[jeffdavis]

"We learn mathematics from the most basic principles and upwards."

Interesting point, although I'm not sure it's 100% true.

For instance, we learn mathematical skills that are readily applicable to life at an early age. Solving a word problem might be the mathematical equivalent of writing a working program that actually does something. And we memorize "formulas", like the simple one to multiply large numbers, at an early age, but don't learn why it works for quite a while.

Induction and abstract algebras might be considered more fundamental, but are introduced much later.