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Warning: Extremely long post. Not really even the full story but one must stop somewhere.

My problem is the following:

I am a pure mathematics PhD student in (a remote part of) Europe and am part of a Doctoral Programme, which means that financially I am in a good position (relative to other grad students anyway). This is the same university in which I completed my undergraduate education. I was chosen together with a handful of other applicants from a pool of over hundred candidates (all natural scientists, not just mathematicians). I'm on my first year.

During my stay I have struggled to find a suitable problem (In fact I have overheard graduate students leave work early in my university because the feel that they didn't have much to work on). Basically my supervisor suggested some problems, I didn't like them, I tried desperately to invent my own problems to fill the void and to find something in the intersection of my interests and my supervisor's interests (and expertise). I realize now that with many of those problems neither I or my supervisor could really judge whether the problem was good or not (or whether it was known or not). During the summer the possibility that this arrangement is nonsensical started to dawn on me and I started to wonder if I should just consider moving to another university in another country to do a PhD.

My interests have sharpened and shifted somewhat during my stay as I got a better understanding of the current state of the field. On a couple of occasions I tried to tell him about my interests. Quite recently my supervisor told me that I need to start working on something and offered some problems that I didn't care about. Inspired by some advice of Sir Michael Atiyah ("Advice to a young mathematician") and AMS blog post "Tips for New Grad Students" I brought up the possibility of changing supervisor/university/country. He was certainly not relieved, and was concerned about the reputation of his research group, among other things.

I have discussed my concerns with doctoral programme coordinator and the person in charge of the PhD studies in our faculty. I am considered extremely fortunate to be part of the doctoral programme and losing a student would be unfortunate for the faculty. Changing supervisors or universities is something that doesn't generally happen here.

To an outsider the differences between my interests and my supervisor's would probably appear like splitting hairs. Indeed this is the position of my supervisor. The topics are likely to be outside of his expertise. He has offered to study together some of the subjects that I am interested in and to later study abroad with a more knowledgeable professor (the supervisor does have connections). He claims he will eventually find suitable problems if we study the topic together. Basically I envy students who get to study in a big active university or get to work with a guru who dispenses expertise and problems matching students' interests. I would be glad if I was offered even a low hanging fruit problem if it at least would teach me something in a modern and interesting field. It seems backwards to me that to learn a field together with the supervisor, instead of learning the stuff from the supervisor.

Our relationship has suffered as a result of this debacle. I think he is frustrated about my doubts.

So should I: Go seek the frontier where the actions seems to be (I believe the things that interest me are being actively studied):

Pro: Potentially more efficient and stimulating PhD experience.

Pro: Potentially more prestigious university and/or supervisor.

Con: Changing universities is risky, the fact that I got funding in one university doesn't mean I will get it elsewhere, etc.

Stay where I am and try to make it work:

Pro: Safe in the short term.

Con: Uncertain if I will get suitable problems and sufficient knowledge to tackle such problems and continue a career in research.

Con: I have learned that people doing their undergraduate and graduate studies in the same university do less well.

Con: The track record of the supervisor to get PhDs to good places is not great.

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    "It seems backwards to me that to learn a field together with the supervisor, instead of learning the stuff from the supervisor." - Nope. That is exactly how it's supposed to work. – ff524 Sep 28 '14 at 19:40
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    In that case I must be have been seriously mistaken. Is it not the case however that to pose a problem one ought to have good grounding in that field? At the very least to reduce the risk of doing work that has already been done. – user22341 Sep 28 '14 at 20:03
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    He was certainly not relieved, and was concerned about the reputation of his research group, among other thingsSo what? Always remember that this is your PhD, not your advisor's or your department's. Your first priority should be your own success, not your advisor's or your department's. – JeffE Sep 29 '14 at 2:02
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    it not the case however that to pose a problem one ought to have good grounding in that field?Absolutely not! Anyone can ask questions. On the other hand, if you want any hope of solving a problem, or even determining whether the problem open, you probably need a good grounding in the field. On the gripping hand, trying to solve an unfamiliar problem, whether it's actually open or not, is excellent motivation for grounding yourself in a field. – JeffE Sep 29 '14 at 14:28
  • "neither I or my supervisor could really judge whether the problem was good or not" - that is really important to understand. – user14102 Apr 28 '15 at 6:36
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First of all I agree with @Pete L. Clack's answer. Changing supervisors is not the end of the world, it happens all the time and it is your right to do so. But the question you should ask yourself is why should you change?

I assume that your supervisor is an expert on the "great" math area you want to focus on, otherwise you would not have chosen him. By that assumption, expecting your supervisor to spoon-feed you a specific problem that you will like 100% and all you have to do is just solve it and get a PHD is an unrealistic goal in any PHD program. Supervisors suggest possible problems or usually specific scientific areas to focus on, close to their expertise. Then the problem is gradually refined as time goes by, as the student works intensively on the suggested area. This is a gradual process that does not happen magically overtime. In that sense, you cannot simply dismiss ideas (ideas are hard to come by) without sufficient knowledge of the research area ("could not really judge whether the problem was good or not") for some vague idea on what you want to do, without actually be able to judge if the problem you are suggesting has any merit or not. Choosing a problem is something that needs research maturity which frankly you do not have. At least in your first year of a PHD, you should trust others (your supervisor) to "show" you the way. You should at least start by his suggestions, do the required research literature search, get a firm grasp on the problems he is suggesting and not just "brush them off", because "you do not like them".

Note that your supervisor also seems like a nice guy, who is willing to study more on a area he is not familiar with, to help you. Not many professors a) admit their lack of knowledge on a subject b) go this far to help an inexperienced student like you. And believe me, this is an important quality for any supervisor. Also, lack of knowledge on a tiny area now, does not mean that when he actually does his "homework", he will not be able to guide you towards the new area. Professors and researchers change directions and progressively expand to areas less familiar to them when they "run out" of problems on their main expertise and this also something that happens quite a lot.

So, I suggest caution. Your funding is good, your supervisor seems nice, your university / department is reputable. Do not blow them all away for a mislead ambition on what problem you consider important or not. You can always walk away but you do not need to do it now, before you examine your options carefully.

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    This x1000. "I envy students who get to study in a big active university or get to work with a guru who dispenses expertise and problems matching students' interests." - this is a completely unrealistic picture of PhD research. – ff524 Sep 28 '14 at 19:39
  • It might be that I'm unrealistic, and it is certainly reasonable that a supervisor would prefer to supervise research close to their expertise. The way I got study with him is that I studied under him during my undergraduate years and made a Master's thesis for him. In our research plan we deliberately left things a bit open, but now I realize that it might have been better if we would have been more specific about what kind of research we should pursue. If I had to choose a supervisor again I would base my topic closer on the supervisor's recent publications and supervised theses. – user22341 Sep 28 '14 at 20:01
  • On the suggested problems: It is true that I do not necessarily have the maturity to judge good research problems. When I said "I don't like them" I suppose what I meant by that is that the I didn't feel a great sense of "aim" in the general research program. I would do routine problems if I felt that I would learn useful tools in the process. – user22341 Sep 28 '14 at 20:17
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I don't really know your situation, so this is just a first impression but: slow down. Take a breath. You're describing frustrations with things not working out...but you're still in your first year of the PhD program. Where I come from, students find advisors and problems much more gradually than this. If you were given problems "quite recently", then how do you know you don't care about them? If you don't care about the problems suggested to you because you have your own problems that you want to work on: find out if your own problems are viable, and if so find out who can help you with them. But if you don't have anything else you're dying to work on, I'm tempted to say: spend at least a month or two working on every problem your advisor gives you before you decide it's not for you. Why be so picky?

However, if you feel sure that you are not interested in anything your advisor is doing, then...sure, go study with someone else. The "reputation of the research group" is not really a sensible thing to be worrying about at this stage. Look, I went to (what is, along with a few others) the top PhD program in mathematics in the US. Nevertheless in the five years that I was there I watched students: (i) drop out of graduate school entirely, (ii) switch to a math PhD program in a different university and/or country, (iii) switch to a different department at my university, (iv) switch fields and/or advisors within my math PhD program. I never heard a peep about any of this damaging the reputation of the department or the university. People change programs all the time. Someone who is telling you otherwise may not be looking out for your best interests...

Added: Maybe my answer is US-centric. Other questions and answers on this site have suggested that European academia may be less flexible on these matters. If so: maybe consider going to school in the US. In every US PhD program in mathematics I know about, you apply to the program as a whole rather than to any research group or to officially work under any one faculty member. Then you have a period of 1-3 years to find your footing, pass some general qualifying exams and decide who you want to work with and then more time to decide what you want to do for your thesis. The whole process can take longer than in Europe, but in your case it sounds like you would find it more pleasant than your current situation.

  • Maybe I was a bit unclear. I have been a PhD student for 9 months (started January). Problems have been suggested the whole time. Only recently the supervisor told me that I am his responsibility and if I don't have any work done at the end of the year that would be bad. He was very sceptical of some of my own problems. – user22341 Sep 28 '14 at 19:49
  • @PeteLClark Yes, there are a lot of differences in PhD programs between US and Europe (as there are within Europe). For instance, in Italy PhD programs have a fixed duration of three years; moreover, the topic is chosen by the advisor at the beginning of the period and it's not so easy to change it. Changing the advisor is even more complicated, although it can happen. Interaction between advisors and students, however, seems more close here than in US. – Massimo Ortolano Sep 28 '14 at 19:54
  • As for slowing down, I would like to be careful and considerate and take my time to figure out how to proceed. In contrast my supervisor seemed to me more impatient: he suggested that the students who are more certain about wanting to part of the doctoral programme may deserve it more than I do. I think he expects fast decisions (others in the university in the know want us to take our time to figure things out). – user22341 Sep 28 '14 at 20:46
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    @LostSoul: I was guessing that you started in January, yes. (Otherwise you would have started in the fall semester, and your question wouldn't make much sense.) "As for slowing down, I would like to be careful and considerate and take my time to figure out how to proceed". Sounds great. About your advisor: I am wary of criticizing people secondhand, but given only the picture you are painting, it doesn't sound like you are the best match. If he's pushing you in a direction that you don't want to go, then...don't go. Europe consists of "free countries" just like the US. :) – Pete L. Clark Sep 28 '14 at 20:49
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    @Massimo: Thanks, that squares with other information I've heard. It may indeed not be possible for the OP to continue in his program with a different problem and/or advisor. But what I'm saying is: he certainly can leave if he wants to, and if his departure actually makes the entire research group crumble, that's an unfortunate infrastructural issue that is no longer his problem. A worldwide blackball is probably not going to ensue. – Pete L. Clark Sep 28 '14 at 20:51
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The most important thing is to have great communication with your supervisor. More than just "we talk respectfully to each other" - you need to feel backed up and supported and understood by your supervisor. You need rapport.

If you don't have this, even at the beginning when everything is easy, then you are on a trip for disaster later as things get harder.

Reading between the lines, my sense is that this important rapport is not there.

If it seems hard to change now, wait till 2 years down the track when you discover just how poorly understood you are by your supervisor.

However, before you decide if this means you should change supervisor, you need to assess where the gap is. Maybe you need to change you?

Some of your statements are a little worrying.

It seems backwards to me that to learn a field together with the supervisor, instead of learning the stuff from the supervisor.

What is is that you think you will be learning? In your PhD you are learning how to do research. It is an apprenticeship, not a life work. It's your first, not your last.

You will be learning from your supervisor how to do research. Together with your supervisor, you will be learning about some small new element in a field of interest, in the process.

He has offered to study together some of the subjects that I am interested in and to later study abroad with a more knowledgeable professor (the supervisor does have connections).

On the face of it, this is a generous offer. Can you look back at it and see if this generous person might actually be a good partner ... or whether in fact he's making this offer only to try to save face from losing you?

This is the crux of it, in a way. If you can appraise the difference, you will be able to make the right decision.

Basically I envy students who get to study in a big active university or get to work with a guru who dispenses expertise and problems matching students' interests.

This would be a bad reason to change. The grass is always greener on the other side - you have no idea what debarcles all those folk are dealing with!

Priority #1: establish whether you can have rapport with your supervisor, take it from there.

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For what it is worth....

y experience also supports the idea that professors and programs are more flexible in the U.S. After working in academia with a Master's degree in the U.S. and now working on a PhD in Switzerland, I have experienced and heard about how much less flexible the professors in Europe are (mind you, there are exceptions on both sides of the Atlantic).

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Another thing, when you find a job, it is not always exactly what you wanted to do. It is difficult to find a job where you are happy all the time. I imagine as a post doc, you get to work with problems that you are not super excited about. Is it realistic to find a job where you are super happy and everything is fine? I doubt that? Life will always be like this; you will work with things you are not really interested in.

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    +1 for good explanation and caparison. – Enthusiastic Engineer Sep 29 '14 at 13:02
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    "Life will always be like this; you will work with things you are not really interested in." To my mind the whole point of an academic career is that you get to work with things that you are really interested in. (The trouble is that when you are starting out, it may take some time to find your interests.) Most postdocs in mathematics I know work only on problems they are super excited about. Are your experiences different? – Pete L. Clark Sep 29 '14 at 16:02

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