Was I right to insist I be listed as a co-author if my contribution was to be included?

Question

I've done most of my research during my Mathematics PhD with a single collaborator who is not my advisor. He has definitely served as a mentor and has been something of an unofficial advisor - even though he is at another institution. I started working with him at a period when things were not working out with my advisor and I needed someone to do research with. He can be demanding and our relationship has been something of a stressor - but overall he was good to work with. As time has gone on, the dynamic has shifted towards one where I am making the primary intellectual contributions and he is tagging along.

Last week he told me that he was resubmitting a paper he wrote with a different co-author. He said that for one of the responses it would be useful to use a technique I developed and had shared with him in an Overleaf a year ago and asked whether I'd be willing to write that up for him.

I assumed that by writing this section, I would be added as a co-author to the paper. The section contained some ideas that I developed which I was hoping to save for future work. Overall this was a pretty small contribution and I wouldn't say this technique is the most important thing I developed during my PhD.

Nevertheless, I was distressed to find that I was only put in the acknowledgements. I raised the issue with him over email and he became genuinely furious. We had a very tense conversation over the phone. Among other things, he repeatedly raised the idea that I am not appropriately "respecting the lines of authority" and that I should essentially just be quiet and accept his judgement on this matter.

He’d probably say that he feels I’m not appreciating the time he’s put in to my collaboration with him, that he has vouched for me in the past, that he adapted and amended the ideas I shared, and that he had suggested the line of work that led to these ideas.

About those last two points while it is true that these ideas I had developed came out of my thoughts on a paper he suggested I read, I personally don’t feel that is enough to justify taking credit for those ideas. He presented a very slight generalization of the ideas I gave and a slightly edited version of the proof I wrote which took about two weeks to formulate when I came up with it last year.

I’m very distressed. While I don’t consider this set of ideas to be crucial to my PhD work, I was very proud of them. But at the same time, perhaps I don’t understand how things work in academia and I should “respect the lines of authority” – to use his phrase.

I asked that he remove my contributions from the paper. He obliged but indicated that this was the end of our professional relationship, that I should be more grateful to him for his efforts in our collaboration, and that I need to learn humility.

Am I sounding unreasonable? Is this just how things work? I would hate to be inappropriate and I appreciate that he’s been a good collaborator but I also feel I should stand up for my academic integrity.

He seemed to have a lot of bottled anger and I wonder if he is annoyed that I'm leaving academia after he's put time in to mentor me with the hopes I'd be a productive collaborator. In our call he went on for some time about how "ridiculous" it was that I was taking time off of research to focus on getting a job in industry.

He's taking his sabbatical to work at this research institute - so I'm wondering if he's also annoyed that I'm not helping him further his career by making the most of this research year.

Answer 1

In general, the rule for who should be an author on a paper is whether they have made a "significant contribution" to the paper. From what you've written here, it sounds like your former collaborator wanted to use an unpublished technique you came up with, and even had you write-up that technique. It is entirely reasonable, based on this description of events, to want authorship on the paper this technique is first presented in. (If you had previously published the technique, it would perhaps be more appropriate for that publication to be cited rather than adding you as an author, but that is a different debate.)

What he has done for you/the paper doesn't matter for the question of whether YOU should be an author. It doesn't matter if he put a lot of time and effort into mentoring you, if he pointed out the paper you read that inspired the idea for your technique, etc. Those have nothing to do with whether YOU should be an author on a paper. All that matters for that question is what YOU have contributed to the paper.

appreciate that he’s been a good collaborator

Good collaborators don't play authorship games with grad students. (Or anyone else, for that matter.)

Answer 2

I honestly don't understand this. Granted, I come from a different field (biology) and we only have your side of the story, but from what I read, you actually wrote a section of the paper. Your words are included in the paper. That is precisely the definition of "author".

This is beyond the normal academic squabbling of whether or not your contribution was significant; you have actually written a section of the paper yourself, so you authored that section and since that section is part of the paper, you authored part of the paper and should therefore be included in the list of people named as authors.

Unless this "section" was only a couple of words buried in supplementary data, you are an author under any definition of the term I can think of. As for respecting the lines of authority, that feels like pure nonsense. You are a grad student, you are not a child. You are a working adult and this was your work. What authority? This person is a collaborator, so isn't even your supervisor. There is no authority here.

So no, unless there is much more to it that you aren't sharing (or aren't aware of), you're fine and their behavior is not OK.

Answer 3

First of all: the entire situation seems quite a mess; more about this towards the end of this answer.

Yet, given the somewhat limited information in the original post, I'm surprised by the very clear stance that some of the other answers take on the situation.

Contributions and authorship in mathematics

It is certainly not true that contributing a technique or insight or result or proof is always considered to warrant co-authorship in mathematics. One can frequently read passages in math papers that say something like "We are grateful to John Doe for providing us with a proof of Theorem 3.5" or "We are indepted to Jane Doe for communicating Counterexample 4.3 to us (private communication)".

Like WhatTheDuck says in their answer, the crucial question is how "significant" OP's contribution was. But in contrast to WhatTheDuck I find it impossible to determine this from the information given in the question. The main reason why I find this impossible is that significance is highly context-dependent. It's very easy to imagine two different papers A and B of similar quality und relevance and a theorem which would be a very significant contribution in paper A but only a nice-to-have in paper B.

One thing to keep in mind here is that authors are listed alphabetically in papers in (pure) mathematics. There is no concept of a "first author" or "main author". So if, say, mathematician A develops a deep and lengthy theory in a paper and mathematician B proves a theorem for the paper which provides some additional context but which is in no way essential for the theory, then adding B as a co-author would strongly misrepresent the contributions of A and B. In this case it is very common that A is the sole author and only thanks B somewhere in the paper.

From the description in the question it seems impossible to say how significant OP's contribution was in the context of this paper. So I don't think we can judge whether OP was right to insist on being a co-author.

Two more comments:

• Whether OP has written the section themselve is irrelevant for the question (although I find it quite weird that the colleague explicitly asked OP to do the writing).

  (By the way, most likely it will actually be quite difficult - even for the OP and their colleague - to clearly determine how much of the section was written by the OP, since the colleague apparently made some adjustments. Moreover, it's not even clear what precisely "writing" means in the context of writing a paper.)

• Even knowing the degree of novelty of the techique developed by the OP would not suffice to judge how significant OP's contribution was. It is absolutely possible to use a highly novel and innovative technique to make a contribution to a paper which adds, for this paper, only minor or peripheral insights. (The technique might of course still be of very significant use in another paper.)

All this said, let me stress again that I'm not saying that OP doesn't deserve authorship in this situation. I'm merely saying that, given the information in the question, it is impossible to judge whether or how much OP deserves to be an author in this situation.

Social aspects

Much more worrisome than the authorship question at hand, is, from my perspective, how the situation evolved at a social level. Person A believing that they should be a co-author while person B disagrees is one thing - but going from there to a full-grown argument, summoning "lines of authority" and the like is something very different.

General advice

I think we can't say whether OP was right to insist to be listed as a co-author. I'm also not sure we can give good advice regarding OP's relationship with their colleague, as their seems to be a lot of frustration involved (possibly on both sides) and we don't know much about the background.

Yet, there is one generic piece of advice which works, in my experience, quite well when it comes to authorship in mathematics (and a lot of mathematicians seems to follow it, be it consciously or only intuitively):

• Put the bar of what constitutes a "significant contribution" quite high when it comes to the question whether you should be a co-author somewhere.

• Put the bar much lower when it comes to the question whether someone else should be a co-author of one of your papers.

When mathematicians interact who follow those guidelines, it regularly comes to situations where someone suggests to "remove my name from the paper because I have not contributed enough to be an author" or where someone says "I think you should be a co-author of this paper" and the other person replies "probably not". Obviously, those disagreements are much easier and much more pleasant to resolve than the one described by in the question.

Answer 4

I am working in physics, where papers typically have 10+ coauthors and adding one more is usually not a big deal. A single author's contribution can be 5% or even less. In our field, someone who wrote some part of the text and contributed some ideas would be definitely considered a co-author. However, in mathematics things are usually different and papers typically have just one or very few authors. When I see a paper that has 2 authors, I would assume their contributions are comparable or at least 2:1 but not 10:1. Say, if a scholar named Smith proves an important theorem, he wants it to become famous as the Smith theorem and not as the Smith et al. theorem. Therefore, keeping that in mind, if I am about to write a single-author paper, I would rather do all the work myself or at least make it clear to someone I ask for help with writing well in advance that they are not going to make it on the author list. In your case it is hard to form an opinion without knowing how many authors there were in total and what were the proportions of their intellectual contributions.