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That’s not the whole story. Many areas of mathematics add new words which allow your writing to be more compact or expressive. While compaction primarily allows old ideas to be rewritten more intuitively and succinctly, expression allows us to describe fundamentally new ones.
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
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