I am in the first half of my PhD (Pure Mathematics) in the U.S. In this period of time I've read all of my advisors papers (apart from the very early ones), discussed all of them with him, and improved on many of them. My advisor is great: he has been extremely helpful, he'd always read all my stuff, and I definitely learnt a lot from him. I think he also got something from me, since I was able to answer a conjecture and a couple of questions that he had formulated/thought about for quite some time.

However, I feel like I know all the stuff he does at this point: he has very little left to teach me, as I noticed in the last six months.

My current situation is not too bad, I am capable of finding my own projects and most of my publications are based on my own ideas (I have 10 preprints/publications), so I could just go on like this for 2-3 more years. However, I think it would be better for me to go somewhere else, to learn from some other mentor, maybe in some different but related field.

Indirect sentences make me believe that my advisor does not want me to leave, although I never asked him directly. Before I do so, I would like to hear your opinion (I understand that the information I gave is not exhaustive, but nevertheless...).

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    Can you stick with your advisor but start collaborating with other professors or researchers in your department? – littleO Dec 27 '18 at 13:56
  • This is a possibility. The problem is that even the professors closest (research-wise) to my advisor work in rather different subfields. I think I could do it, but I am not sure if it is the best use of my time. What do you think? – Santaro Dec 27 '18 at 14:14
  • Opinions are, well, opinion-based. We cannot say what you should do or what is best for you; only you can. It seems, however, that you are a successful PhD student, won't have any problem obtaining your PhD and continuing your career as a scientist. Your desire to learn more, from different people, is admirable. You don't need to be invited anywhere to work with other scientists. I guess you already know some names besides your advisor, maybe met them on a conference or a workshop. Reach out to them. Or ask your advisor to connect you with someone outside your uni. (...) – user68958 Dec 27 '18 at 15:05
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    (...) You can spend the remaining years of your PhD studies working on different topics than your thesis will be about. You can go to conferences and network. You might be able to visit some other institute for a week/month/semester. You need to either find out what are your options by yourself, ask your colleagues, or talk honestly with your advisor about your research path. – user68958 Dec 27 '18 at 15:07
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    If I were in your shoes, I would look for fellowships, grants to be a visiting scholar and working with other elite researchers, I don't know how is the situation in pure mathematics. The most important is making connections with well-established academic researchers in your field, but you must have a discussion with your supervisor, s(he) the only one can really optimize the coming years through fulfilling your thoughts and ideas how the next two years should be fruitful. – user39171 Dec 27 '18 at 15:30

If your professor really doesn't want you to leave, he needs to offer you a permanent position. It may be that keeping your association going would be good for you. But you need to leave the nest eventually and fly on your own.

But it sounds like you are in a good position to finish your doctorate early. I suggest that you do that, at least. Accelerate anywhere you can.

There is no reason that you can't explore a position elsewhere as you get closer to the end, to see what is on offer. It is good to have options.

To maximize your future, stay as helpful and cooperative as possible.

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  • My advisor said I am ready to graduate (I have been ready for a while actually). However, he suggested that I stay a bit longer in the program, so that I have done more stuff. I take it you disagree with this? – Santaro Dec 27 '18 at 13:15
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    I don't have all the details. Your funding may affect the decision. So might the state of the economy. But if you are ready, you should, at the very least, explore your options there and elsewhere. – Buffy Dec 27 '18 at 13:17
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    @Santaro Have you started asking around and applying for positions? Best time to to look for your next job is while you still have one. – Anyon Dec 27 '18 at 13:26
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    People seldom get invited. You've got to look, and ask. – Buffy Dec 27 '18 at 13:29
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    Another option to consider: you could spend a semester/year visiting another institution, while continuing your phd. – Federico Poloni Dec 27 '18 at 14:03

Push on out of there. You are a capable, independent researcher now. This is normal in second half of Ph.D. but happens at different speed for different people (some never get there). Write up your thesis and dump it on the committee.

Of course advisor wants to keep you since you are so productive now. But you need to do what is right for you. You have already done enough for the old man with the 10 coauthorships--lot better than the unpublished slugs. Go find new mountains to climb. Don't dawdle in grad school, if you are a superstar.

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