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I'm doing my PhD in mathematics (Germany) for four years, and I have agreed with my supervisor that I should finish within the next half a year.

I am not very confident that this is a realistic perspective. I have worked on various things in the past four years but have hardly been successful in any of these endeavours. Apart from actually developing results, it was already hard to find good questions to work on. My supervisor has made it clear that it's not his role to help me find good problems to work on.

Anyway, I have been working on a particular project for three years. I have some results, but I would them deem quite disappointing for the time I invested. The project involved some algorithmic developments, which ate most of the time; but certainly, no one will award me any degree for having developed and implemented some algorithm that's neither particular efficient, nor particularly interesting, nor about which any theoretical properties I can prove. To summarize, my results are very, very weak (I'd say much less in mathematics than what I did in my Master's).

Thus, I'm constantly asking myself: "what could I write my thesis about then?"

When I approach my supervisor and tell him that I don't estimate my results by any means sufficient for graduation, he tells me to stay confident and to continue working on my project. I have started suspecting that telling me to stay confident is just the way of least resistance for him, which allows him to avoid an uncomfortable discussion.

I already noticed that my sleep quality, ability to concentrate, to enjoy pleasant moments or to optimistically look into the future have drastically deteriorated, and I am asking myself almost every day: "what could life look like when I actually have failed?"

How could I deal with the situation?

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    Unfortunately, we outsiders cannot really assess whether you are dealing with imposter syndrome or are actually not accomplishing things. The person best equipped to make that assessment is your supervisor. An honest conversation with them about your doubts as to whether you have gotten ~85% of the way through a PhD-worthy project is in order. In general PhD students have a tendency to overestimate how profound a thesis really needs to be, but that's not an absolute truth.
    – Ian
    Apr 27 at 16:34
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    (Cont.) Context from who's saying this: I dropped out of a (US) math PhD program after a total of 9.5 years (counting leaves of absence) this year. I heard a lot of this "you're just dealing with imposter syndrome" along the way to this outcome, and I deeply resent that.
    – Ian
    Apr 27 at 16:34
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    "My supervisor has made clear that it's not his role to help my find good problems to work on." Welcome to German academia.
    – Sascha
    Apr 27 at 18:03
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    @Ian - that is a very valuable perspective; please put it in the answer box!
    – cag51
    Apr 27 at 22:25
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    @Ian I don't come to this Q&A that much, but I've still noted that the imposter syndrome lever is pulled very early and often. Also at Workplace stack, where it's the new season's 'XY problem' 🙄. Anyway, it's refreshing to hear someone call it out. Hopefully enduring for all those years has given you some helpful insight to the world beyond just your PHD topic 😐 Apr 27 at 23:18

12 Answers 12

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I am a pure mathematician, and I have to say that I am perplexed about your supervisor's attitude to finding problems to work on -- I would have said that suggesting good projects is one of the primary functions of a PhD supervisor. As a PhD student in pure maths, it is challenging to judge what an interesting problem even is.

At the very least, your supervisor should constructively discuss your own project ideas in terms of how interesting/useful they are to the wider maths community. They need to critique and engage with your work -- just telling you "keep going, eventually you'll get something" without actual advice sounds like they're not doing their job at all. In my view, that is not OK! (Doesn't mean it's not still quite common, unfortunately.)

If your supervisor is unwilling to have an honest discussion about the state of your work, and not willing to help you, I would suggest talking to some other faculty member you trust. Does the department have an ombuds person to approach? Usually there should be a specific person that you're meant to talk to in order to discuss problems with your PhD progress in general and your supervisor in particular. If there is not, is there anyone you would trust with this discussion?

Hopefully such a discussion would open a way forward; this could for example entail:

  • Writing up all the separate projects you've worked on so far, tying up some loose ends, leading to a satisfactory thesis,
  • (If you have a bit more time:) Becoming a visiting student with a different professor (at a different institution) and doing a better-supervised project there to round out your PhD work,
  • or, if it comes to the worst, cutting your losses and jumping ship (I think this should be the last resort, unless you're desperately unhappy and sick of everything).

Which of these are reasonable or feasible is difficult to judge without knowing the details.

(I found myself in a somewhat similar unmoored position after 2 years of PhD in the UK -- I had one smallish publishable project at that point -- and got my PhD to a satisfactory conclusion by going abroad for 7 months to visit someone who was working on what interested me most. He ended up being an amazing unofficial supervisor; so far the mentor I've learned most from in my career.)

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    Fully agree: my first advise to any student whose PhD advisor tells them that it's not their responsibility to find good problems to work on would be to change the advisor. It's not their responsibility to solve those problems, but it's exactly their primary responsibility to find problems that are both interesting and solvable for their students.
    – Iiro Ullin
    Apr 28 at 5:23
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    Many professors throughout the world have this style of advising (if it helps I am in pure math as well). I personally find it extremely demanding of the students, but not completely unreasonable - it does tend to produce people that are more self-sufficient at the end of the phd, and of course the advisor should always help the student to refine the questions they are asking, if not to produce them. Apr 28 at 11:39
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    @Charlotte Glad it worked out for you. I also feel that supervision is very poor and irresponsible - almost mentally cruel.
    – Trunk
    Apr 28 at 14:55
  • ...and got my PhD to a satisfactory conclusion by going abroad for 7 months to visit someone who was working on what interested me most. Most people would not even think of imposing on another uni's staff so you were not only bold in doing this but bloody lucky to get anything from it. To say the least it is an unreproducible option for most.
    – Trunk
    May 7 at 11:55
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    I don't think it's that rare -- the uni I went to had a whole official programme for visiting students, and I in fact know plenty of other people who went to a different university to work with a different supervisor for part of their PhD, and obtained funding to do so (It wasn't free in my case either; I had a grant to pay for the fees). Of course I am very thankful to my supervisor there for taking me on, but he is not the only one by a long shot. I was introduced to him by my original supervisor, though, and I had another professor as a reference.
    – Charlotte
    May 8 at 23:36
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Health issues, including burnout, should be handled by a health professional. Most larger universities (I hope) have an office where you can connect.

But, for pure math, there is a skill that you need to develop. I assume you are working on real and serious problems or you wouldn't be getting stalled. True research results can't be scheduled. You can schedule work time, but not a finish point. You are working with the unknown and it remains unknown until you have some breakthrough, often just serendipitous, when insight finally (possibly after decades) finally strikes.

Doctoral research exhibits a three bears aspect. Some problems are too hard to do in the limited time. Some problems are too easy and have no significance. Others are "just right" and you can come to some significant results and finish.

I worked on all three types. The first was too easy and I was able to develop proved theorems every day. I gave it up after a couple of weeks after talking to my advisor. It was fun, but had no real significance.

The next problem was too hard and I couldn't begin to crack the titanium-like shell around it. Very frustrating. No insight. Gave that one up also, luckily.

The third problem was "just right" and I developed some very nice results over about a year. Process was steady, but not easy. Insight came. The dissertation was quite impressive (so some other faculty members said).

The trick is to know when to give up a problem. Put the hardest ones in the "future work" folder and maybe return to them when you have a secure position and no limited time scale.

Math is just like that. Some other fields likewise. But the unknown is, by its nature, unknown, perhaps in surprising ways.

I think Einstein worked for about ten years to come up with the insights leading to special relativity.

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    +1. Minor clarification about a tangential point: probably you mean that Einstein worked for about 10 years on general relativity (there were 10 years between the 1905 paper on special relativity on the 1915 one on general relativity, and it did not take 10 years to write the special relativity paper).
    – Andrew
    Apr 27 at 20:51
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    @Andrew, no, I intended special relativity. He started thinking about the speed of light around 1895. Discussed it with a few others, seeking insight.
    – Buffy
    Apr 27 at 21:40
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From my comments on the question, at @cag51's suggestion:

Unfortunately, we outsiders cannot really assess whether you are dealing with imposter syndrome or are actually not accomplishing things. The person best equipped to make that assessment is your supervisor. An honest conversation with them about your doubts as to whether you have gotten ~85% of the way through a PhD-worthy project is in order. In general PhD students have a tendency to overestimate how profound a thesis really needs to be, but that's not an absolute truth.

To give you some context about the person saying this, I dropped out of a (US) math PhD program after a total of 9.5 years (counting leaves of absence) this year. I heard comments to the effect of "you're just dealing with imposter syndrome" many times along the way to this outcome, and I deeply resent that.

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Given what I know about German math PhD programs, your PhD advisor is probably supporting you financially as a PhD student (correct me if I am mistaken here). If so, most likely, you will have to finish within half a year from now if they say so. Given that it takes substantial time just to write results of a dissertation, you simply do not have time for new substantial results. Unless you already have done so, my suggestion is:

Ask your advisor for a meeting during which you explain what you have done in your projects and ask directly if they (your advisor) think that this is enough for a PhD thesis (in their opinion). If "yes," then start writing no matter how unhappy you are with the results. If "no," ask how far are these results from a PhD thesis and what else needs to be accomplished. If the gap is small and you feel that you can bridge it within the next half a year, then work on both: Writing your current results and working on bridging the gap. If what they describe is enormous, then ask how you can possibly finish the work in the next 6 months.

A bit more specifically, since the main outcome of your work appears to be an algorithm, then much of your thesis will be a detailed description of the algorithm and explanation why it works, plus some theoretical background. Additionally, if there are competing algorithms, then discuss these and explain the difference, including advantages and disadvantages of the one that you came up with. The rest will be a computer code and maybe some examples of applications. (I saw such PhD dissertations, about 100 pages long, in my area of math.)

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I think it's clear from the OP that the supervisor is one of these people who feel uncomfortable having to actively supervise and just ducks out of all serious discussions on it.

There is no point in speculating here on why this is so - we have to advise you on what to do. The programme has been ongoing for 4 years now and you estimate that you has no more than the equivalent of a weak M.Sc. right now.

There is no more time for risking. I think you must go to his Head of Department and discuss a change to a more active and engaging supervisor as soon as possible.

EDIT

I note from some of your previous questions on this forum going back to 2019 that you have had a problem with this supervisor almost from the start. It should not have come to this - I mean you should not have left it go so far. I say this as someone who was in a similar situation. But better late than never - you have to rid yourself of this supervisor. Finding a fruitful topic can only get easier after doing this, I feel, since this guy is psycho-emotionally toxic to you.

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I felt the same way although I was in physics, not maths. So I think it is relatively normal and part of the process. A PhD is training in research after all. Since you seem at odds with your supervisor's opinion I think seeking the advice of a trusted 3rd party might help. Here 'trusted' would look like: someone who understands the field, who you trust the opinion of and someone who knows you at least a little.

I would also perhaps look for some guidance from your institutions welfare section - all counselling / well being people would say it is better to chat early. It can be so helpful to chat things through with someone not academic

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Someone much brighter once taught me (by example) that finding the right problem to solve is more important than finding the right solution.

30 years ago, I started a Phd that I dropped out of 4 years later because I was in a similar position to yourself. Strangely, I saw some people who I wouldn't trust to tie their own shoelaces get PhDs faster than those brighter than me, leading me to suspect there is a good amount of luck involved (or the department just wanted to be rid of them).

After I left, I got a job in my field, made new friends, and otherwise got on with my life. It turns out that I didn't need a few extra letters after my name to have a meaningful existence.

If you decide to quit the PhD program, its not the end of your story, its just the start of a new chapter taking place in a much bigger world.

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  • Interestingly, exactly same experience and now I live much much happier in comparison to when I was a PhD student. May 4 at 18:10
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You don't need interesting results to receive a PhD, just novel.

I think you are creating an unrealistic picture of a PhD in your head. Your PhD work does not need to be impressive in relevance, importance, interesting-ness, cool-ness, or anything like that. It just has to be:

  • Novel, if only a tiny bit (you can't only reproduce an existing study and leave it at that)
  • Follow the scientific method (for applicable disciplines)
  • Described in the dissertation (says nothing about papers)
  • Presented in a defense (says nothing about conferences)

Now obviously doing your PhD work in one area may end up being more useful than another, after finishing the PhD. For graduating per se, it is irrelevant. Or rather, at early stages (like qualifying exams) schools block research areas that are not suitable for graduation. So if you've been approved to work on that topic, you can rest assured that your school considers it acceptable for graduation.

The big question here is, how do you know that your work is sufficient for graduating? This would be a tough question, had your advisor not already told you (by saying you should graduate) that it is sufficient.

There is a separate matter of how you will get a job after your PhD, or what else you will do. But that's outside the scope of this question. However, in some sense, your advisor is not obligated to sustain you indefinitely as a student until you find the perfect job.

You should go to your advisor and tell him you'd like to start a thesis. Ask him for help with the outline. What should the major chapters be? Should all of your results be described in one part, or should there be multiple parts (each with its own intro/method/result/discussion sections)? Which one should come first? What are some past dissertations he can suggest to you as an example?

That will probably give you a good idea. Then try to start writing something - anything. Even just a table of contents or final concluding page of the thesis. If all else fails, you can start writing up the methods sections for things you've already done. Show this to your advisor and ask what to add next. Rinse and repeat.

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A PhD advisor has several functions, but the most important is setting standards for the candidate (and hence also for himself). It's his responsibility to decide whether the results are sufficient for a PhD. My advice is: don't barricade behind a mistake, i.e. wrap up what you've done and let your advisor take responsibility and decide whether your work is enough. After you've got your certificate, you can use it as toilet paper if you wish, but in any case it will be a closed chapter and you'll be free to move on with your life.

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  • But what he's got now isn't enough for a decent Masters, let alone a doctorate. Besides, doing that leaves the blame on himself rather than the supervisor - which will enable the supervisor to carry on acting as he does. What kind of advice is that?
    – Trunk
    Apr 30 at 22:08
  • @Trunk Who's saying that's not enough? That's for the advisor to decide. Blame? Which blame? My advice above is to let the advisor take the responsibility for setting and enforcing standards. May 1 at 16:08
  • Suppose supervisor says he's got enough done - even though he knows it's not. External examiner comes and cuts OP's thesis to ribbons. Supervisor stands pat. External examiner now takes the blame for OP's failure.
    – Trunk
    May 1 at 16:33
  • @Trunk I see "a priori" no reason why the external examiner should cut anything to ribbons. Fear is always a lousy partner. Play all the cards you've got as skilfully as you can and look forward to success. May 1 at 16:58
  • Only card OP has is the ability to change supervisor. If he reneges on playing this, he will have no card to play soon. No college will entertain applications to change a supervisor after the thesis is submitted - or close to submission time.
    – Trunk
    May 1 at 19:40
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I have watched several very successful (at the end) PhD graduate students both in my and other places over the last 24 years. Each of them worked on one project up to the last few months, produced very little (their afvisos knew it and complained to me) and then suddenly got great result. So this dynamics is not uncommon. Perhaps your advisor's suggestion is not that bad?

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Somewhat lateral input maybe but hopefully useful (from someone who had a similar, but seemingly smaller-scale struggle with his own doctorate thirty years ago).

  1. This is the advice I now give anyone doing research: "write the conclusions you think you want first". You can then decide with everything you're doing whether it (a) supports one of your draft conclusions; (b) refutes one of your draft conclusions (which is also interesting, and you can just add the word "not" ); (c) neither supports nor refutes any of your draft conclusions (in which case, stop doing it- it's a waste of time, or, if interesting, something you can put in a section about suggestions for further research in the area). The point is, this will help you focus, which is absolutely essential to finish in a finite time.
  2. Use a large piece of paper, whiteboard, post-it notes, mind map or whatever, to assemble everything you think you have researched and found. It's quite possible that you will, from a few feet back, spot a jewel you hadn't noticed. (In any case the exercise will help with drawing up the conclusion list.)
  3. Be encouraged by the fact that even if you're not finding anything earth-shattering, if you have done sufficient diligent research, you are making a contribution by researching and documenting something that doesn't work. That is in itself valuable to other workers in the field!
  4. In the end, it's down to you, both whether you decide to pursue it (in which case, do so whole-heartedly) or abandon it (in which case you must reconcile yourself to that decision, to avoid future regrets). One of my friends and colleagues rightly described a doctorate as "a licence to drive" - which partly entails suggesting new areas of research yourself (rather than being dependent on a supervisor).
  5. Assuming you do decide to finish (maybe in spite of your supervisor), and sort your draft conclusions out to achieve, then to get finished in a finite time, you could do what the same friend did: made a deal with himself that if he wrote a page of his thesis in a day, he could go boozing that evening. There wasn't a single day he didn't get drunk :-) Good luck
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In my opinion, changing supervisor will work definitely. You can prepare a report on what you have done up to now, and negotiate with other professors preferably outside of "Germany".

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    Changing supervisor and country four years into the doctoral studies probably means starting over and losing a lot of time. And there is absolutely no reason to suggest leaving Germany, or to put Germany in quotes.
    – wimi
    Apr 29 at 18:20

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