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I'm publishing my first paper soon with three collaborators. We made a conjecture towards the end of the paper and intended to publish with the question still open. Another mathematician heard of the problem and found a solution to the conjecture. Now we have two options:

  1. publish our current paper on our own, with the conjecture open, after which our friend would publish their solution as a separate paper, or

  2. include their work at the end of our paper and make them a co-author.

Though our paper is pretty good already, the new work is strong and would make a nice addition, so the first option seems nice. On the other hand, I'm an undergraduate senior (entering graduate school this Fall) and so are two of the other collaborators. Thus it seems like adding another professor as a co-author may make my contributions (which I have worked very hard on) appear less substantial. Also in favor of option 2: if the other professor publishes separately, the citation may make our paper look good.

What do you think?

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    so your work is incomplete and you are hesitating in whether or not you should complete it? I will definitely go with the second option and target a better journal. – seteropere Mar 29 '13 at 20:32
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    "since the paper is a bit "low level" for somebody in his position" I will consider this as an opportunity to list my name next to his. – seteropere Mar 29 '13 at 20:38
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    Mathematics papers sometimes include an appendix written by someone else (a MathSciNet search for "With an appendix by" returns 984 hits). That's one way to include this other researcher's contributions in your paper while making it clear who contributed to what. It's sometimes used in these sorts of cases, where a paper makes use of or is enhanced by someone's work but their contribution can be isolated in a way that distinguishes them from the coauthors on the paper itself. – Anonymous Mathematician Mar 29 '13 at 20:56
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    @AnonymousMathematician That's interesting. Do journals generally have policies outlined for this or is this a pretty standard thing? – Samuel Handwich Mar 29 '13 at 22:25
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    I personally would take option 2. At this stage in your career, it is a great opportunity to be able to publish with an established mathematician (as a full co-author, not hidden away in the appendix) and is much much more valuable than a measly citation. Besides, it's common lore that a mathematician's work starts getting cited only by the time he dies... – user6431 Mar 30 '13 at 1:13
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I think it is not important which option makes your paper look good, but the best question here is "what is the right thing to do?" If you are such a talented and hardworking undergraduate student who can write a publishable paper, you will certainly have a very bright future in grad school and later as a researcher. So, don't worry how your first paper is going to be evaluated or cited. Hopefully you will write better papers and you can prove yourself in the future. Regarding publishing research papers, the right thing to do is that you publish your paper as perfect as it is possible for you at the moment, which means it is better you add the solution (and one more co-author) to your paper.

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  • +1 and don't forget that this could be a nice introduction for potential future collaboration. Their participation so far is already a strong indicator that they find your line of research interesting/worthwhile – Jeutnarg Feb 22 '17 at 21:45
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I can add that the timing issue is also important, especially to that established would-be coauthor. Sometimes someone decides to write a paper, and it never comes to life. However, it is also important how adding the proof to the existing paper would slow down the process of getting it out.

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