The sentiment here expressed is no doubt somewhat tongue-in-cheek, so it's unclear how seriously to respond to it. But, for the record, obfuscation is not the whole job of any mathematics professor. Most strive ceaselessly to make themselves clear. (And usually fail, alas.)
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I'm not sure how true that is, but stipulating it: a) There are a surprising number of mathematical cranks lurking around math departments/the internet who will happily waste your time without understanding a thing.
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b) Internal representations don't necessarily transfer. If I mostly do homological algebra with kinesthetic representations, and you think syntactically, I'm not sure what I can tell you. "uh so this is like a string of p-1 red beads and...wait the _string_ is red, and..."
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Burst guess is it has something to do with the intimacy of it all. When you’re working on math, it’s intimate. I’ve had a number of meals, dreams, drives, etc with problems spinning in my head... then when you spend your time doing that, you identify with that. So intimate + mine
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