A fellow student and I are part of the same graduate student research group (in applied mathematics), under the same PhD supervisor. The (relatively new) student came to the group with an idea for a thesis, and we helped him come up with a different research idea that more suits our research interests, but still ties to his original goal.

The current formulation of his research problem is mostly due to input from me and our mutual supervisor. As in the model is based on our suggestions across multiple meetings.

Being interested in this student's research problem as well (or at least my formulation of it), some months ago I offered that we collaborate on it. Not much came out of it, mostly, I think, because this student is still very inexperienced, and his mathematical maturity is not so high.

Some time ago I came up with a different partial solution for the aforementioned research problem. As part of our (failed) collaboration I asked him several times to update his simulations to consider this solution, but he seemed to be against the idea, believing that the original formulation is better. Our meetings mostly consisted of arguing about which model is better and me trying to teach him some mathematical concepts he can use to analyze his work.

A few days ago I have (independently of the student or our supervisor) come up with a solution which is better, and completely different from what the student has been trying to analyze. The solution invalidates a lot of the student's work up until now (he has been working on this problem for a few months), since it is simpler and more effective.

I want to write up this solution in a paper and publish it. I already have basically all of the results written down (except one lower bound which I am still working on), and a nearly complete first draft.

Here's the problem. Do I include this student as a co-author? I am conflicted, because this paper really is my own original work. However, it is based on the research problem which our group "handed over" to this student. I do not wish to put him in the unfortunate situation of having months' worth of work invalidated, and everyone in our group views the problem I have solved as "his" problem. However, it is also true that this paper consists entirely of my own research.

Ideally in this case I would approach the student and ask him to collaborate with me on the paper, as in, refine some of the results, or simplify some of the proofs. However, based on many conversations with him, I believe that the student is too inexperienced to do this, and is not familiar with the main mathematical tools I have used to prove the paper's result.

How should I proceed?

Some more details: I should mention that I have no personal qualms about sharing authorship. I am mostly worried about two things:

  1. whether it is the most ethical thing to do;

  2. I feel that if I include him as a co-author, he will want to make a contribution to the paper. But I want to have complete creative control on the paper, and feel that sharing creative control with him is going to slow me down.

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    @J_mie6: What if someone else publishes in the meantime? – Mehrdad Jun 28 '18 at 14:13
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    It sounds like you are asking for advice from strangers on the internet that your advisor (who knows more of the details of the situation) is more qualified to give. Since a wrong decision on your part could cause disharmony in your research group you should involve your supervisor in the decision sooner rather than later. – John Coleman Jun 29 '18 at 11:22
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    Talk to your advisor! This is what he's there for! – Steven Lockton Jun 29 '18 at 18:01
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    Elegance is not the same as validity. – David Diaz Jun 30 '18 at 1:27
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    @MishaR the fact that the OP discussed the problem with the student, knew about failed attempts and failed directions, knew the current problems in the current direction etc. A large part of research (which unfortunately often goes unpublished) is the failed attempts at tackling a problem. If the OP had started from zero, discovered the problem on his/her own, had made the set of failed attempts personally, and then had zeroed in on the new solution, then s/he could be a sole author. – user1952500 Jul 5 '18 at 21:07

11 Answers 11


Welcome to the wonderful world of academia! I appreciate your consideration of your fellow Ph.D. student. I would suggest to invite the student to do some work on the paper, and then have him as second author. Perhaps the student can work on that lower bound? Or write down why the other approach does not work? Or more simulations? You can probably come up with something. If he refuses, you can publish on your own. Either way, if the results are good you get a first author paper, and the other student gets something for his work.

I would run this by your advisor, he might have further advice.

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    I have thought about letting him write the simulations, edit the bibliography, and so on. The problem is that I don't want him to feel like my 'task mule"--we are both students in equal standing, and no matter how gently I put it, I feel like he will be hurt if I reduce his contribution to a few simulations (the simulations are very simple to write). Unfortunately he will not be able to contribute to the mathematical analysis--he is simply not experienced enough. I should mention that this student is much older than me, which also contributes to my not wanting to make him uncomfortable. – user94422 Jun 27 '18 at 19:02
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    Having been in similar situations as your fellow PhD student, I'd be happy to be a task mule if this leads to a better understanding of the problem and a paper. Let the student work on a part he can cope with, and let him learn from you. Also, you can directly ask him if he's fine with being a task mule. – svavil Jun 27 '18 at 21:10
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    @svavil You and Stefano convinced me to take this route. Thankfully this is only a part of his dissertation and he still has a lot of room to build on it. – user94422 Jun 27 '18 at 22:43
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    From the question, it sounds like you and the other student are not "both students in equal standing". He may be older than you, but it would seem you have been pursuing your studies longer, either in the program in general, or in this particular research area. Your seniority apparently played a role in your ability to solve the problem. – Phil Miller Jun 28 '18 at 4:07
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    Are there first and second authors in applied mathematics? – Carsten S Jun 28 '18 at 14:20

There is a larger issue at hand that you seem to be missing.

Yes, I do believe that you can publish your own work, and probably independently if neither your advisor nor your colleague helped. And I understand that there are some field-dependent conventions in mathematics that would be best to discuss with your advisor.

That being said, I believe that, being a senior and more experienced student, you should not have allowed the situation to have reached this point. That is to say you should not have scooped your colleague in the first place. You offered your help to collaborate with your colleague and ended up quite literally stealing his project and are now thinking about publishing it because he was not able to work as fast or as efficiently as you (because he is inexperienced, as you said). This is something that should have been discussed with your advisor at a much earlier stage.

You should understand that this will probably not be the last time that you can benefit from collaboration, and you don't want to be known as the person who steals other people's projects. Healthy collaboration is an intrinsic part of academia (and society, in general). You are expected to be trusted to review other people's papers without scooping them, and in the future you will likely advise inexperienced students in their own projects, many of which have been suggested by you, and that you could solve with much less effort. More importantly, you will be partly responsible their success.

Speaking from your advisor's standpoint, I would consider your action harmful to the group's health. While I generally applaud collaboration between students, in my group, projects and milestones are set with the understanding that students can benefit from them, and that they can help them progress in their more ambitious goals (i.e., a dissertation). This is particularly important for inexperienced students. Should there be a major change of directions (such as a student unable to make progress and someone else benefiting from it), I would like it to be run through me (or other senior member of the lab) first so that it can be arranged for nobody to be in a losing situation. In your case, your colleague is in a losing situation, his name going in the paper or not.

The moment you noticed a solution to the problem, you should have informed your colleague (and possibly your advisor) and both of you should have worked on it, together.

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    This is right, you don’t knowingly work on grad students thesis projects. There’s a lot of other problems out there! – Noah Snyder Jun 27 '18 at 22:27
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    This answer really starts to highlight the real issue - why were you concentrating on his topic and not working on your own... If you had stuck to your own you would not be in this situation,... – Solar Mike Jun 27 '18 at 22:30
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    The problem is that my (honestly idealistic) supervisor told me a number of times that we should all work on each other's problems. And my colleague quite literally isn't familiar with the mathematical tools used in the solution (to the extent that it would take him several semesters to catch up), so our former collaboration felt very fruitless. But I see that your viewpoint has merit. – user94422 Jun 27 '18 at 22:38
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    @user94422 Then you should've discussed with your advisor that you are collaborating with your colleague, but believe that the problem is, at this point, too complicated to be tackled by them, and together you should've found a way to deal with the situation. But you offered to collaborate, and did the exact opposite. Honestly, there are tons of ways this could've handled better from the beginning. If I were your advisor, my suggestion at this point would be that you help and/or wait until your colleague comes up with the solution independently, unless the contribution is a breakthrough. – FBolst Jun 27 '18 at 22:59
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    @Tom The premise is that you want people to be happy to share their research with each other. If you ask a person for help and that person then scoops you, you won't ask for help again. To see that the downsides exceed the benefits: If everybody acted like you'd advise the OP, their colleague would never have shared their problem, and you'd still have to wait for the result anyways, only there would be no trust in Academia. – sgf Jun 29 '18 at 12:24

My contribution to my first paper (which happened to be in applied mathematics) was a 15 minute hallway conversation with the other author. He put me down as a co-author, had me read drafts. I asked him why he put me in. "No one gets penalized for having collaborators, and I found our conversation enormously helpful." I've respected that guy ever since.

Don't sweat it, add him as a co-author, and move on. You received tremendous help from him, reward him with coauthorship. Writing the paper as a solo author, makes you looks selfish and greedy in this situation, for no real gain.

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    Including the student as a co-author is not the issue here. The real problem is that publishing "invalidates a lot of the student's work up until now". – Dmitry Grigoryev Jun 29 '18 at 23:07
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    Invalidation isn't the issue here. The OP is concerned with the ethical ramifications of 'scooping' their peer, and loss of creative control. – Mazura Jun 30 '18 at 1:35
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    AFAIAC you could have just written the first sentence of the second paragraph. +1. – einpoklum Jun 30 '18 at 22:45
  • I agree that it is wise to include all parties that participate and ensure more collaboration in the future. Quite a few journals allow details about contributions to be mentioned. Maybe it is the start to a long lasting collaboration with many new results to disseminate – Vass Jul 1 '18 at 4:56
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    My reading was that the OP's concern about invalidation was in the case in which he publishes as a single author. If he publishes jointly, invalidation just becomes past time and effort and is no longer an issue. IMHO. – PatrickT Jul 1 '18 at 9:31

You may not like this but I would like to point something out to you. The student you "helped" is entitled to be an author on the paper, I am not sure if you have noticed that if it was not for their approach to the problem then you would have not made yours. It also appears that they introduced you to the problem.

If I was you I would be very careful and go and talk to someone trustworthy such as your PhD supervisor. If we assume they are not a total unethical monster then they will be troubled by the whole thing. They will want to find a solution which is best for everyone.

One option would be to write a paper in which both students present their proofs, you could write the paper (together with your PhD supervisor) in which you introduce the problem and then show the two different approaches to the problem. I am assuming that both of your solutions are correct.

You should keep in mind that sometimes the solution which is the nicest for a maths person is not a good solution when it comes to trying to write a spreadsheet. I will give you an example, if you consider a radioactive decay chain where you start with A which then decays into B, then C, then D, then E then F etc etc.

Then a mathematically nice way to deal with it is the Bateman equations, but if you read the thesis of Logan Harr (http://dtic.mil/dtic/tr/fulltext/u2/a469273.pdf) you will find that the lovely looking Bateman equations are not so useful afterall under some conditions. I love the Bateman equations but I know that excel and other maths software can not use them sometimes to solve some radioactive decay problems.

I would also like to suggest to you that you think long and hard about what sort of person you want to be known as. The fact you are already thinking about this problem and asking for advice is a good sign. What you did in scooping the other student is something which I think is harmful to the wellbeing of the group as a whole. Now you need to think "what is best for me". Sometimes "what is best for me" is not stamping on other people or stepping over their bodies in the rush to the glittering prize.

Think for a moment, what is good for me is a good workplace with good relationships with the other PhD students.

If you rip off student X, they will tell the others. You will never be trusted again for a long time.

The other student might lodge some complaint against you with the university (possible, I have seen it happen once in my life).

Not only the student you wronged but the others may refuse to cooperate with you.

Your PhD supervisor's view of you may decline, even if they never say anything in the back of their minds they will know what you did. This could affect the reference they write for you in some adverse way.

Outsiders from the group may hear about the story over either beer, coffee or some other liquid they might start to regard you as a bad person.

My advice is go and have a friendly talk to the other student, see if you can work out a solution to the problem which you are both happy with. Do not for goodness sake try to bully or browbeat the other person into submission.

I would also advise you that your opening offer in a negotiation may have a lasting effect on the discussion and your future relationship with a person. One reasonable and good way of starting it is do the following.

Summarise the state that the two of you are in and how things are. Then ask the other person what they want. Asking someone what they want is a very useful thing to do which can limit the size of the problem.

You might want to chat with a postdoc about the problem or your supervisor before having that chat. If the two of you can not settle the matter between you, then go and see your PhD supervisor. The chances are they will be more happy if the students settle their differences in a reasonable way rather than needing to deal with the two of you as if they are dealing with angry children who can not get on with each other. The PhD supervisor is normally a busy person who has lots of things to do which you do not know about and you should be glad that you are not troubled by. I would say that the best days of my life at university were as a PhD student, I sadly did not understand that at the time. I look back at my PhD student days and wish that I had made better use of them.

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    +1 for the first paragraph. Suggesting the problem is a significant contribution. (but I'm a bit unclear if OP solved the problem suggested by the other student, or the one suggested by the advisor) – The Photon Jun 29 '18 at 15:27
  • I don’t know that someone causing you to pursue other options merits authorship. In my humble opinion, authorship is accompanied with a certain prestige and those listed as co-authors should be able to explain and defend their contributions. Einstein didn’t list Schrodinger or Bohr as a co-author because they influenced him not to solve his theory in a particular way. On the other hand if there was some foundational contribution, it would deem fitting. – vol7ron Jul 7 '18 at 17:30

There is a saying in German which roughly translates to “fruit of the forbidden tree.“

I think this applies here. You're making the argument that you should be allowed to independently publish independent results. And you're right.

But ... had you asked here if you should work an a problem given to a student with the possibility of breaching their trust by invalidating their work, what do you think the answer would have been?

Giving a problem to a student means accepting that they'll work on it differently, slower. That's the compromise you make. You are essentially proposing to take the problem back and provide a solution yourself (which you happen to already have).

That's a severe breach of the mentor-student trust. The student would/should be rightfully outraged.

It might not feel like stealing their work, because the results are independent, but you are. You are stealing their potential work by using your position of power (experience, mentorship).

Don't do this. Do not use the fruit you obtained by cheating someone else.


You are, of course, entitled to publish your own work. You need to cite others who gave you assistance, including members of your research group. Assuming you have stated the issue fairly there should be no controversy ethically, though your advisor should be consulted.

However, if this solution came together quite quickly with only a bit of work and a little consultation, it is unlikely that the problem itself has sufficient merit to ground a dissertation. That is to say that even if your colleague had solved it himself it would not be enough for the degree and more would have to be done. At best, it would represent an intermediate result.

Problems are like that. It is a Three Bears issue. Some problems are too hard (Papa Bear) and no one seems to make progress on them. Others are too easy (Mama Bear) and results flow like water. But the good dissertation problems are "just right" (Baby Bear). These take serious work and lead to deep insights. It may be that the problem at hand is just one of the second kind. In my own doctoral studies (mathematics), I worked on problems of each kind. It was fun to get a theorem solved every day (Mama Bear) but not very satisfying at the end. Like potato chips.

You having solved it, however, may give your colleague a better basis for finding the Baby Bear problem he needs to succeed. Understanding your solution may help him advance. It may be an important part of his own development.

It is your advisor who has the responsibility to guide the other student. Working collaboratively on the paper with the other student would be good, and generous, but not, I think, ethically required. But you want to have peace in your research group, so be guided by (private) advice from your advisor.

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    It was indeed not meant to be his dissertation topic but more of an "appetizer" upon which he can build. I think the result itself might merit a publication of a short paper in a conference. However, he has spent several months trying to solve this problem, so it's going to bum him out nonetheless. – user94422 Jun 27 '18 at 19:09

I think he should be a coauthor, even if he did a small fraction of the work. Clearly the paper wouldn't exist without his contribution.

I recall an anecdote told by mathematician Paul Halmos (it may be in his autobiography). When an editor asked him how much of a joint paper was his, how much the coauthor's he refused to say. He would not distribute credit for joint work.

In my own bibliography there are joint papers in which I have done (almost all)/(almost none) of the work. In mathematics the convention is to alphabetize authors, so there is no first author.

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    Counterexample: Adleman, Rivest, and Shamir didn't alphabetize the name for their encryption, and everyone knows that it would have sounded much better than RSA. – Hans Janssen Jun 28 '18 at 7:06
  • @Geliormth Names out of alphabetical order is not as unusual in computer science as it is in mathematics; checking the recent submissions in arxiv.org/list/cs.CR/recent shows quite a few papers in which the authors are not alphabetized. – user420261 Jun 28 '18 at 7:28
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    Names in alphabetical order is for pure maths, not applied maths in general. – KraZug Jun 28 '18 at 8:18

You should share authorship. Since you write that the group views the problem as 'his', if you solve it and publish on your own that will reflect poorly on you. As a general rule of workplaces, people do not appreciate that you make them redundant. The ethics of a situtation matters less than perceptions and feelings. Making people dislike you is net loss even if it could be argued to have been 'the right to thing to do'. The second point you make is less important.

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    This is very wise +1. The climate in the group could suffer really bad if you do too much on your own of others problems even if you did basically all the work yourself. Don't step on other peoples pride (unless you really have to because someone really is trying to undermine you). – mathreadler Jun 28 '18 at 15:39

Unless it is a groundbreaking idea (which I doubt from what you said), I would say to share the authorship and move on, even if it means to be second author. Think of yourself after ten years: would this paper make a difference on your resume? If you really want to publish it with sole authorship, you might consider giving your colleague a chance to solve it himself/herself, and publish it only after your colleague gave up on it and moved on to another problem. There are a lot of good research problems, you would not want to make yourself disliked for something unworthy.


Everyone here seems to assume that sharing authorship with the other student would be good for him, but I beg to differ. In some fields one cannot afford to be an author of a paper, and be unable to explain it or give a talk on the subject. For example, if the other student went to a conference and a senior colleague asked him about the paper, he could ruin his reputation and chances of future employment. Or if the main author made mistakes or even commited misconduct (plagiarism, fake results, etc), the other student could be held responsible as an author.

There are good reasons for the rule that only people who make substantial contributions can be authors. If I were the other student, I would be reluctant to accept authorship in this case.


I'm going to go out on a limb and suggest something different than the other answers: I suggest that you bury this paper. Set it aside, don't submit it, don't mention it again to your advisor or fellow student.

This was supposed to be his research project. If he didn't feel comfortable collaborating on it with you in the way that you wanted, you should have backed off. Now that you have invested in this work you have quite a dilemma: if you publish it, this student now has to find a new research project. Depending on how much he has invested in it, his response could range from being seriously irritated to never wanting to speak to you again. And honestly, you can expect the same range of possible responses from your advisor.

By submitting this, you will get a publication in exchange for burning a lot of bridges and sacrificing a lot of goodwill from people you need in order to succeed in academia. Put the paper aside. If the student changes problems then you can consider publishing.

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