I am writing a paper in mathematics. It relies heavily on a result from a different topic that I phrased, felt that it should be true, but I did not know how to prove that result. I asked someone who works on this different topic to help me with the proof, and he has found a proof for the desired result. Let’s call him Bob.

I would like to thank this person and ask him if he wants to:

  1. be a co-author in the paper,
  2. just be acknowledged in the paper:

    The author wishes to thank Bob for generously allowing him to use his proof of [result].

    At the beginning of the proof of the result it will be mentioned that:

    The proof is due to Bob.

Bob says that he would be happy to be acknowledged and does not think that he should be a co-author (unless he can further contribute to the paper). He also mentions that he is not working on my topic and hence not enough familiar with what the paper deals with.

My question is: Which of the two options (1 or 2) should be chosen? It should be emphasized that the result I have been helped with is critical for the existence of the paper. Moreover, is it okay to submit the paper to a journal as a single author, and ask the editor to have the opinion of the referees on whether Bob should be a co-author or not?

I read Should all authors on a paper be comfortable explaining every aspect of the paper?, I guess that there are differences between mathematics and other topics, aren't they? For example, in brain research people from different topics collaborate and we do not expect that one will understand what exactly the other did, but in a math paper I would expect that every author will understand what his friend did. Or perhaps I am wrong?

  • @Wrzlpmft, thank you for your beneficial edit. – user237522 Oct 8 at 14:28
up vote 69 down vote accepted

The answer depends on how firmly Y has declined authorship. I don't think it's appropriate to ask the referees to decide on authorship.

  • You cannot list Y as an author without his consent. If he has firmly refused to be an author, that is the end of it.
  • If Y has simply indicated that acknowledgment is a sufficient form of credit, but left the door open to being an author then it's up to you. I have responded in this way sometimes when I felt my contribution was sufficient for authorship but I didn't want to step on anybody's toes. I try to err on the side of being generous with credit, so I would say to him

"I feel that your contribution warrants authorship. Are you willing to be listed as an author?"

If he still says no, then just acknowledge him. You can include the statement of how critical his part was in the acknowledgment.

In the comments, there is a suggestion to state in the paper that Y has declined authorship. I don't think this is wise; it needlessly draws attention and may make people speculate as to why. If I were Y I would not want that statement in the paper.

  • Thank you for your answer. I will again discuss co-authorship with him. Perhaps the decision of being a co-author or not, strongly depends on the level of the proof of result R. Since result R is in topic S, which I am not enough familiar with, I do not know what the level of the proof is. Anyway, I will leave the decision of being a co-author or not to him. – user237522 Oct 4 at 12:12
  • I would consider adding "Y has declined co-authorship" in some form, depending on how the acknowledgement is worded; some may find it odd that someone who contributed enough to be considered one is merely acknowledged, not, er, an author. – Nic Hartley Oct 4 at 19:23
  • 1
    @user237522 Of course, there are valid reasons not to do it -- which is why I said consider, not "you must". If it makes sense, and there are no reasons not to, it could at least avert confusion. – Nic Hartley Oct 4 at 20:46
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    @NicHartley, ok, thanks for the clarification. (As I commented above, I will consider adding the line you suggested). – user237522 Oct 4 at 20:54
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    I would consider adding "Y has declined co-authorship" in some form — I think this is a bad idea, because it risks suggesting to the reader that Y thinks the paper is bad. – JeffE Oct 8 at 15:22

No. Indeed a co-author could have provided invaluable input with a single insight/subresult to the paper or a part of the paper. I don’t think an editor can evaluate the contribution of any co-author.

If both of you feel the contribution is enough (and novel) then your other party should be a co-author.

  • Thanks for your answer. The insight was mine, but most of the proof of that insight was his (I was too lazy to try to complete the proof myself, so asked for help, and he proved it). Anyway, I will later (after my paper will be ready) again discuss this with Y. – user237522 Oct 4 at 2:25
  • (I did not mean that the editor will evaluate the contribution of Y; I meant that the referees will) – user237522 Oct 4 at 2:28
  • @user237522 from your comments this person should definitely be co-author. – ZeroTheHero Oct 4 at 2:29
  • Could you please be more specific? Which comments exactly? (I agree that I feel that he should be a co-author. It is my problem that I was too lazy to complete the proof myself). – user237522 Oct 4 at 2:34
  • @user237522 Actually proving a result, even if the proof is guided or dependent from someone else’s insight, is IMO sufficient to be granted co-author status, unless the proof is quite trivial (undergraduate level). If really the proof was that trivial to complete, you would likely have done this yourself irrespective of your degree of laziness. – ZeroTheHero Oct 4 at 2:42

It really depends on the relationship of the two people. If its student prof the person may want his student to have the recognition. He may just be humble. It wouldn't be too disrespectful to add him as either but definitely add him as one.

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    Disagree that it wouldn't be too disrespectful to add him as either. If he has not explicitly given permission to be included as a co-author, then it would be very disrespectful to include his name on the author list (there might be reasons for it you don't know about), and you are likely in breach of journal guidelines when you submit the paper and tick the box that all co-authors agree to the submission of the paper, etc. – E. Rei Oct 5 at 9:12

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