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This post is a sequel to: Collaboration or acknowledgment?

The following has come to my attention. A senior mathematician (let us call him or her Alice) suggested a problem to a young mathematician (Bobby) who proceeded to solve it on her own and wrote up the result. Bobby agreed (*) to let Alice be listed as a coauthor, but Alice also insisted to include her PhD student (Charlotte) as a coauthor because they were thinking about the same problem, despite the fact that Alice and Charlotte did not even have partial results.

(*) Bobby had no problem with Alice joining her as a coauthor for the reasons mentioned by Igor Rivin below (I include you as a coauthor, you write me a good recommendation). Thus, the credit was unfairly diluted by including Charlotte who had not contributed.

Question: Is there a way for Bobby to manage such a situation without creating conflict?

Full disclosure: I am Bobby's PhD advisor. I can not interfere directly because Alice is a powerful person in the field known for aggressive backing of her PhD students and I do not want to inadvertently hurt Bobby's career.

Update: Following the advice of Joel David Hamkins, Bobby will be the sole author. There is nothing in the paper that Alice and Charlotte could point to as an idea they already had in mind. Looking back, what bothered me the most was not that Bobby's credit would be diluted but that someone who did not deserve it would be rewarded.

I will award bounty points to JDH for his uplifting Thanksgiving Day Answer, but, of course, any new comments are welcome.

Martin Sleziak
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    It seems academia is a more appropriate venue for this question. – Andrés E. Caicedo Nov 23 '17 at 14:15
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    Collaboration or acknowledgment was on mathoverflow. Different disciplines might have different standards and this example is math specific. – user0100661 Nov 23 '17 at 14:18
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    Doesn't matter. You can always tag it appropriately there. See this for an example. – Andrés E. Caicedo Nov 23 '17 at 14:20
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    The junior/senior issue here is a confounding element, but in my opinion, asking a good question is often a good enough reason to be co-author. I have several papers, where someone asked me a question (sometimes on MathOverflow), which I answered, and I asked them to join as co-author. – Joel David Hamkins Nov 23 '17 at 14:28
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    What about including a PhD student as a coauthor? – user0100661 Nov 23 '17 at 14:30
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    How do you include someone as a "coauthor"? As far as I know, all authors of a mathematical paper are considered equal. – Jose Brox Nov 23 '17 at 14:59
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    Did the senior mathematician help the student, even without having partial results? Did they talk together, did they share ideas? It is impossible to give an answer with so limited information. Furthermore, the name order in a mathematical paper is purely alphabetical, ther is no "first" and "second" author. – Francesco Polizzi Nov 23 '17 at 15:29
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    Francesco, the advisor talked to the PhD student but neither of them had specific ideas about how to approach the problem. The solution came entirely from the young mathematician. By coauthor I mean one of the authors. Is it ethical to include a PhD student on the paper who had not contributed anything and when the young mathematician is himself a recent PhD? – user0100661 Nov 23 '17 at 16:11
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    "Is there a way for the young mathematician to manage such a situation without creating conflict?" For starters, I don't think it's helpful at all to discuss matters on a public forum, where the dramatis personae might stop by and recognize themselves. – Christian Remling Nov 23 '17 at 17:19
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    At least tone down the title. – James Smith Nov 23 '17 at 18:43
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    I agree with @JoelDavidHamkins. But it confuses me how someone can put himself on a paper as a coauthor. – Igor Rivin Nov 23 '17 at 19:19
  • @Igor Rivin: A senior mathematician suggests they write the paper together and, by the way, he would like to include his PhD student as a coauthor. – user0100661 Nov 23 '17 at 19:23
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    @Christian Remling: Public forum might be the right place because some people do not even see this behaviour as unethical. – user0100661 Nov 23 '17 at 19:25
  • @James Smith: Can you please suggest a better title? – user0100661 Nov 23 '17 at 19:25
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    I'm voting to close this question because it is about academic practice, and because it seems likely to degenerate into discussion based on only partial information – Yemon Choi Nov 23 '17 at 20:22
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    From your description it is completely possible that the senior mathematician reached the final formulation of the question with the help of the PhD students. In that case, the student certainly deserves credit. Generally, my advice is that it is always better to err in the direction of generosity. Otherwise, people would not like to work with you. – Yiftach Barnea Nov 23 '17 at 20:50
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    @YiftachBarnea: I cannot go into details but that is not the case. It was the type of problem where you have to find the answer to solve the problem and where the question itself was not invented by the senior mathematician. Your advice is very good though. – user0100661 Nov 23 '17 at 21:08
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    I would like to disagree with the comment made in the edited version of the question. Just because I have voted to close this question, you should not infer anything about my views on the ethics of the situation that you have described but for which I do not have any sight of the actual evidence. https://en.wikipedia.org/wiki/Rashomon_effect – Yemon Choi Nov 23 '17 at 21:23
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    To clarify my comment above, I did not intend necessarily to defend the professor's action in this case, since you haven't provided sufficient information to judge. Although I find question-asking to be often sufficient for co-authorship, I also believe that this decision on this should rest largely with the other author: the theorem-proving author should invite the question-asker to co-authorship. As described in the question, with the senior person adding his name, it seems off to me. But we need to know more. Let me add that I am put off by the moralizing tone of the question. – Joel David Hamkins Nov 23 '17 at 21:29
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    @YemonChoi: It is impossible to present the actual evidence but the question makes sense without evidence. It seems that it is easier for people to justify the situation that take it at face value. – user0100661 Nov 23 '17 at 21:30
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    I am shocked to see how many people try to protect the status quo, and say things like "we don't have enough information, so we can't judge". Yes, there's enough information! And yes, it's wrong for a senior mathematician to push for a PhD student of his to be coauthor of a paper of someone else! It's wrong, and it's unacceptable. – André Henriques Nov 23 '17 at 21:32
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    Part of the information that we lack is what the contribution of the PhD student was. I have had research collaborations where I requested to add one of my students as co-authors, because that student and I had extensive joint work on the problem, even though there would be no way for the third author to know about this directly. (But also: I would never "sign my name" as co-author; the co-authorship issue would be discussed openly and with the goal of reaching broad agreement.) – Joel David Hamkins Nov 23 '17 at 21:34
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    @JoelDavidHamkins: As I wrote, the senior mathematician and his PhD student did not have any partial results. When you requested to add one of your students, at least your own contribution was clear. – user0100661 Nov 23 '17 at 21:38
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    @AndréHenriques Let me blunter, then. If this is what happened, it is out of order. I see no point having an MO question which is there just to solicit responses like that, especially when I quite honestly do not know the background context. Just because someone tells me "this is what the situation is", that does not prove to me "that is what the situation is". I have seen many other things spun as "X, which is obviously wrong" when actually what happened is "Y, which has some features in common with X but has a completely opposing emphasis" – Yemon Choi Nov 23 '17 at 21:38
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    @AndréHenriques I mean, why don't I post MO questions saying: is it acceptable for people to have introductions to their papers which are verging on plagiarizing expository passages in papers I have written? Answer: if I wanted to open that can of worms, I would post it on a blog or G+ or whatever. Or maybe even see if "tea" is still open these days. – Yemon Choi Nov 23 '17 at 21:41
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    @YemonChoi: I tried to make it clear that it is out of order and I did not ask anyone to be a judge. I asked how to better handle such a situation. One good advice was to be generous. – user0100661 Nov 23 '17 at 21:42
  • @user0100661 thanks for the revision. – Yemon Choi Nov 23 '17 at 21:45
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    I think the question is interesting and it would be good to move it to academia and let it open. My opinion is that it is ok to be a coauthor if one poses the problem/has the idea and also worked on it to provide good evidence that the problem might have a positive solution. Just posing the problem as a sheer guess is not enough in my opinion usually. In case the Phdstudent also worked on the problem and provided some evidence,it is ok to include him I think. It also depends of course on how big the problem and the solution are.Ifyou wrote a300 page solutionyou probably deserve topublish alone – Mare Nov 23 '17 at 22:03
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    @Yemon Choi. I'm think that we agree: "if this is what happened, it is out of order". But we're not being asked to judge whether this happened or not. The fact that this is what happened is the premise of the question. The question is: what to do then? Now, I'm afraid that there is not good answer to that question. But the fact that there is no good answer doesn't mean that it was bad question to ask. – André Henriques Nov 23 '17 at 22:04
  • @YCor: I updated the question. – user0100661 Nov 23 '17 at 22:11
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    Since the question says the Alice signed the paper I'm assuming it means Alice actually wrote some of it. Writing is not a negligible part and often requires solving hidden details that were not apparent "on the board". If this is the case, then Alice is a legitimate coauthor to begin with, and if she feels that Charlie played a significant part she can suggest to add him, and will have equal say in the matter either way. So here is my advice to Bob: next time, if you want to sign a paper alone, write it alone from beginning to end. Then it will be only you who decides who to put in \author. – Yonatan Harpaz Nov 23 '17 at 22:21
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    @YonatanHarpaz Thank you. That was exactly the source of my own confusion (what does "sign" mean? How can one insist on being coathor if one had nothing to do with the paper to begin with?) By the way, people insisting that their students be coathors on papers they did not have much to do with is not a new phenomenon by any means. – Igor Rivin Nov 23 '17 at 22:31
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    @user0100661 "A senior mathematician suggests". Why do you say yes? There are a number of possible reasons. 1. S/he had something to do with the paper. In that case, S/he should be a coauthor (unfortunately, in mathematics there is no mechanism to order the authors). 2. S/he had nothing to do with the paper. In which case, you are under no obligation to include him/her as a coauthor. However, you might have decided that there is a quid pro quo (I include you as a coauthor, you write me a good recommendation). In that case, you can weigh the positives and negatives, and don't need us to help. – Igor Rivin Nov 23 '17 at 22:34
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    @user0100661 I should say that a lot of these things are cultural. In applied mathematics, the advisor is (almost) always a coauthor on papers constituting a student's PhD thesis, in pure mathematics, almost never. Since I come from the latter world, I believe that this is a better practice, but I am aware that applied mathematicians might consider me insane. – Igor Rivin Nov 23 '17 at 22:36
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    The question basically suggests that Alice has stolen credit for Bob's result. -- Is this reading basically correct? If yes, then I think Bob has all the right to approach Alice and complain. If the paper has not yet been published, he may reasonably claim the right to publish the result for himself, acknowledging that the question is by Alice. If the paper has already been published, then things get really awkward, since the issue is then no longer an issue between the three colleagues, but a public issue. A public issue, which Bob has all the right to discuss in public. – Stefan Kohl Nov 23 '17 at 22:53
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    @StefanKohl: Yes, this is correct. Bob had no problem with Alice joining him as a coauthor for the reasons mentioned by Igor Rivin. Thus, rather than stealing credit, the credit was unfairly diluted by including Charlie who had not contributed. Igor Rivin also mentioned that this is not a new phenomenon, which I am surprised to hear. – user0100661 Nov 23 '17 at 23:04
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    @user010061: I think that the words "unfairly diluted" perfectly capture the essence of the question. I suggest rewording the question to include those words. – André Henriques Nov 23 '17 at 23:13
  • @AndréHenriques: I updated the question. – user0100661 Nov 23 '17 at 23:16
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    My final comment for now: the latest edit says: "I do not agree that it is not useful to discuss these issues in a public forum." But this is one of my points. MathOverflow is not a place for discussing the issues of academic mathematicians in a public forum. I don't think it should be a place for soliciting opinions or `bringing things to people's attention' – Yemon Choi Nov 23 '17 at 23:57
  • @YemonChoi: What is the difference between this and "Collaboration or acknowledgment?"? – user0100661 Nov 23 '17 at 23:58
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    @YemonChoi: This post is a sequel to "Collaboration or acknowledgment?". The question I asked is not that far from the topic of that post. Why is my question off topic while "Collaboration or acknowledgment?" is not off topic? – user0100661 Nov 24 '17 at 00:02
  • Thanks, I understand now. Well, all I can say is that the post you refer to is from some years ago, perhaps when academia.SE was in its infancy? I am not a fan of the older question in any case, for much the same reasons that I mention above – Yemon Choi Nov 24 '17 at 00:04
  • Can you please clarify a point which was raised above. If the junior mathematician wrote up the result, what does it mean to say "The senior mathematician also signed the paper"? Does this mean "the junior mathematician agreed to let the senior mathematician be listed as a coauthor"? – Yemon Choi Nov 24 '17 at 00:07
  • @YemonChoi: Yes. I rephrased the question. – user0100661 Nov 24 '17 at 00:14
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    @Yemon Choi: I think that the reason why so many people feel defensive and uneasy discussing this topic is because it is taboo. – André Henriques Nov 24 '17 at 00:23
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    @user0100661: This is the wrong forum for this question. If it gets reopened, I will vote to reclose it. Not for the reason that I am part of the "old mathematician network" (I am outside academics), but for the reason that MathOverflow is for resolving mathematical issues, not political ones. (There are also opinion and discussion related problems with the question.) However you may feel, this is not an appropriate (for this forum) sequel to the question you cite. Better asked in workplace.se or academia.se. Gerhard "Takes His Votes Extremely Seriously" Paseman, 2017.11.23. – Gerhard Paseman Nov 24 '17 at 02:13
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    Could you kindly change the title? I suggest something like: What to do about unwelcome requests for co-authorship? – Joel David Hamkins Nov 24 '17 at 03:08
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    Although there are several excellent responses, overall I find this discussion tends to be depressing and divisive, and so I agree with those who ask to put it elsewhere. – roy smith Nov 24 '17 at 04:38
  • @JoelDavidHamkins: Thank you for the suggestion. I changed the title. – user0100661 Nov 24 '17 at 11:02
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    @AndréHenriques Email me if you wish to discuss this further. One thing I have learned in my not-so-illustrious career is that many things concerning (mathematical) academia are not as clear-cut, nor as black-and-white, as actual mathematics. One thing I learned at school is also the difference between primary and secondary sources. – Yemon Choi Nov 24 '17 at 12:23
  • @user0100661 it appears that someone already has (none other than jdh now that i glance up)... – James Smith Nov 24 '17 at 16:26
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    I was in a pretty similar situation as a graduate student where I really don't think anyone was behaving badly, so I don't think it's obvious that someone is behaving badly here. Fortunately I was C and was social aware enough to see that A was unhappy, and so I just worked on other things instead and stayed off the project. So I know how to give advice here for C but not for A. – Noah Snyder Nov 26 '17 at 17:49
  • @NoahSnyder: This is a very good point that most people forget. C has a say, but in the example I am talking about, C is neither as innocent nor as noble as you. – user0100661 Nov 26 '17 at 21:58
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    I have problems with this question not only because ethical situations are largely off-topic, but because as others have said, we really do lack full information. And I urge removal of this "[don't put the future]" before [on hold] -- it's a meta-commentary on the community reaction which logically doesn't belong to the question, and smacks of guilt-tripping. – Todd Trimble Nov 27 '17 at 02:45
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    I am finding the repeated editing of this question really quite wearisome, verging on disingenuous. – Yemon Choi Nov 27 '17 at 03:11
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    @ToddTrimble: It was just a joke. – user0100661 Nov 27 '17 at 10:46
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    @YemonChoi: I have edited following people's suggestions and never changed the gist of the question. Why is it disingenuous? And why is the question still on hold? – user0100661 Nov 27 '17 at 10:48
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    The question is (currently) on hold because five respected users have voted to put it on hold. There are currently four votes to reopen – five are needed. – Gerry Myerson Nov 27 '17 at 11:49
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    FWIW, I don't think it's been emphasized enough that according to the information in the post, B (who I guess we're supposed to sympathize with) doesn't seem to be morally impeccable here either. Igor Rivin mentioned the quid pro quo aspect (you can be a co-author if you write me a good recommendation), which to me seems fishy. In fact, A may feel B is using her, and that she fully deserves to be a co-author without conditions, and so may be feeling, "well, if we're going to play that game, then..." I think this question is a poor fit for MO, and you won't get a better answer than Joel's. – Todd Trimble Nov 27 '17 at 14:22
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    Just one more thing: there are flags calling for the OP not to make any more essentially trivial edits. Each edit bumps the question to the top of the Active page, thus pushing other questions off the front page that are also crying out for attention. – Todd Trimble Nov 27 '17 at 14:27
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    @ToddTrimble: Please read carefully what I wrote. A insisted. B did not mind given the situation. Of course B should have been the sole author. – user0100661 Nov 27 '17 at 14:27
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    No, what you wrote is that A insisted that C be listed as co-author; that's not the part I was referring to. I was referring to the part where you wrote, "Bobby had no problem with Alice joining her as a coauthor for the reasons mentioned by Igor Rivin below (I include you as a coauthor, you write me a good recommendation)." Listen, all we have to go on is what you wrote, and all I'm saying is that based on that, it wasn't clear to me that B's actions were totally above board. Maybe they are, but the description left me confused. – Todd Trimble Nov 27 '17 at 14:38
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    @ToddTrimble: Fair enough. I thought the meaning was clear from the context, but clarification is needed. By the way, Igor Rivin's comment was added later to give an idea why including Alice as a coauthor is somewhat justified. – user0100661 Nov 27 '17 at 14:47
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    I guess I don't see that as a great justification, but I can see that B might be in a bit of a bind, particularly if A is the type who might do B harm if she doesn't get her way. (But again, I can't shake the feeling that there could be more to the story.) Just cements the feeling that MO isn't the right place for this -- it's not really mathematician-specific in the first place. OTOH there's Academia, and there's also an SE site about dealing with workplace environments which merit consideration. I wish you good luck. – Todd Trimble Nov 27 '17 at 14:55
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    Concerning the added piece of information: "I am Bobby's PhD advisor. I can not interfere directly because Alice is a powerful person in the field". If even you, user0100661, are afraid of Alice, then I would say that Bobby has no chance. When facing bullies, people should stand up and help each other. It is an advisor's duty to protect a student against a bully. – André Henriques Nov 27 '17 at 22:23
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    @AndréHenriques: I'm not afraid of Alice. I do not want to cause any problems to Bobby later on, but I can assure you that I am doing my best to handle the situation indirectly. – user0100661 Nov 27 '17 at 22:28
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    Note that, even though this might be directly harmful to Bobby, there is some argument to be made in favour of confronting Alice: calling bullies out can prevent them from repeating their bullying in the future... (I'm just reading the subtext of "Alice is a powerful person in the field known for aggressive backing of her PhD students "). – André Henriques Nov 27 '17 at 22:34
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    @AndréHenriques: It may come to that, but first I try to give good advice and let Bobby handle this herself and try to resolve it amicably. The discussion here has given me a good perspective of the variety of attitudes that people have, and why one should to be careful. – user0100661 Nov 27 '17 at 22:43
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    @AndréHenriques: In addition, I have never actually seen myself how bad this problem is, so there is a chance that I will have to confront Alice in the future. – user0100661 Nov 27 '17 at 22:48
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    I consider this an abuse of the forum, partly for withholding information, partly for soliciting opinion, partly for instilling discussion of the wrong nature (this forum is not meant for politics), but mostly for continued editing. There was a better way to handle this, and you ignored it. – Gerhard Paseman Nov 28 '17 at 17:36
  • @GerhardPaseman: I accept your criticism and promise to never ask another question on this forum. Nevertheless, the whole process has been extremely helpful. – user0100661 Nov 28 '17 at 17:43
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    I think this conversation has run it's course. Let's stop the discussion in the comments, now. – Scott Morrison Nov 28 '17 at 19:55

3 Answers3

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Well, of course the young mathematician should simply discuss the matter with the senior mathematician and perhaps the student until they can come to an agreeable arrangement. My advice is that they should all talk about it. Co-authorship is a matter upon which all authors must agree. What other answer could there be?

If it seemed that the professor or the student had little or no contribution, then the young mathematician should say so and inquire why the professor should be co-author, or why the student should be co-author. If there was not sufficient contribution, then the young mathematician should simply say so and there should be a discussion about it. Perhaps the senior mathematician will point out that the contribution was greater than realized, or that there were other aspects of the collaboration of which the young mathematician is not aware. Or perhaps not, and the senior mathematician will agree that the young mathematician should proceed solo.

But apart from the particular situation described in the post, let me now mention several further reactions that I have more generally to the issues about co-authorship that this question raises.

The first and most important thing to say is that collaborative research is one of the great joys of mathematical life, and I strongly recommend it. To discuss a mathematical idea with another mathematician, who can understand what you are saying and who has thought deeply about the very same topic, gives enormous satisfaction and meaning to one's life as a mathematician. Collaborative research is our mathematical social life. For my own part, I am thankful on today, Thanksgiving Day, for the opportunity that I have had to interact with all my collaborators; I have learned so much from them. (See the list of my collaborators.)

Therefore, my advice is that one should seek out collaborations wherever they are to be found. Often, after one has proved a theorem, then in joint work it becomes much better, strengthened or simplified, or a collaborator finds new applications or uses. If someone asks a question and you answer it, then perhaps the mathematics is not yet finished, but only begun. Aren't there further natural questions arising from the result or its proof? This could be the beginning of a collaboration rather than the end of one.

Another part of my view is that one should be relaxed about collaboration and co-authorship. Except in extraordinary cases, the stakes are low. A mathematician seems to get basically as much respect and credit for a result, whether or not there are co-authors on the paper, and so I question whether there really is any meaningful "dilution" as mentioned in the post. It is simply no big deal to have co-authors or not.

Therefore, why not be generous? If someone has made a contribution to your project, even when the contribution is light, then invite them as co-author. Few mathematical collaborations are perfectly balanced contributions, and in most collaborations one person has had a more important insight or made a larger contribution than the other. But so what? Perhaps the co-author invitation will be declined, and that is fine, or perhaps they will join and then proceed to make your result even better. I have had many collaborations where at first we had a result, which seemed fine and complete, but then in writing the joint paper we were able together to improve the result or give further applications, which wouldn't have happened without the joint interaction. I think you will often be surprised.

Another point, as I mentioned in the comments, is that asking a good question in my view is often sufficient for co-authorship. I have several joint papers that arose from someone asking me a question (in some cases on MathOverflow), which I answered, and then asked them to join as co-author. And I've had some the other way around as well. I find it more natural in such a case, however, for the theorem-prover to be suggesting the idea of co-authorship, rather than the question-asker, which is part of why the situation in the OP seems wrong to me.

Another point is that it sometimes happens that person A, perhaps a junior person, asks a question that person B, perhaps a senior person, answers, settling the question; but the situation is that person A simply cares more about it or has a stronger vision of what the result can become than person B, who is not as interested. In this case, the solution is that person A should do the work of writing the paper, with person B as co-author, even though the result may have been due to person B. The point is that person B would not bother to write this paper on their own, but the joint authorship brings the mathematical paper into existence. The result can be a great paper, and I know of many papers following this pattern.

In summary, pursue collaborations; be generous about co-authorship; be relaxed about co-authorship; enjoy joint mathematical interaction; make great mathematics.

Joel David Hamkins
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    "In summary, pursue collaborations; be generous about co-authorship; be relaxed about co-authorship;" Yeah, but *with people of some noticeable strength or, at least, with people you like personally". As far as I understand the question, it is all about "Why should B dilute her credit to give C a free ride to the PhD defense?". I have no answer to that. – fedja Nov 24 '17 at 03:50
  • You don't like the answer that the authors should discuss the matter? Co-authorship is a matter on which all authors must agree, and if C really made no contribution, then C should not be co-author. This would of course be the central issue to be discussed. In any case, as I mentioned, the latter part of my answer which you quote was not intended to be about the specific situation of the OP, but about co-authorship more generally. – Joel David Hamkins Nov 24 '17 at 04:05
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    Apparently they have already discussed the matter (perhaps, without C) and it is exactly the result of that discussion that created the current situation. You gave an excellent overview of the general attitude towards co-authorship and I share it in many respects. I'm just trying to say that this special situation is exactly when particulars may outweigh generalities. The way I see it (to put it bluntly) is that A finds C hopeless and desperately wants to create an opportunity for her to defend (I've seen such cases). Maybe I'm wrong but if not, it puts things in somewhat different light. – fedja Nov 24 '17 at 05:33
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    This is an excellent answer! I have one more thought to add in favour of solving things by amicable discussion: even though Bobby is less senior, he is not as helpless as it might initially seem, and Alice has a strong incentive to find a good and fair compromise. Indeed, if the situation were to sour, and if it were to become public knowledge that Alice had acted in ways that are not correct, then that would be a big thing for Alice... because let's not forget that reputation is an extremely important thing for all mathematicians. – André Henriques Nov 24 '17 at 09:58
  • @André, Bobby is a she: "a young mathematician (Bobby) who proceeded to solve it on her own...." – Gerry Myerson Nov 24 '17 at 11:15
  • @fedja I don't think we disagree. – Joel David Hamkins Nov 24 '17 at 15:21
  • @JoelDavidHamkins Neither do I :-) – fedja Nov 24 '17 at 21:59
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    I agree with the relaxed attitude on principle, but there is the problem that if a junior person and a senior person collaborate, then the contribution of the junior person is sometimes questioned by hostile members of hiring committees. Also, it sounds like Alice is promoting her own student and exploiting Bobby in a shameless way. – CatO Minor Nov 25 '17 at 15:53
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If several people work collaboratively on a problem, they all get to be authors even if all the ideas that finally led to the solution came from only one of them. That is a perfectly ordinary situation.

The question then reduces to that of whether the situation described comes under the description of "collaborative work". I think that needs more detail to judge and there will always be a grey area.

If what actually happened was that the Alice said to Bobby "Charlotte and I are working on an interesting problem, namely ..." and then Bobby went away and solved it, I would call that a collaboration.

OTOH, if what happened was that Alice said to Bobby "here is a problem for you" without mentioning that Alice & Charlotte were working on it too, then Bobby has a good case for being sole author. Whether Bobby should insist on that right is another question.

In a practical situation I would recommend a somewhat greater degree of generosity towards a student than towards a seasoned researcher.

Brendan McKay
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    What if the problem does not come from Alice? If several people have already worked on it without discovering the answer? If Alice mentioned it to Bobby as an interesting problem that people care about? What happens if you discuss a problem with someone at a conference and then solve it without any of the ideas from that conversation? Honestly, I can think of more cases where it is definitely not a collaboration than where it is. – user0100661 Nov 27 '17 at 21:48

  • If what actually happened was that the Alice said to Bobby "Charlotte and I are working on an interesting problem, namely ..." and then Bobby went away and solved it, I would call that a collaboration.

    In that case, let it be known that I am working on the Millennium Prize Problems. All of them. You better give me co-author if you solve one!

     – Harry Wilson Sep 04 '22 at 17:34
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Unwelcome requests should be denied. Period.

Wlodek Kuperberg
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