[robot_no_419]

I never said it was the most intuitive, just the most streamlined and most efficient. I'm having a hard time understanding why you think it's not the best organized. Most math courses are taught with a pretty straight forward approach: start with the axioms and definitions, prove the easy and auxiliary theorems that are easily derived from the axioms, prove the fundamental theorems that make the subject useful. In other words, the shortest path from the axioms to the important theorems. I don't see a way to make it more organized or compact, but I'm open to hear what you think is a more condensed or organized way to teach math.

And no, this is rarely the most intuitive or contextual way to learn math. Another analogy - a library doesn't sort their books by which ones were best reads or most influential, but by topic and author. Similarly, math curriculums are organized by a hierarchy of which theorems can prove the next theorem with no explanation of which ones are important. Organization doesn't always provide intuition.

[trasz]

What you describe is probably the least efficient way to learn math - or anything else for that matter - because you’re trying to learn things you can’t, at that point and for a while afterwards, reason about. They don’t have connection to anything else. Compare that with the opposite - learning stuff you can already mentally associate with parts of known reality.

[zozbot234]

> learning stuff you can already mentally associate with parts of known reality.

This is not always feasible or effective. Sometimes it's just better to start by doing some simple reasoning about things in isolation, and build the proper connection and context afterwards.