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Indeed, a counter example is geometric algebra (not algebraic geometry, sigh), which I really like. It starts out by talking about stuff you already know from linear algebra etc, but has no trouble showing you how you can easily make clean constructions that would be
confusing and burdensome in the old ways (if you even thought to do them, which you wouldn't). I have never read a GA book that dissolved into trivial details before getting to the point. CT, on the other hand, always seems to, so I feel like there is no there there.
I mean, there probably is something useful that you get by trying to distill relationships down to their most abstract, but one is also kind of talking about nothing at that point, so ... ??? I would like one of these authors to
stop trying to be so concerned with sounding smart, and just tell me what the point is, but nobody seems interested. Which makes me think maybe there isn't really a point.
Oh Jonathan, your strings are so much fun pull :) I was overstating the case for formalism for comedic effect. GA is a splendid counter-ex, and so is… geometry. It *can* be fully formalized, but this misses its point. Good for housekeeping, bad for teaching. /
CT is a tough pedagogical sell, bc it is from housekeepers, for housekeepers. Builders like you stand to the side, dumbfounded, wondering why they put the glasses upside down into the cupboard.
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