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I'm a PhD student in math and currently I'm stuck at a problem. But my advisor has some idea and it seems to me that he might even solve it soon.

Earlier I had an idea which seemed to be working, but a few days back we found a gap in that idea.

If my advisor solves the problem, will I still be able to include that in my thesis or be a co-author in the paper?

My guess is no, because that would be plagiarism. But I don't understand what would happen in that situation.

Having this conversation with my advisor seems awkward. That's why I'm asking here.

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    "Having this conversation with my advisor seems awkward." It shouldn't be. Communication is important. Not having conversations with your advisor is more awkward than having them.
    – Stef
    Commented Nov 24, 2022 at 10:38
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    It depends on how much work you have done in the process and how much the work the solution involves. There is a difference between "I did a puzzle but couldn't place the last few pieces, but my supervisor could and finished the puzzle" and "I could only place the corner pieces of the puzzle so I gave it to my supervisor who completed it"
    – ljden
    Commented Nov 25, 2022 at 5:59

4 Answers 4

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If your advisor essentially scooped you and published the results on their own, then you and your advisor have much deeper issues in your working relationship than this paper.

In reality, I imagine that your advisor does consider you a key contributor to the paper. When collaborating on a project, it's not uncommon for one of the collaborators to have a key insight -- but often that insight is only possible after months of working closely together trying approaches that do not work, making partial progress, and learning from these experiences. It often becomes very difficult (and pointless) to really decide who contributed what. Additionally, there are many "routine" tasks that need to be completed in any project that you can contribute to, such as filling in the details of the argument, carefully writing and editing drafts of a manuscript, making suggestions on how best to present the ideas, and so on.

I also would not feel awkward about simply asking your advisor about this. It's completely within your rights as a researcher to ask for clarity about plans for publication of the work you are doing. And it would be quite a poor advisor indeed who did not have some picture in mind of what publications their students were involved with.

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As your advisor is partly responsible for the success of your thesis, there is nothing awkward about discussing what work would you be presenting as a part of it.

But now it seems a bit early for that. Do not count your chickens before they hatch; you should be a co-author on the paper, but the story with this proof does not end there. Indeed, the results and ideas are bound to be connected to some other interesting problems, and being able to recognize these new problems and approaches is a big part of your education as a PhD student.

In other words, "I obtain proof of this theorem all by myself or I will get no PhD" is not a great approach overall. It is perfectly normal to only make a little dent in a bigger problem, to collaborate, to present a collection of smaller results as your thesis. You do not have to be unethical and lie about personal contributions; it should work out without that. And, again, there is nothing wrong in seeking advice on further research direction from your advisor - the clue is right there in the name ;)

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I imagine this problem is a subset of an even larger problem, and that larger problem is going to form the bulk of your thesis / paper. If so, then you'll still be able to include the result in any publication, and you'll still be an author (the only author in fact if it's your thesis), but your advisor will be a co-author (they almost surely already are going to be a co-author anyway).

Even if the problem is large enough that it can be a paper on its own, you'll still likely be a co-author because as you wrote, "Earlier I had some idea which seemed to be working, but few days back we found some gap in that idea." It's not that you didn't do anything.

Finally, there's a decent chance your advisor will solve some but not all of the problem, and leave you to fill in the gaps. If so, then you'll be at least a coauthor - your advisor might even argue you should be the first author.

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My answer here is intended only as an addition to the insightful answer already given by @Allure.

During the course of my own PhD, I worked with a colleague (here called Q for convenience) of my supervisor. I had collected a large body of empirical results concerning a particular perceptual phenomenon. Q is/was exceptionally experienced at the development of mathematical models to describe perceptual phenomena. I worked together with Q, largely as a provider of the empirical data for, and verifier of, the model. The model was ultimately discussed in one of the chapters of my thesis, and presented in detail in an appendix.

Critically, at the beginning of the thesis, where the declaration of originality was required by my university, I explained that the model was essentially developed by Q with some contributions from me. The model forms a very useful part of the thesis ... but the thesis itself was substantially more than the model. Moreover, just as with the thesis, the model formed a part of a larger peer-reviewed publication on which Q and my supervisor argued (as @Allure commented!) that I should be first author.

As @Allure also remarks, no matter the problem your supervisor is working on, and might solve, it almost certainly a subset of a larger problem, just as the model development represented only one part of the research in which I was engaged. There are likely to be many more reasons to be delighted than to be despondent.

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