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private_messaging comments on How valuable is it to learn math deeply? - LessWrong
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Yes, but it is genuinely the case that imprecision and low quality of answers indicate lower utility of an activity, or lower gains due to mathematical skill. Furthermore, what you are saying contradicts existence of mathematicians who did contribute to philosophy (e.g. Godel). edit: I mostly meant, the stories of such - it seems to me that mathematicians who come up with important insights not so rarely try to apply them.
It doesn't; "many mathematicians avoid..." doesn't imply that all do.
Well, not existence per se, that was a very poor wording on my part, but specific circumstances of their contribution. I think that whenever a mathematician has relevant novel insights, they not so rarely apply it to various relevant problems including 'fuzzy' ones. Or, when they don't, applied mathematicians do.
It's just that novel mathematical concepts are very difficult to generate in general and even more difficult to generate starting from some broad problem statement.