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I have dedicated time and effort to solve a theoretical problem posed by two other people. Now I think I have resolved it, and I have material for a publication.

Should I involve them as co-authors?

Here are more details:

  • those other two people (hereafter, "they") are academics (as I am), but not colleagues: I have met one of them once, the rest of contact was by e-mail.

  • while I resolved their problem, I have no idea of the relevance or applicability of it (they are in a less theoretical field than I am). I assume they do;

  • their only contribution has been to make me aware of the open problem I resolved;

  • my work has developed completely independently, with methods, techniques and formalism utterly different from theirs; indeed, I think they'd never have been able to reach the result with their approach;

  • at one point, they informally made me their collaborator, by just saying "welcome to the project" by e-mail, and sending me a draft of their attempts to resolve the problem; we had very little contact on the project, besides that;

  • one of them is "strategically relevant" for me: despite the mere feeble connection established by the fact that we were working on the same problem, he provided recommendation letters and proactively promoted me when I was in need;

  • I already have a paper illustrating my solution; however, since I don't have the competence to understand how this result is useful in the application domain, my paper at the moment is missing proper introduction, conclusions, and, generally, context;

One strategy could be to publish two disjoint papers, one with their problem with due context, and the other with my solution.

However, I would like to hear any piece of advice or consideration on how to move: I would like to do what is globally most convenient for me (e.g., balancing the good of having a publication with that of keeping my allies in the academia), while not infringing any ethics.

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    Just keep in mind that if they consider you part of the team, and you publish the solution by yourself, you could make enemies.
    – Mangara
    Dec 7, 2015 at 0:06
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    Without knowing further the details of what was said, there is a good chance you are interpreting their contribution to you differently than they do. In their point of view, they could have done a substantial amount of work to find the problem and begin tackling it, giving you explanation on what needs to be done. In essence, I believe if you could truly hurt relationships, as this sounds not too different from being actually part of a research group on a project, solving it in your own way before someone else on the team, then publishing on your own because you did it first.
    – user-2147482637
    Dec 7, 2015 at 4:46

8 Answers 8

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If you solved an open problem working independently, the polite thing to do is acknowledge the source(s) of the problem in your paper, and perhaps send a preprint to the source(s).

But, if they have not contributed towards the project, it would be inappropriate to include them as co-authors. Co-authorship is properly used to recognize joint work, not as a gift. If you are able to write a publishable paper of your work, there is no reason etiquette would require offering them a co-authorship, based on what is written in the question here.

On the other hand, it might well be reasonable, depending on your field, to ask someone else if they would like to join with you to extend your work to something that is publishable. For example, if you cannot provide enough context or application to make a publishable paper, and they can, then you could collaborate with them.

The main drawback of the collaboration (I don't view collaboration in itself as a drawback) is that it would take time for them to work on their piece, delaying publication.

One polite alternative would be to send them your preprint and ask them whether they feel it is publishable, or whether additional material is needed. If they say that additional material is needed, that might open the door to a collaboration.

P.S. added a few days later I do agree with others here that it would be very valuable to discreetly inquire about what the others meant by "welcome to the project". The question describes them as "not colleagues" and "their only contribution has been to make me aware of the open problem I resolved"; this answer is written under the assumption that those are correct. If the others don't think they are correct, you run a significant risk of burning bridges. The advice to write a joint paper combining your work with theirs, which was also mentioned in other answers, shouldn't be dismissed too easily.

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    I didn't think about sending them a pre-print. That could be a way. Thanks for the swift answer.
    – anon
    Dec 6, 2015 at 18:20
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    If someone solved a problem that I was unable to solve and which I had mentioned to them, I would definitely appreciate a nice email with a preprint - at least, just so I know that the problem has been solved!
    – Oswald Veblen
    Dec 6, 2015 at 18:20
  • Of course, I am definitely going to tell them. I just didn't know which messages to add to the communication, and that's another reason why I posted this question.
    – anon
    Dec 6, 2015 at 18:24
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    In acknowledging their work, I'd try to include several citations from their previous work to boost their citation count and help them out with the beancounters.
    – user0721090601
    Dec 7, 2015 at 14:19
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    upvote for the 10k reputation mark :) (and a great answer, of course)
    – user3209815
    Dec 8, 2015 at 8:57
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It seems to me that a joint paper, containing their application of the result and your proof of it, would be better than two separate papers. As you said, you don't have a proper introduction, conclusion, and context for your paper as a stand-alone paper; they, on the other hand, lack a solid technical result for their paper if it's a stand-alone paper. Since they've already welcomed you to the project, I'd recommend continuing in that direction. Send them your result and act as though you regard it as part of that joint project. This approach also has the advantage of continuing and, I hope, strengthening your relationship with the person you described as strategically relevant.

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    @DanRomik The "welcoming" has already ben done; see the fifth bullet point in the question.
    – Andreas Blass
    Dec 6, 2015 at 22:07
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    I think this is very similar to the situation of graduate students with regard to the field. If the other team has done substantial research in finding the problem in which no one knew had to be solved (maybe for something new to happen), then they discussed with the OP about their current approach, and invite the OP to collaborate on solving it, it seems there is very much an obligation to continue as part of the team.
    – user-2147482637
    Dec 7, 2015 at 4:43
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    I deleted my earlier comment since it had a confusing typo that changed a lot of the meaning of what I was trying to say. I meant to say that I agree a joint paper would make more sense, but disagreed with the recommendation to "act as though [...]", which sounds manipulative and borderline dishonest. Just be straightforward, say what you did and what you are proposing and I don't see why any reasonable person would take offense.
    – Dan Romik
    Dec 8, 2015 at 2:17
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It sounds like you resolved a part of a problem, and they resolved the other, but that neither makes nearly as much sense without the other. That is, I perceive your-and-their enterprise as larger than just a mono-thematic one, involving both your part and theirs. From what you say, joint paper(s) would present things most coherently.

Presenting your work together with them, in the context of their work, would also be the most friendly route, to my perception.

(It's not that every smallest fragment of a paper has to have equal contributions, etc. That hardly makes sense, in the first place... "Localization of contribution"?...)

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  • Thanks for your useful considerations. You were quick, too! Quite appreciated.
    – anon
    Dec 6, 2015 at 18:16
  • This answer touches on a key point: the OP contributed a solution, the others contributed the problem and context. Formulating problems is a task worthy of merit, hence, I believe the others deserve authorship. (Albeit, there's insufficient information to make a concrete judgement call.) These aspects are developed in another answer: academia.stackexchange.com/a/59678/22768
    – user2768
    Jan 30, 2018 at 13:56
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They made a significant contribution to your work by posing the problem.

They shared their work with you:

at one point, they informally made me their collaborator, by just saying "welcome to the project" by e-mail, and sending me a draft of their attempts to resolve the problem; we had very little contact on the project, besides that;

Even if you had little contact since them, the fact that they sent you their work is a significant contribution, as well. And even though you took a different approach, you still considered and rejected their methods, a significant part of solving the problem.

They helped you out:

one of them is "strategically relevant" for me: despite the mere feeble connection established by the fact that we were working on the same problem, he provided recommendation letters and proactively promoted me when I was in need;

They can make a needed contribution to your paper:

I already have a paper illustrating my solution; however, since I don't have the competence to understand how this result is useful in the application domain, my paper at the moment is missing proper introduction, conclusions, and, generally, context;

Add all this up, and the case for including them as authors seems overwhelming.

  • It would be wrong to exclude them, given their contributions.
  • It would be "not nice", given how generous they have been to you.
  • They can help strengthen the paper.

Limiting the author list does not help one's career in any way in many fields. What matters is that you are the first author on the paper. Yet despite this, in my experience some people seem to look for ways to limit the author list. Don't do this: there is no upside, and it will create a reputation that you are not a good team player and someone to avoid collaboration with. Be as generous as possible with the author list (for anyone who made a meaningful contribution to the work).

It is possible that in your field the size of the author list is a bit more relevant, but I still think generosity is the way to go. Recognizing anyone who has made a meaningful contribution is just the right thing to do, and your personal connections are often more important to your career than slightly strengthening your publication record.

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  • I was entirely with this answer up until the point where you categorically claim that limiting coauthors can never help someone's career. I think that statement is too strong. In my field -- mathematics, which seems to be close to the OP's field -- there is no inherent credit given for being a "good team player". Moreover coauthors are never ranked...which means that if the authors look approximately equally qualified then they all get the benefit of the doubt, but if one stands out as being more senior / qualified they are often suspected to be "the brains of the operation".
    – Pete L. Clark
    Dec 9, 2015 at 7:00
  • Finally, I will say completely explicitly that in hiring, tenure and promotion decisions in my (mathematics) department I want to see some solo papers. If there are none then I look much more carefully at the coauthorship and try to figure out whether the candidate is working independently enough. E.g. if all papers were coauthored with the same senior person: big problem. Nevertheless I want to say that I entirely agree with your advice in this case.
    – Pete L. Clark
    Dec 9, 2015 at 7:02
  • Just to be explicit about it: if this is a paper in math or sufficiently close to it, then the OP will probably not be "the first author". That concept does not exist in our field, and your answer should take this into account.
    – Pete L. Clark
    Dec 9, 2015 at 7:04
  • @PeteL.Clark, thanks for the feedback, I have changed the answer slightly.
    – user24098
    Dec 9, 2015 at 7:06
  • Mathematicians often underestimate the effort of formulating the problem cleanly in the first place. This is a completely different skill than solving the problem. If that is the case here (also their discovery of the strategical importance of the question in the first place), then, yes, you may deprive them of credit by not having them as co-authors. That being said, perhaps they can come up with a good scenario where and how to use it, and so you can write a truly joint paper.
    – Captain Emacs
    Jan 9, 2016 at 20:25
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Posing a theoretical problem could be even harder than solving the problem. The issue arises in the "welcome to the project" part I assume.

What are the agreed conditions of being a part in the project?

Did you reject their welcome or not?

If not, that shows you that you silently approved to be with them. Instead of eating yourself by not making them co-authors and regret, better to make a joint work with clear conditions...

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  • What are the agreed conditions of being a part in the project? - That's the point -- there were no agreed upon conditions.
    – aparente001
    Dec 9, 2015 at 1:45
  • @aparente001: and that is the problem the anonymous OP has got themselves into. There is a moral there: always be sure, when you talk to someone about research, that you are clear about whether you think you are working independently or as a group. Disputes about authorship and co-authorship are far too common, unfortunately.
    – Oswald Veblen
    Dec 9, 2015 at 12:33
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The Britsish Medical Journal recommends that authorship be based on the following 4 criteria:

  • Substantial contributions to the conception or design of the work; or the acquisition, analysis, or interpretation of data for the work; AND
  • Drafting the work or revising it critically for important intellectual content; AND
  • Final approval of the version to be published; AND
  • Agreement to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

The important (and relevant) point is that

all individuals who meet the first criterion should have the opportunity to participate in the review, drafting, and final approval of the manuscript

To me, it seems clear that "they" conceived and formalized the problem.

Link to the BMJ.

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One of my professors once said

Give love, and you receive love.

He was referring to acknowledgement and the like (co-authoring) in academia: If you acknowledge others and "make them big" you get made big by them as well.

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  • While I agree with your conclusion in this specific case, the maxim, unfortunately, very often fails to hold.
    – einpoklum
    Dec 9, 2015 at 16:18
  • @einpoklum: You mean that you don't get the "love" back?
    – Make42
    Dec 9, 2015 at 16:31
  • I wasn't necessarily talking about myself personally, but - yes. To say the least.
    – einpoklum
    Dec 9, 2015 at 17:52
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I think that it is time to shine on your own - it has to happen someday, if you want to move up, so why not now? It was your work. Your accomplishment. Sometimes, you just have to flaunt a little bit and be your own man /woman. I know it's hard to do, but you may not solve another open problem for who knows how long. Good luck.

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