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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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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.) –  Steven Landsburg Feb 22 '13 at 19:44
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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. –  mathprof Feb 22 '13 at 19:49
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mathprof: Presumably the things you taught (perhaps implicitly) include such things as "How to form general conjectures from a series of examples" and "How to recognize an interesting problem" and "How to decide when you've wasted too much time on one approach and need to find another". These skills are plenty valuable to Wall Street traders and computer programmers, and you might underestimate how much you're contributing to your students' mastery of these skills. –  Steven Landsburg Feb 22 '13 at 19:57
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Do you have children? –  Jeff Harvey Feb 22 '13 at 20:02
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(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. –  André Henriques Feb 22 '13 at 21:38
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closed as off topic by quid, Michael Renardy, Lee Mosher, Felipe Voloch, Douglas Zare Feb 22 '13 at 21:26

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2 Answers

Are you implying that your effort is wasted if he/she moves out of academia ? That is a very narrow viewpoint. There is plenty of math to be done outside of academia. The reason math is still well funded in academia (compared to say art or literature) is because of the applications of math outside academia.

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It's more subtle than that. When I teach large service classes, I could easily let them consume most of my time, and I take steps to avoid that. I still teach reasonably well, but I know I could do (say) 20% better if I put in twice as much time. I'm happy to spend extreme amounts of time on my graduate students who will remain in academia. But when I spend extreme amounts of time, and the students then leave academia, I wish in hindsight that I had put in half as much time and done (say) 20% worse. I asked the question to seek an explanation why I shouldn't feel this way. –  mathprof Feb 22 '13 at 20:02
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Because that 20% extra time will produce better mathematicians who will have do better math, in or out of academia. There are plenty of companies (not just finance or programming) which hire mathematicians: example various national labs, companies like Google,Microsoft,IBM,HP, Disney research have their own research labs with fairly eminent applied mathematicians for example. Plenty of things learned during a Math PhD. are relevant to these jobs (and many more). –  Piyush Grover Feb 22 '13 at 20:23
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Not to mention a whole plethora of companies currently working on 'big-data' such as Linkedin and Facebook. These companies are facing enormous challenges which will no doubt in turn lead to more interesting problems in Math in the future. To be solved, perhaps by one of your Ph.D. students. –  Piyush Grover Feb 22 '13 at 20:27
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But your response isn't specific to this aspect of my job. I could select any of my various responsibilities as a professor, and devote 12 hours of each day to it. Then I would do a little better at that aspect of my job, and much worse at all other aspects. Currently I spend a lot of time mentoring grad students. My question is whether it makes sense to put so much time into that aspect of my job, and less time into research/refereeing/teaching/etc., in cases where the student leaves academia. That's not clear to me. –  mathprof Feb 22 '13 at 20:28
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It oversimplifies things to use the vague phrase "do math" to describe different types of work. Doing cutting-edge research in academia requires a certain skill set. Having worked part-time at two of the companies you listed, I can tell you that the skill set needed for work in those companies is not identical to what's needed in academia (not that this should be a surprise). –  mathprof Feb 22 '13 at 20:48
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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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@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. –  mathprof Feb 22 '13 at 21:14
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