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I'm a Ph.D. student in functional analysis, and struggling to understand why most research-level math in FA is useful. I talked to my advisor about this, and his response was, quite literally, to shrug his shoulders. In so many words, he said that he agrees with me that FA research is mostly useless, and suggests that I ignore the problem until I'm sufficiently well-established in the FA community.

Please don't misunderstand this question as suggesting that FA itself is useless. Clearly it is extremely useful, and there are even examples, albeit uncommon, of very useful cutting-edge FA.

Instead, let me give a specific example of what I am talking about. In a presentation about Ted Odell's work on spreading models, it was asked (my paraphrase):

Assume $\ell_1$ does not isomorphically embed into a Banach space $X$, and all asymptotic models generated by weakly null arrays in $X$ are equivalent to the $c_0$ basis. Is it necessary that $X^*$ is both separable and asymptotically-$c_0$?

This is a difficult problem, and anyone who solves it will be rightly praised as an intelligent and clever mathematician. But are such "clever" mathematicians really contributing in a significant way to human knowledge?

In some of my published papers, I have solved some "problems" in FA which are roughly on par with the above example. This left me feeling very proud. And yet, despite the recognition it has earned me in the FA community, I feel like I have really just been playing a game---the game of pandering to higher-ups ransoming postdocs.

With all this in mind, I suggest the following questions.

(1) Should a math researcher prefer to investigate issues for which there are no immediate practical applications?

(2) Do higher-ups (i.e., people on hiring committees) care about math research which has no obvious practical application? Should they?

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closed as primarily opinion-based by user223391, John Bentin, Brian M. Scott, Henrik, Lee Mosher Aug 12 '16 at 15:24

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ I have voted to close this as being primarily opinion-based. (And I’m already the third to do so.) $\endgroup$ – Brian M. Scott Aug 12 '16 at 15:16
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    $\begingroup$ (You need to use @Brian to be sure that I see a comment.) Look at your two numbered questions. The first and the second half of the second are unambiguously matters of opinion. $\endgroup$ – Brian M. Scott Aug 12 '16 at 15:19
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    $\begingroup$ @user270237: Yes, of course: any answer to $(1)$ obviously is a matter of opinion. $\endgroup$ – Brian M. Scott Aug 12 '16 at 15:22
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    $\begingroup$ It's not that these questions are uninteresting. It's that this is not the correct forum for them, as they are currently stated. $\endgroup$ – Lee Mosher Aug 12 '16 at 15:23
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    $\begingroup$ @user270237: People demonstrably do have different opinions on the subject, and there is no objectively right answer; that makes it a matter of opinion. (My own opinion, for what it’s worth, is that one should ideally do the research that interests one, irrespective of its possible use.) $\endgroup$ – Brian M. Scott Aug 12 '16 at 15:34