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This is a follow-up from Patching things up with advisor? He has been avoiding me since I found a simple answer to a problem he thought would be challenging

I'm a math PhD student in the western world. Last year, I solved a question that my advisor hadn't solved himself. This led to conflict between us, in which we he would tell me things like "solving this problem won't get you a job", "you should consider industry", etc.

I applied for postdocs independently, without substantial support from him. He did write me a recommendation though. I managed to generate interest from some top people in my field, and got a postdoc I wanted.

I recently again got a result that supersedes his previous work. This is related to the above problem as well. There are minor flaws that can be ironed out easily. My advisor magnified those errors, told me that it is all completely wrong and far from a solution, and told me to forget about this problem and do something completely outside of my current expertise. When I asked him if I should publish my results when I managed to iron out the flaws, he told me I should completely forget about it for now. He then suggested five different things I should do instead of this problem.

The troubling part is that my advisor first blurted out a way to iron out the tiny flaws. Then he went back on his own comment and said that this strategy would never work, and I should forget about it.

I don't trust my advisor's judgement anymore.

  1. Should I change advisors? This is the last semester of my PhD.

  2. Should I not publish these results? They are important, but not enough for the very top journals. However, publishing them will obviously destroy ties with my advisor forever.

  3. Should I completely change fields? This would reduce conflict with my advisor.

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    I'm assuming the post doc is for the future and that you haven't yet finished your doctorate. Is that correct?
    – Buffy
    Feb 7, 2023 at 15:51
  • @Buffy- Yes, that is correct. Feb 7, 2023 at 15:52
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    If it's easy to iron out the minor flaws, why don't you do that? Then, once these flaws are resolved, what does your advisor think?
    – Bryan Krause
    Feb 7, 2023 at 16:38
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    @BryanKrause- I am worried that my advisor will shout at me for focusing on this, instead of the things he told me. Feb 7, 2023 at 16:43

2 Answers 2

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My suggestion, if you can manage it is: to finish your degree as soon, and as simply as you can, and move on. You don't need to publish the "new" results at the moment, and will need to consider whether he has any authorship claim to the work or only an acknowledgement. You don't need Euler's permission to extend his work (or anyone's).

Develop an independent career, and new collaborative opportunities. Let referees judge the quality of the paper you submit, rather than depending on someone who may prioritize their own career over yours.

Once you finish the degree, Changing fields is sub-optimal at this moment, but future studies may lead naturally to that, as it might for anyone.

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  • Can I ask for insight on why he might be doing so? Is it because he simply dislikes me, or perhaps I am "eating" into his own work, and that is in some way dishonorable for his own student? Does he perhaps see me as a competitor for future grants? Feb 7, 2023 at 16:08
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    Any of those are possible, but none necessary. There is some chance he is correct in fact and that you should be doing other things. But the advice is the same. Get done and then you can make your own choices.
    – Buffy
    Feb 7, 2023 at 16:11
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    Relatedly, consider getting advice from other local professors and/or students to get more opinions. We on this site have very limited context.
    – eykanal
    Feb 7, 2023 at 16:41
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It's a difficult and unpleasant situation. Your current advisor's behavior is unusual, but I have seen this before (long time ago).

Here are my suggestions:

Postdocs (in math) normally start in August-September. Your dissertation defense is likely to be in May or during Summer. My suggestion is to start writing your paper (which supersedes your advisor's results) now. You do not need your advisor's permission to write one. I assume that you have enough results for your dissertation without that work. Writing takes time (including polishing the presentation). Since it is already February and you will be busy with finalizing your dissertation, chances are that you will not even finish writing before the Summer starts. After your thesis defense and after everything related to your degree is finalized, finish writing your paper, put it on the arXiv and send to a journal of your choice.

Caveat 1: arXiv requires an endorsement if you are not an established mathematician. However, given that you got your postdoc, chances are that you already have one or more papers posted, in which case you do not need an endorsement (which usually comes from your advisor). If this is your first arXiv submission, just submit to a journal and wait until your postdoc starts before putting the paper on the arXiv.

Caveat 2: If you are not 100% sure that your proofs are solid, after your defense send the paper to your postdoctoral advisor and ask for an input (before submitting the paper to arXiv or/and a journal).

After you have submitted the paper, email a copy to your current advisor, saying in in the email that you have managed to iron all the kinks in the proof, thanking for suggestions of future directions, all the help, etc. There is a chance that this will not help and you will have spoiled your relationship with PhD advisor forever. You still have your new postdoctoral advisor whom you will be asking for future recommendation letters (as well as other mathematicians in your area).

This situation is unpleasant but (I believe) it should not prevent you from publishing the results.

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    What happened to the PhD student in the case that you're referring to? Did they finally publish their result? Was there a fallout? Feb 7, 2023 at 19:46
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    @RyanHendricks: That case was a bit different. The student was not in his last year, did not apply for a postdoc. Instead, the student applied to a different PhD program in math, switched to a different area (not too far, but sufficiently different). Now, the student is a full professor. Feb 7, 2023 at 19:51

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