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patrissimo 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.
Real analysis is the first thing that comes to mind. Linear algebra is the second thing.
Lately I've been thinking about if and how learning math can improve one's thinking in seemingly unrelated areas. I should be able to report on my findings in a year or two.
This seems like a classic example of the standard fallacious defense of undirected research (that it might and sometimes does create serendipitous results)?
Yes, learning something useless/nonexistent might help you learn useful things about stuff that exists, but it seems awfully implausible that it helps you learn more useful things about existence than studying the useful and the existing. Doing the latter will also improve your thinking in seemingly unrelated areas...while having the benefit of not being useless.
If instead of learning the clever tricks of combinatorics as an undergraduate, I had learned useful math like statistics or algorithms, I think I would have had just as much mental exercise benefit and gotten a lot more value.
I first learned calculus using infinitesimals.