A while ago I asked a senior mathematician a question. He made some suggestions for some papers to read and had a broad outline for what steps might work. Then I read those papers and proved a theorem and wrote it up and sent it to him.

He thought that what I wrote could be strengthened to make a more interesting paper. He suggested that I agree to co-author the paper so that he could "teach me good mathematical style." I agreed.

But it became clear over time when we met that he just wanted me to do all the work. When we met he would say things like, "Try to prove this..." I could tell that he wasn't interested in proving anything himself, even though the draft so far had results that were all due to myself.

Well, I am not a sucker. I will do everything I can to stop him from getting his name on the paper if he is not actually trying to prove anything.

He also seemed to lose interest in the project. We stopped talking because I had other things to work on, but we are generally on good terms. What should I do? The paper is just sitting in my computer doing nothing. But I want people to know that I did prove something that might be publishable.


6 Answers 6


You are a bit unreasonable. He pointed you to the right direction to derive the proof. He did not do nothing.

It is also not true that senior academics who always tell students what to do and never do any "actual work" are just trying to exploit the students. They are experienced researchers who (may) know what to do to come up with the results, and they are just trying to point the students to the "right" direction.

"right"? Of course, sometimes, they are wrong. However, their margin of error is much lower than their students'.

  • 2
    I don't disagree in any substantial way with this very good answer—just enough to note that "their margin of error is much lower than their students'" is an absolute statement that is, surely, not always true. But a very mild qualifier (something like "is usually" or "is probably") would make me agree unreservedly.
    – LSpice
    Jan 16, 2023 at 0:01

Actually, if I were your advisor or mentor, I'd do pretty much the same thing as a way to help you to becoming a better mathematician. He may well have had proofs (or proof ideas) into the things he was suggesting, but felt (as I feel) that minimal hints to students (an probably mentees) is better than giving solutions.

Math is funny in a way, in that it is possible to be a co-author on a paper in which another person does the majority of the "work" but who provides the necessary insight (the "a-ha moment") that makes it all come together. A five minute conversation over coffee could, in principle, result in primary authorship, though mathematicians don't usually think in terms of "first author".

If you are sure that the person has not contributed intellectual content to the paper (a risky bet) then you can publish on your own. Or you can explore with them whether you should do so. But, his "suggestions on how to prove it" might be enough that you ethically need to include him.

My suggestion, possibly not shared, is that you try to continue to work with him to strengthen the work and get it published, possibly with both as author.

Time in the saddle or relative number of keystrokes are both meaningless measures of contribution in math and in some other fields. And, math maturity is measured in insight, which normally comes from hard work, though it can be communicated. But communication is facilitated by that hard work.

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    That depends on the hint, but mathematicians are usually pretty generous about such things. If my "hint" was the crux of the proof, then, maybe yes. If you couldn't have done it without my "hint" then maybe yes.
    – Buffy
    Jan 14, 2023 at 23:43
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    I would say rather than "you can publish on your own" that "you can ask the other part if it is OK for you to publish on your own". Of course one can always make such a decision unilaterally, but the certain bad feelings and possibility of accusations or perceptions of academic dishonesty if one has done so without even consulting the other person are surely so severe as to make the consequences of asking (difficult and unlikely to end well as that is) seem trivial.
    – LSpice
    Jan 16, 2023 at 0:03
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    @LSpice, you cut a fragment out of a sentence that provides context. I'll stand by what I wrote.
    – Buffy
    Jan 16, 2023 at 16:27
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    Re, no matter how one person, especially a junior researcher, feels, making a decision like this unilaterally without at least talking to the senior researcher is almost guaranteed to have bad consequences (and deservedly so—I would be very upset if a co-author of mine cut me out of a paper and didn't even give me the chance to bow out gracefully in private discussion). Let me note explicitly that you do suggest discussion in your next sentence; I only think it should be more urged. But of course it is your answer; I just comment.
    – LSpice
    Jan 16, 2023 at 16:31
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    @WilliamMartens - you can thank them in the Acknowledgments without adding them as an author. I agreed to co-author this paper though, so if it ever gets published it will be a joint paper.
    – cgb5436
    Jan 17, 2023 at 12:16

There is often a dilemma about whether a contributor has done enough to deserve co-authorship or merely a mention in the Acknowledgement sections.

I would say that, when it comes to practically-intensive fields like medical research or basic biological laboratory research, it can be argued that someone limiting themselves to contributing ideas that move the project along toward publication rather than actually doing any lab work or writing anything that appears in the final draft merely deserves an acknowledgement (as opposed to co-authorship).

However, in a theory-intensive field, and especially in a field which is completely theoretical, such as Mathematics, ideas are everything. If the contributor has given you very significant original ideas, ideas without which you could not possibly have produced the work you have in hand now, I would say that they definitely deserve co-author credit. Besides, you did agree to it, it's only ethical to keep your word.

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    It is not only ideas, it is also directions and providing context (related articles).
    – usr1234567
    Jan 16, 2023 at 7:44
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    @usr1234567Yes, I lumped all that into "ideas". Anything short of doing lab work or writing part of the manuscript.
    – Deepak
    Jan 16, 2023 at 11:55
  • "you did agree to it, it's only ethical to keep your word." - this is not, as a general rule, true, especially in situations where a person with greater power convinces a person with lesser power to say yes to something, which they didn't need to say yes to, but the latter person didn't know they didn't need to say yes to.
    – user253751
    Jan 17, 2023 at 15:32
  • @user253751 You're implying coercion. Nothing in the OP suggests coercion at the outset.
    – Deepak
    Jan 17, 2023 at 16:22

Usually, in situations like yours, the first advice is, "you should have talked about authorship before you started to collaborate". In your case, this happend and you should not publish on your own without the senior researcher. You are bound to your agreement to have him as a co-author. If you are not satisfied with the extend of his contribution, you should talk to him.

Further, I expect if you finish your first draft and show it to your co-author, he gives helpful hints on how to improve your writing and overall presentation. Factor in these future contributions before you make your evaluation of his contribution.


tl;dr: Rather than "have to", consider the possibility that you might be "lucky enough to be able to" and see if it could be a better fit.

In my opinion @buffy nails it as usual, but I'd like to add some additional spin and context.

Those familiar with it will know my answer by a single reference to Erdős number. As discussed in answer(s) to the History of Science and Math SE question Which mathematician traveled to and moved in with each collaborator? where Erdős would not only invite himself into the academic world of various other mathematicians, he'd also invite himself into their homes!

The idea that the more senior and/or experienced mathematician saw that discussing together was going to be productive and so would a priori decide for both parties what would happen next might seem at first weird in the 20th century to most, but as several answers point out things are a little different in mathematics; and mentorship is much more common and probably much more important than in many other academic fields.

You have to trust your gut, but if your gut allows for the distinct possibility that you are being mentored, that you will learn a thing or three from this interaction, that the road to paper acceptance might be a little smoother and faster, and that there's nothing that smells particularly predatory about the interaction; in other words, if you can't identify any clear harm here, I'd say go for it!

I have seen mathematicians' web pages which list their interactions or even the "lineage" advisors of advisors prominently, and heard accounts of grand-advisors and great-grand-advisors firsthand.

Collaboration is often hard for people; demonstrating that you can do research with and write a paper together with another mathematician, and that you can accept mentorship are great qualities to show.


from https://www.mathscareers.org.uk/erdos-numbers/


The question, well posed by OP, is what to do if I feel that a senior academic is trying to take advantage of me?

What the senior academic (SA from now on) is doing has been carved out by other answers, however there is an important part that are the feelings of OP.

OP genuinely feels that the SA is exploiting them. Although this can be the case, given the details in the question, I agree with the other answers that quite likely there is a healthy collaboration, that the SA is investing their own time to support, push and improve the work of OP, without exploiting OP. But OP is still feeling exploited.

I do not want to speculate on the OP-specific deep psychological reasons of this, I would like to remark that it is common for young academicians to be exploited, it is common for academicians to be willingly exploited (please note the praise that is often given to "hardworking" people). Such an self-imposed exploitation is possible only because working in a certain department/group is percevied as being part of a close-knitted group, where the needs of the individual have to be sacrified to the higher good of "scientific progress". It is a primordial behavior, it is deeply seated in the mind of people, it surfaces again and again in the academia (where the brightest and bias-free minds are, supposedly).

In general terms, this is typical of religious sect, the same sects impose a shame on the people leaving them, similar to the shame some academicians give to their (ex-)colleagues leaving the academia to work in a company.

Therefore, I guess the OP is feeling exploited because the senior researcher is from an external group, is not from the same group, so the primordial defensive response of one's own group is coming out.

I suggest OP puts themselves in the shoe of the SA: assume the SA has already enough to do and is approached by a brilliant colleagues from another group with a very interesting question. SA knows that has zero time to spend on the question, but can give out for free all SA's expertise and experience, only in a discontinuous pattern. What would OP do?

  • 1
    I think the exploiting / self-exploiting and the religious parts are misleading. I like the first two and the last paragraph thou.
    – usr1234567
    Jan 17, 2023 at 15:00

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