nshepperd comments on Some rationality tweets - Less Wrong
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I learned a lot of math (undergraduate major), and while it entertained me, it has been almost completely useless in my life. And the forms of math I believe to be most useful and wish I'd learned instead (statistics) are useful because they are so directly applicable to the real world.
What useful math have you learned that doesn't involve reference to useful or existent things?
I've hypothesised before that learning math might be useful because a) you get lots of practice in understanding abstraction and how abstract objects can meaningfully be manipulated using rules, and b) you hopefully learn that proofs are nobody's opinion. So basically a lot of practice in using basic logic. Neither of which require study of useful or existing things.
Though obviously it would be preferable if the actual content were about useful stuff as well, to get double the benefit, it's not inherently useless.