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I am firm on the problem I want to work (with publications and arcticles to support, for which I have already done significant work)) and I'd like to know if there are any PhD programmes that accept students primarily based on research proposals? Especially in the fields of mathematics or machine learning theory. A google search couldn't give much results. I am interested to know any in the US and Europe.

Most of the universities in US do not seem to be interested in research proposals and they don't ask for it.

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    It's good that you know what you want to do. But that does not imply you need to use the research proposal you have been working on to get into a PhD program. Instead, identify which faculty you want to work with, then figure out what it takes to get them to supervise you. – Anonymous Physicist Nov 17 '19 at 4:45
  • You can state your research plans in a "statement of purpose" if a research proposal is not requested. – Anonymous Physicist Nov 17 '19 at 4:45
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If you are asking whether some university will accept you solely based on a research proposal, then I think the answer would be no. You might be able to find an exception of some university-proposal combination that would make it work, but that isn't how it works. Universities accept students into doctoral programs based on the evaluation of a set of criteria that suggest that the student has both the appropriate background and the likelihood of success in the program and thereafter.

Having a proposal is probably a plus, but, in the US, at least, it isn't required, as you note. It isn't likely even evaluated.

However, assuming that you have an appropriate background, then you might be able to find a professor somewhere, certainly in the EU and possibly in the US, who is willing to work with you to advance your entrance into a program. In some places, the professor is even an essential link. But the proposal alone isn't going to be sufficient. You will need to convince people, at a minimum, that you can succeed with that proposal and the result is likely to be sufficiently significant.

However, I think that being too committed to a particular proposal is likely to work against you, rather than in your favor. You need to find an advisor who is either hugely interested in that topic or willing to spend time advising and evaluating something that has less importance to them. Both of those reduce your chances. The latter is, perhaps, more likely than the former. Some professors are happy to have students who need little shepherding and who are self directed enough to get the job done. But I doubt that the majority of people work like that.

So, the bottom line is that you have a chance, but you probably need to be a bit more flexible and you need to attend to the qualities in your background that suggest success.

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  • In addition to this: you will work on what your thesis director wants you to work on, not on what you necessarily want to work on. If the two coincide then good, but it’s note a given. – ZeroTheHero Nov 17 '19 at 14:59
  • You certainly have enough there to be considered. Time away from academia might be an issue (small-ish). The fact that you have a proposal indicates seriousness. I would give you a look, myself, but not a shoo-in. But the actual research you do needs to be acceptable to some advisor and you might need to either move to something of joint interest, or search hard for a professor who is immediately interested in your proposal and wants to help guide it. I wouldn't be that professor, however. But that is just because my interests are elsewhere. Finding the university-advisor combination (more) – Buffy Dec 18 '19 at 13:24
  • will be the big problem unless you are willing to be flexible on the research. That would make it easier to find a position. Few students in the US work as independent researchers without an advisor's participation. But note that in math, "participation of the advisor" doesn't imply loss of control, nor does it imply joint authorship of the result. Participation means guidance, primarily. But the advisor needs to be interested. Caveat: A few "advisors" might be willing to get totally out of the way, but they still need to judge the work at the end. Best to work with them along the way. – Buffy Dec 18 '19 at 13:25
  • I meant it in a general sense. But I work in a rather specialized area (or three) in CS, no longer in math. But, I think your quest is worth pursuing, in any case. – Buffy Dec 18 '19 at 13:43

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