also a deliberate policy to force you to think abstractly...it is only through abstraction that any reasonable amount of useful mathematics can be covered. There is simply too much known to continue the older approach of giving detailed results.

I need to discuss science vs. engineering. Put glibly:
In science if you know what you are doing you should not be doing it.
In engineering if you do not know what you are doing you should not be doing it.