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I am a graduate student in pure Mathematics. My supervisor gave me an idea to work on, and in 6-9 months I found enough stuff to write 3 papers. After I did that, I was eager to work on some new idea, but my advisor only gave me learning projects, so that I just read many papers without doing any sort of research. After 6 months, I would like to start a research project, but all this reading didn't really help me in finding one (of course I thought about questions on my own, but since the area is quite old and competitive, I was not able to find a reasonable question that was not already answered). My advisor still does not give me anything concrete to work on, but merely suggests to read this or that paper. All of this is very weird, because his other students are treated very differently, they all have projects that started from ideas of the supervisor, and some of them even publish with him!

I am quite desperate, because I get really anxious about wasting my limited time, and I would like to know what you think about this.

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    Three papers in pure maths in such a short period of time seems quite a high number. If these are short papers, perhaps your supervisor wishes you to learn more background and more context, so that your next bit of research can go deeper? But if these are substantial papers then I sympathise with your current frustrations
    – Yemon Choi
    Jul 15, 2018 at 20:48
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    One is very novel, one is a nice result that was overlooked but not technically difficult, one is less interesting.
    – Fuzuj
    Jul 16, 2018 at 2:16
  • Maybe he is afraid that if he gives you a problem you are not challenged by you will lose your respect or patience.
    – mathreadler
    Jul 16, 2018 at 19:15

4 Answers 4

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Now that you've written three papers, you've shown you can solve problems. But you still need to learn the other important side of research: coming up with problems to solve. We can't know your advisor's motives with certainty, but I would guess he expects you to spread your wings and become more independent. Instead of asking him for projects, I suggest coming to him with project ideas of your own, and asking what he thinks.

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    This. When I had a student who blew my expectations out of the water, I let him choose his project within the general subject area. He showed he could do it and letting him have that control gave him more motivation.
    – aeismail
    Jul 16, 2018 at 3:01
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You have already written 3 papers. This is a lot for a graduate student in pure mathematics. Although, technically speaking, you are still a graduate student, in terms of your research stage, you are already a postdoc. Hence your advisor is treating you like a postdoc.

As a general rule, in order for you to get a permanent position, you will have to formulate and solve some problem completely independently of your advisor. Your advisor thinks you have enough experience to start learning to do so.

If it turns out you can't develop the skills to be an independent researcher, it's probably best for you to find out earlier so that you can embark on a different career path.

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    Ouch. That last paragraph was pretty brutal. I think that most productive mathematicians don't actually work in isolation. They are surrounded by others who have good ideas and generate a lot of synergy within a department. Also, the OP has quite a lot invested already. I don't find it surprising that a doctoral student in math can't come up with a problem, especially in a well trodden field. While that is, indeed, the highest level of mathematical thinking, it takes time to develop - and a supportive environment.
    – Buffy
    Jul 16, 2018 at 1:28
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    @Buffy: The job market is pretty brutal.
    – Alexander Woo
    Jul 16, 2018 at 3:15
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    Downvoted for the last sentence. Nobody is born with the skills necessary to be an independent researcher. Yes, it's best to find out early which of the necessary skills you lack, but the appropriate response to finding those gaps is not to give up, but rather to develop the necessary skills, with the help of your advisor, since that is in fact their job.
    – JeffE
    Jul 16, 2018 at 10:07
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    By the way, I agree with your answer's first paragraphs. Don't take my objection as being general. The first paragraph, especially, was great advice.
    – Buffy
    Jul 16, 2018 at 12:27
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    @JeffE - Yes, it's true that by 'can't develop' I mean 'can't develop quickly enough to a high enough level', but given how utterly brutal the job market is in pure mathematics now (and it looks likely to keep getting worse - I think it's reasonable to believe my PhD-granting department has hired its last ever permanent faculty member with research responsibilities), 'quickly enough' and 'to a high enough level' are strong qualifiers. I don't think it's too essentialist to say that I could not have been an NBA player no matter how hard I worked and what training I got.
    – Alexander Woo
    Jul 17, 2018 at 2:20
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You should talk to your advisor about this. Some questions you might ask are “I’m excited to start a new research project, do you have any more concrete suggestions?” Or “When you read papers how do you go about finding concrete projects to work on?” Or “I don’t think I understand how reading papers leads to a research problem to work on.”

I’d also encourage you do go to talk to other people and go to conferences and try to develop collaborations. Once you have done one project with your advisor it’s good to start working with other people too.

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  • I would emphasize the second paragraph more. Getting a sense from many mentors about their idea generation process is probably useful.
    – Dawn
    Jul 16, 2018 at 15:56
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I can imagine several scenarios, but don't have much information here to go on. The most hopeful one is that it is just a communication mismatch, or a mismatch of expectations. The only way to solve that, I think, is directly by asking him for guidance to the end. If

If he treats other students differently it could be a variety of things. Hopefully he respects you and your abilities, but if not you have a serious problem. Is it that the other students are more advanced already? Or that they have worked with him for a long time?

Another possibility is that he is overextended in his own work and advising and you are just the one with the short straw. Finding a different advisor might be a solution to that, if you can find someone more compatible who works in a close enough field that you aren't set back too much. I've mentioned in answers to other questions that some junior faculty are working toward tenure themselves and don't have time to advise effectively.

A wild, and unlikely, scenario, is that he is afraid of your abilities. That is rare, but possible. The correct behavior on his part, if he sees you as a superstar eclipsing his own, would be to get you going and get out of your way. This is the Good Will Hunting scenario.

Another answer here is also possible, though not all doctoral students have yet made the transition of thinking deeply enough to come up with their own problem. It is the ideal, to be sure, but takes seasoning and maturing that not all students attain until they finish their degrees (I'm an example, actually).

You also mention working in a well worn subfield in which problems are just hard to come up with and results even more so. When a field of maths is new there is little known so a lot can be learned quite quickly. As the field matures it gets harder and harder and mathematics moves on to something newer, though not all mathematicians do so. This was exemplified in the switch from Classical Real Analysis to Functional Analysis fifty or so years ago.

I don't expect that I gave you an answer here, other than to try to talk to your advisor and improve communications, but hope I gave something to think about at least. Maybe one of them will lead to a solution.

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  • For sure I do not eclipse him, but his current students are definitely worse than I. I often help them with their work, and I am much more knowledgeable than them. I believe that he wants me to find my problem in his area, but as I said I think it is just too classical for me to find something reasonable. Thank you very much for your time.
    – Fuzuj
    Jul 15, 2018 at 21:08
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    Is there any possibility that you and the advisor and one or two other students can have one (or a few) brain-storming sessions in which you speculate, even quite wildly, about problems? If your department has a "coffee lounge" for faculty this can be quite informal. If it happens during "coffee time" it won't feel as burdensome as a formal meeting. The big question in math is always "What would it be nice to know if we could figure out how to know it?"
    – Buffy
    Jul 15, 2018 at 21:15
  • Other wild ideas. Do you share an activity. Do you both bicycle for exercise? Racketball, ... Anything informal. I used to mix with some faculty this way in grad school, though not my (very formal) advisor.
    – Buffy
    Jul 15, 2018 at 21:18
  • Ok, I understand your suggestion. I have a tendency of working on my own and only asking my advisor. I will try what you suggest, thank you.
    – Fuzuj
    Jul 16, 2018 at 1:59
  • @Fuzuj, excellent. Take full advantage of the synergy available in a math department through both formal and informal communication. Over time you learn to contribute more and more as well as to integrate ideas that come from different sub-fields than your own. Each field has "special ways of thinking" that help solve problems, but "out of left field" ideas can also tweak the brain into creativity.
    – Buffy
    Jul 16, 2018 at 12:31

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