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sark comments on The Value of Theoretical Research - Less Wrong
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...combined with the fact that a lot of pure math does not (or havent yet anyways) lead to applications. It pays to put effort only into math that is immediately practically useful.
We need proper counterfactuals here, cases where a practical use of math counterfactually would not have been possible without previous development as pure math. And also, what-if the pure mathematicians have been directly working on practical math instead?
I think a decent argument could be made that Einstein would have been unlikely to have been able on his own to work out the necessary math he used in special and general relativity. On the other hand, this is much more of a severe issue for gen relativity, and it isn't implausible that once he had constructed the basic theory others would have listened to him enough to work out the underlying math.