But another is that the audience for many of these communications is quite small. You're talking about how to "do math", but the techniques in different fields of math are radically different! My cognitive tools work well in algebra, and much less well in analysis, for instance.
I couldn’t do that; I had to integrate syntactically. So I’m also much better with algebra. However, I did eventually develop visualization abilities (for abstract algebra and such). In retrospect, I’m pretty sure I could have learned to visualize surfaces much more.
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If someone had said “These are fundamentally different ways of doing math, and some people seem to be naturally better at one or the other, but if you work at it you can manage both, and here’s how to develop your visualization ability” that might have been revelatory.
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There’s stuff that applies only to broader or narrower subdomains of math, but the more general stuff doesn’t seem to get taught either.
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