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These are really common and incorrect generalizations of most mathematicians. I don't think any mathematician relishes the idea that the work they're spending their life working on and thinking about constantly is completely irrelevant to practical applications. Sure, there might be a few who are aloof enough to actually want to work on useless stuff, but they are few and far between.

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This seems like a straw man to me. I never claimed that mathematicians actually dislike applications. Even, G. H. Hardy, purest of the pure, distanced himself from that attitude. My claim is that mathematicians frequently do not care whether their work has applications to anything outside of mathematics (applied mathematicians excepted, of course).

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For the majority of mathematicians who do work on stuff that's way out there, they suck it up, delay the gratification (perhaps forever) and do it to advance the science.

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You believe that mathematicians are not gratified by their work unless it has physical application or may have physical application down the road? This is absolutely false. Do you believe Andrew Wiles was interested in proving the modularity conjecture and Fermat's Last Theorem because Fermat's Last Theorem has any important application? To the extent that physicists are interested in number theory, that's great (see the book From Number Theory to Physics) and mathematicians are happy to contribute, but that is not the primary motive for doing number theory by any means.


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There weren't exactly a lot of uses for finite fields two hundred years ago...do you think Galois had any idea that finite fields would become critical in the late 20th century in cryptographic and communication applications? No way. The motivation for a mathematician is, when you uncover something and research it and publish it, that somewhere down the road it will be a small part of an even bigger idea.

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Galois' motivation had nothing to do with hoped for applications down the road. Galois was interested in proving that polynomial equations of degree higher than 4 have no solution in radicals. Which he did.

I think at this point it would be appropriate to quote Mallory on why one would want to climb Everest: "Because it is there." This is a little flippant, but gets the point across.