Lately I’ve been thinking about if and how learning math can improve one’s thinking in seemingly unrelated areas.
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.
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.