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I apologize if this is the wrong forum for this question -- if so, could somebody please point me to the correct one?

I'm a professor who recently started advising graduate students, and I'm trying to find a way to feel good about the time I spend on my students when they leave academia. I devote loads of time and energy into helping my students reach their full potential, and giving them every benefit of my experience, in part because this will contribute to the development of mathematics. But I'm having trouble coming up with a justification for putting so much effort into mentoring students, if the students will wind up leaving academia. Probably many people on this forum have thought through this and come up with some kind of answer, and I would love to hear about these.

Let me clarify that I understand that advising grad students is part of my job. But there are only so many hours in the day, so I need to find a balance between time spent mentoring students and time spent doing research, writing papers, etc. So far I've made my students my top priority, but then when they leave academia, I have a hard time justifying to myself that I should have sacrificed effort on all other fronts in order to help the student develop.

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    $\begingroup$ Would you feel the same way about students who switched from your area of mathematics to another? Or would you recognize that the skills they've learned from you can still be valuable, even if they're not doing exactly the same sort of work that you are? (Posted as a comment, not an answer, because I think the question is off topic here.) $\endgroup$
    – Steven Landsburg
    Commented Feb 22, 2013 at 19:44
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    $\begingroup$ No, I wouldn't feel the same way, since the student would be able to do better mathematics as a result of learning something from me. But if the student goes to Wall Street or computer programming, then I don't think that the things I taught were relevant, and I don't see how to justify sacrificing my research time for this end. $\endgroup$
    – mathprof
    Commented Feb 22, 2013 at 19:49
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    $\begingroup$ Do you have children? $\endgroup$
    – Jeff Harvey
    Commented Feb 22, 2013 at 20:02
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    $\begingroup$ (I wish I could have posted this as an actual answer) The time and energy that you spend on your students doesn't only benefit them personally. Indirectly, it also benefits all their mathematical friends, who will also get to learn about your field of research. If you organize seminars, then all the participants of the seminar will benefit, not just your graduate students... And if you've created a lively math environment around yourself, then this might attract other good grad students, who might then go on with research. $\endgroup$
    – André Henriques
    Commented Feb 22, 2013 at 21:38
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    $\begingroup$ Some very talented people are not certain they want to devote their lives to mathematics, or they think they are but change their minds. Even aside from the benefit of having mathematically trained people in other areas, if we excluded everyone who was unsure we would miss out on a lot of talent. It can be disappointing to help someone try mathematical research if they then decide it isn't for them, but providing this opportunity is still a great service for them and for the profession. $\endgroup$
    – Henry Cohn
    Commented Feb 23, 2013 at 0:01

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How you feel about this will depend on who you are, maybe also on who the student is, and also other circumstances. What are the student's reasons for leaving academia?

If the student leaves academia because his thesis does not seem to be good enough to get him the kind of academic job that he wants, I could imagine feeling a couple of other things than "I shouldn't have put in so much effort". I might even feel that I should have put in even more effort; I might feel that the student has let me down and should have put in more effort; I might feel that in hindsight I shouldn't have agreed to work with that particular student and resolve to be choosier in the future but give it my all when I have chosen; I might feel relieved that the student is not embarking on a very hard road with little chance of satisfaction.

If a student who had done good work then surprised me by seeming to reject the academic life and its values in favor of making big bucks on Wall Street, I might feel a bit resentful and taken advantage of, but I think I would not really feel that I had wasted my time: the student has put in more time and effort than I have, and really who am I to tell him where to go from here?

How would you feel if a student told you right up front that she wanted to study for a PhD under your guidance and then go into business or industry? Would you try to change her mind? Would you decline to take her on as a student?

EDIT Maybe you should consider cutting down on how much of your time you allot to this part of your job anyway -- not because sometimes your students leave academia, but partly because you have other kinds of work to do, too, and partly because the student ought to have primary responsibility for the success of his or her graduate studies.

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    $\begingroup$ @Tom: thanks for your answer. I actually did have one student who told me up from that he just wanted to get a PhD as fast as possible and then go to Wall Street. I made it my top priority to help him write a strong dissertation in the fewest number of semesters possible. It's only in hindsight that I question whether I should have prioritized differently. I've also had two students write good-to-great dissertations and then unexpectedly (to me) leave academia. I appreciate your suggestion to consider spending less time on students in general. I need to think through the pros and cons. $\endgroup$
    – mathprof
    Commented Feb 22, 2013 at 21:14

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