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I am a PhD student in pure math, now in my second year. I understand that different PhD supervisors have different levels of involvement with their students' projects, and I very much appreciate how engaged my supervisor is with what I am working on. However, there is something that concerns me regarding whether the input my supervisor has is appropriate.

He is mind-bogglingly quick and can sometimes outline proofs of new results during our meetings, which I then spend days making sense of, writing up properly in full detail, refining arguments where necessary etc. Sometimes he sends me notes via email containing unpublished results, with very little context. I do not ask him to do any of this, however I am very grateful for his help. Is this type of input unusual?

My main concern is that when writing up my thesis I may have to add in lots of disclaimers such as 'this proof has been communicated to me offline by...' to acknowledge that the original idea is not my own. Would this look really bad? Also, some of what he has sent me are results that I likely would have been able to do by myself given a bit more time, but I cannot demonstrate that now because he has beaten me to it.

Communicating my concerns to him is tricky because in my experience he does not respond well to questions unless they are of a strictly mathematical nature and I do not want to appear ungrateful for his efforts. Any suggestions or advice would be much appreciated.

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    "My main concern is that when writing up my thesis I may have to add in lots of disclaimers" - regarding this specific issue, will a stapler thesis be appropriate in your field/institution? In that case, most of the "meat" of the thesis consists of published or publishable manuscripts, which can be coauthored; you don't have to outline the specific history of every line of work in a coauthored paper, just cite it as "Student and Teacher, 2022".
    – Bryan Krause ♦
    Sep 16, 2022 at 15:00
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    @BryanKrause I'm not familiar with this type of thesis and am unsure if it is allowed in my department. My field is pure math and most PhD theses I have seen from my department are 50-100 page texts of as-yet unpublished material, although many students do end up making a research paper or two from the contents of their thesis afterwards.
    – Student
    Sep 16, 2022 at 15:10
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    @BryanKrause, stapled theses are uncommon in math.
    – Buffy
    Sep 16, 2022 at 15:11
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    @Buffy I'm mildly skeptical. Might depend on what area of math.
    – user137975
    Sep 17, 2022 at 0:58

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Yes, he is probably doing too much. Of course, he has more experience in the field than you do, so can see solutions more quickly. It is hard to say what to do, unless you think it would be safe to have a conversation and let him know that you need to struggle a bit more in order to improve your skills.

But, you could also set his suggestions aside and work on the problems/proofs/whatever yourself until you reach a conclusion and then review them.

My advisor was probably able to write my dissertation much more easily than I could and one of the major proofs in it was his, since it had the potential for expanding insight (my proof was more standard).

But, if he isn't trying to steal your thunder, then it really doesn't matter if he has a proof before you do, unless he publishes it. If he is doing his job properly and guiding you then you will be first to publish. It is, however, much better that it is your own work that gets explicitly represented in the dissertation. And other people, unknown to you both, might also have had those insights first but didn't act on it. (Note Newton's dispute with Leibniz.)

There is a story (apocryphal?) about a professor who was very arrogant who told a (suffering) student "I don't mind writing your dissertation for you, but I'll be damned if I'll explain it to you when I'm done." I don't suggest that this is the situation you are in, but have included it here to indicate things could be worse.

But you would be wise to spend the time to get to where he got to easily by setting aside many (most?) of his hints until you get through the crux. If I remember correctly after more than half a century that is what happened in my case. The professor provided a proof (and I read it) but I struggled to create my own proof as well.

In math, note that it is (still, I hope) uncommon for an advisor to be a co-author on a dissertation, and the work is considered to be your own. But you need to find a way to make it so.

"Doc, I'll never get to where you are if you give me too many hints. I need to struggle through this for my own insights. Thanks."

Good luck. You have the right attitude.

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  • This is very helpful, thank you. I certainly need to force a conversation with him regarding how much he is doing and whether this will cause problems in terms of excessive contribution to my thesis. Would I need to add footnotes acknowledging his contribution to each part or something less specific? He doesn't seem to be concerned about the balance of contributions himself, but nonetheless I definitely don't want to get in any trouble or get too much of an easy ride.
    – Student
    Sep 16, 2022 at 16:38
  • Could you elaborate a bit on "In math, note that it is [...] uncommon for an advisor to be a co-author on a dissertation"? I'm not sure whether I understand what you mean because I've never heard that an advisor could co-author a PhD dissertation (no matter in which field). On the author hand, I've often seen PhD students in math who write some papers with their advisors and some other papers without them.
    – Jochen Glueck
    Sep 16, 2022 at 19:34
  • @JochenGlueck, I gather from other questions here that it happens in other fields, especially when a stapled thesis is common.
    – Buffy
    Sep 16, 2022 at 19:47
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It depends what type of relationship you want! On the opposite, there are students who have no idea about how to do something, and of course, their supervisors also do not have any idea where to start.

I have seen way more of the last ones. So I would say that experience beats everything when there is a time related project that has an end: a PhD.

Do not worry about the thesis, accept the input, write, let him revise. His job is to help you to pass and if he actually checks your job, amazing! Some supervisors barely ask for progress, or are happy with everything they are shown because they do not know if it is correct or wrong. Better someone to tell you, that is a mistake.

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  • "Some supervisors barely ask for progress, or are happy with everything they are shown": in all cases I am familiar with, PhD's are assessed by someone other than the supervisor so I would have thought that the expectations of the assessor are more important than that of the supervisor.
    – Student
    Sep 17, 2022 at 12:09

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