How much of this argument should apply to more theoretical areas of research like pure mathematics?
I used to be in a math PhD program. Probably would still be if not for some life circumstance. I think it is worth taking a hard look at the value all of this mathematical research actually produces. I understand how number theory has been useful to cryptography. I understand how branches of pure math can have a surprising influence. But when these examples are given by pure mathematicians, it often strikes me as ane…
The entire field of computing was invented by pure mathematicians like Turing and Church working in the 1930s. At the time, no one had any idea what the applications, if any, would be.
It's like any science. Some work has immediate applications. Other work is pure exploration of the unknown.
And it is pure exploration of the unknown that leads to the truly revolutionary discoveries. You can't set out to discover penicillin when you don't even know it exists.