[agentultra]

We learn mathematics from the most basic principles and upwards. I don't think there is a way that you could start with higher level concepts and figure out the theory later. It would be incredibly confusing.

Programming is quite different of course. It's not terribly difficult to write a simple program to keep a database of your puzzle collection or build a website to share your puppy photos. One could start from such humble beginnings and build ever-more clever programs and have a steady career doing so. Computers are just machines after all.

But I don't think that's what computer science is really about. IMO it's the study of the nature of computation. Given it's theoretical nature it only makes sense to me that one would start with small foundational concepts and work their way up the ladder as one does in mathematics.

[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.