Some of you may remember I asked this question last night, and it was closed for being too argumentative. I apologize; I didn't mean to be argumentative or offensive in the slightest. Re-reading my question, I can see how I can come across as frivolous, or, "a troll". But I am honestly curious about the attitude the mathematical community takes towards research collaboration, so let me try re-phrasing my question:

I am a graduate student, and I was wondering whether collaboration could be a two-edged sword for me.

Since I am yet unfamiliar with all the workings of research, having an extra body to work with me will be definitely helpful, and I'll work faster and produce more papers.

On the other hand, I am not famous, and people don't know whether I'm a proficient mathematician, or whether I'm capable of conducting research independently.

So if I decided to collaborate, and when the time comes for me to apply for a post-doc, or a tenure-track position, it's quite possible that this joint paper could be my only paper (I think my field publishes quite slowly). And if that were the case, would people wonder about my ability to conduct research on my own?


closed as off topic by Felipe Voloch, Wadim Zudilin, Loop Space, Andrés E. Caicedo, user9072 Sep 16 '11 at 15:29

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    $\begingroup$ That's one reason why letters of recommendation are useful and people pay attention to them. Make sure to establish contact with one or two people besides your advisor who will be able to write knowledgeably about you. I'm not sure this question is appropriate for MO and, if it is, it should be made community wiki. $\endgroup$ – Felipe Voloch Sep 16 '11 at 12:25
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    $\begingroup$ I object strongly to Wadim's comment and see nothing in the question that makes me doubt SL's future in math. Mathematics may not be about writing papers and getting credit, but if you want to eventually get paid to do research, it is completely reasonable to make sure that you are not inadvertently denying yourself credit for the work you did because of disciplinary mores you don't know about. $\endgroup$ – JSE Sep 16 '11 at 12:58
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    $\begingroup$ SL & JSE, I love your anonymity! I apologize for insulting you, dear SL. I am just sad to see that maths is more about business. $\endgroup$ – Wadim Zudilin Sep 16 '11 at 13:14
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    $\begingroup$ JSE is not anonymous at all. Just click on "JSE". $\endgroup$ – Deane Yang Sep 16 '11 at 13:33
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    $\begingroup$ This probably will never make it to the top of the comments, but I want to point that the correct procedure for "trying again" on a question is to edit it and then have a discussion on meta/ask the moderators to reopen it. The ability to reopen questions is there for a reason. $\endgroup$ – Ben Webster Sep 16 '11 at 21:33

You are correct that the nature of one's collaborative publications is an issue that is considered during hiring and promotion, and this seems to me to be to be a perfectly reasonable career question. Certainly the question of the value of one's collaborative publications is explicitly discussed at hiring and promotion meetings.

But an important point is that there are many different kinds of collaborations, and most of them are not a problem. The issue for the hiring or promotion committee is usually to discover which kind of collaboration it is that the candidate is presenting.

  • One very positive case is when one has many collaborative papers written with many different co-authors, some senior and some junior. This usually reflects well on the candidate, since it shows that he or she is engaged in the research community and may make an enjoyable contribution to the department. Many mathematicians would look well on such a record.

  • Another commonly seen case is that a candidate has many collaborative papers, but all with the same person. In this case, the committee will usually dig a bit deeper, and look to the recommendation letters to find out what the role of the candidates contribution was. Often, such collaborations are enormously productive, with each collaborator making significant contributions, and if the recommendation letters bear this out, then such kind of collaboration is no problem in the hiring and promotion process. I know many instances of long-standing collaborations between two productive researchers, both making a full mathematical contribution, and these contributions will be valued in hiring and promotion.

  • A more problematic case occurs when the candidate has all or most of their publications jointly with one senior person, and one can't really tell if the candidate was making a significant contribution to the collaboration or not. The fear, of course, is that the candidate is simply riding along without having made a significant contribution. The most dangerous case here would be when the senior collaborating partner is also the candidate's PhD supervisor. Such a collaboration need not be a problem, and I know many instances of perfectly fine collaborations of this type, but again the worry is that such a record might indicate that the candidate has only a weak research program of their own, and has not yet moved beyond the support of their advisor. In this case, the hiring committee will usually dig very deep to find out the nature of the collaboration, and want to hear not just from the co-author, but independently from the other recommendation-letter writers.

  • $\begingroup$ Thanks for your detailed answer, I will keep it in mind. In that case, what is your viewpoint on a paper written by several researchers? Say 5 or more. Does that carry the same weight as a paper written by two people? $\endgroup$ – user14449 Sep 16 '11 at 12:51
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    $\begingroup$ It is relatively rare in mathematics for a paper to have so many authors, but I have seen it, and these papers are difficult to assess. Everyone knows that with such a paper that not all the authors have made the same contribution, so again the committee would need to dig deep into the recommendation letters. (The question is whether they will give you this chance, if you are competing with 400 other applicants.) Frankly, applying for a post-doc and having only a single paper, with 5 authors, is not a strong record. $\endgroup$ – Joel David Hamkins Sep 16 '11 at 12:57
  • $\begingroup$ If the question should be CW then this should also be CW. If the OP changes his question to CW, then I hope this gets changed also $\endgroup$ – David White Sep 16 '11 at 14:19
  • $\begingroup$ David, I have made my answer CW. $\endgroup$ – Joel David Hamkins Sep 16 '11 at 14:33

While I agree with much of JSE's post (recently most of my projects are joint, and I am enjoying them much more than my solo work), I have some reservations about his advice. I think at the beginning of your career, you should make sure that a significant percentage of your best papers are solo. Here are some reasons why:

a) If most of your papers are collaborations, the committees would have to "dig deeper" (to quote Joel David Hamkins). Why make it harder for your supporters to support you?

b) Once people know that you are productive and creative, collaborations would be easier to come by and even more enjoyable. In fact, you would probably get more credits than you deserve! (while this is a nice problem to have, now you should make sure that the graduate students who write with you get the fair share of credits).

c) While working solo is harder and more boring, it does train you in different aspects that would be quite useful for your career: for example you have to be more careful with yourself since nobody will be around to point out your mistakes.

One more thing that is already mentioned by Joel, but I think worth repeating: when you collaborate, make sure you diversify (both in people and topics).

  • $\begingroup$ +1. (and if I could, +10) $\endgroup$ – Yemon Choi Sep 16 '11 at 20:24

My sense is that there's a general consensus that the gains to your mathematical life that come from collaboration vastly outweigh any partial loss of credit. In my own career, I spent five years writing almost entirely single-authored papers. In the last six or seven years I have written only collaborative papers. I like a lot of those single-authored papers, but in retrospect, I think those five years were somewhat inefficient. Counterfactuals are hard, but my belief is that I would have gotten a faster start and enjoyed mathematics more if I'd been working mostly on joint papers from the very beginning.

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    $\begingroup$ Speaking of denying oneself credit, this should be community wiki (if it remains open at all) and I shouldn't be getting reputation for this answer! $\endgroup$ – JSE Sep 16 '11 at 13:21
  • $\begingroup$ So why not click the CW button yourself for this answer? Even if the OP changes the question to be CW, your answer will continue to give you reputation until you change it. See tea.mathoverflow.net/discussion/92/… $\endgroup$ – David White Sep 16 '11 at 14:20
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    $\begingroup$ Because I didn't know I could do that! Now I have. $\endgroup$ – JSE Sep 16 '11 at 14:54
  • $\begingroup$ I guess the question is: would you be the same researcher, if you had not spent those five years writing solo? (I guess your answer shows you feel the answer is "yes, or better", but I personally think the question still deserves a mention.) $\endgroup$ – Yemon Choi Sep 16 '11 at 20:26
  • $\begingroup$ I would say "yes" but, as I said, counterfactuals are hard. $\endgroup$ – JSE Sep 16 '11 at 21:56

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