lots of stuff has serial depth required to learn, but math has maybe the most serial depth in some sense, like longest chains of master this; only then, master that; only then, master the next; etc.; and has increasing returns afaict.
"teaching" real math probably looks somewhat like being a good meditation teacher, at least relative to how math is usually taught; you're more trying to get the student to be "turing complete" ASAP, rather than imparting some specific info / understanding, though info also good
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but anyway. why math? because what i'm calling "real math" is about seeing all the way into the core of the structure of things. playing AOE really well... it has way more virtue of empiricism than tasteless math.
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but, you aren't by default led to think about things **more deeply in some general sense** than you've ever thought about things before. (i'm groping for my point here...) in other words: math is about investing heavily in generalization.
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