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I'm presently finishing up my undergraduate degree in Mathematics, and have written a number of papers, three of which have been published in reputable combinatorial journals (think journals published by Elsevier and Springer). From these three, I am the sole author on two of them.

Given that I have invested so much time and energy on 'extra curricular activities' (as my head of department calls them), can they serve as the basis to a PhD thesis? Which is to say, can a considerable part of a thesis consist of previous work which has not been used to obtain any other degree?

This final remark is important, I feel. A fourth paper with my supervisor is in the works, but the material presented there will appear in my undergraduate dissertation. I am then of the opinion that this material should not be used toward another degree.

If it helps, I attend a northern European university, and intend on doing a PhD in Europe/UK/USA.

Edit: I would like to perhaps mention the motivation for asking this question. I have heard stories of people doing research in their private capacity, then doing a PhD in quite a short period of time (a year or so), since they had a lot of material already. I cannot imagine this being the case however. What are your thoughts on this?

vertex
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    However, the situation is perhaps somewhat different. Looking at the edit history and replies to the question, the original author did not mean journal publications when mentioning research, but rather self-study on topics of interest and writing a literature review. – vertex Mar 11 '21 at 18:45
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    In the U.S., if you are admitted to a top-tier PhD program, to just use it to "cash in" your prior work would be a severe under-utilization of the resources of that program, I think, in any case. Comment? – paul garrett Mar 11 '21 at 18:46
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    @paulgarrett you make a valid point there. What sort of resources do you mean? I have a number of PhD student friends at my university, and in terms of resources they hardly have any. Of course, at top-tier universities, you would have access to some of the leading academics in a field, which cannot be underestimated -- that I understand. One reason why I asked was because sustaining myself abroad for 4 years is one thing, while for 2 years is another, in financial terms. I see finances to be a great hurdle which might actually hinder me from following a PhD program. – vertex Mar 11 '21 at 18:56
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    @vertex there are countries in Europe (from the top of my head, the Netherlands, Belgium, Germany; this is likely a non-exhaustive list) where PhD student is a paid job. If finances are a problem, have a look at those. –  Mar 11 '21 at 19:03
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    About money: in the U.S., in math, a PhD student should expect to be supported by a stipend, as well as having their tuition paid. Yes, possibly some teaching-assistant work, but with a little practice the latter is not onerous. True, you wouldn't be living in luxury, but also not going into terrible debt. So money (unless you have many dependents) should not be a decisive issue. – paul garrett Mar 11 '21 at 19:31

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I don't think this is impossible, but I doubt that many doctoral programs would permit it. Not zero, but not many. That is up to your university and an advisor.

You have published some papers which is good and will likely win you a slot at a good place, but there are "papers" and there are papers. If you have proof of some hundred year old conjecture that Erdős et al failed to prove then, sure.

But, since you seem to be good, I'd rather suggest that you spend the time it might take to earn a doctorate to do some even better work, ending up with a truly awesome CV and professors who will strongly support you in your career. I think that most places will still make you pass comprehensive exams, showing that your knowledge and skill isn't too narrow.

In the US, finances aren't a problem (unless you need to support a large family) as you will normally have a TA (or more likely an RA in your case) so that you get both a tuition waiver and a stipend.

But the early work you have done can certainly form the basis of what you will need to do for a dissertation. You might find the faculty of the right institution helpful in extending it, or not. But the experience would be a much more solid basis of a career than taking, what I think is a minimal path.

And, if you are as good as that then I'd think your path won't be all that long anyway. And the opportunity to get a bit of teaching experience as well will give you a better career base.

So, possible? Maybe. Advisable? Not so much.

Buffy
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  • Oh no, my work is definitely not of that calibre! I have published jointly with my supervisor, and they are very well respected in their field (they have worked with the likes of Harary etc). But I don't think this is very important, albeit it might play in my favour.

    I have read another comment which also stated that in the EU, many PhD programs take the form of a paid job. This is encouraging to hear and eases pressure from me re. finances. I enjoy what I do, so I don't actually mind a 4 year program. In fact, I'd rather stay a student for as long as possible :-)

    Many many thanks!

     – vertex Mar 11 '21 at 19:28
  • PS. I'm not counting on my publications for admission, only as a basis. I have a friend of mine who had a paper with the same supervisor before applying for a PhD abroad. The really top tier universities did not accept them after the second interview. So I'm definitely not betting on my work for admission. – vertex Mar 11 '21 at 19:31
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    My mathematical "ancestry" is pretty impressive, but that doesn't really reflect on me. And, since you bring it up, you have the disadvantage of people worrying about how much assistance you got from your supervisor. Better to prove yourself, I think, so that no doubts arise. – Buffy Mar 11 '21 at 19:32
  • Precisely, I agree with you completely. I worry about that sometimes, even if I know what my contributions actually are. Thanks for the good advice. – vertex Mar 11 '21 at 19:33
  • The US and EU (Germany, at least) have very different admissions criteria. Hard to get into a program without an MS in some places in Europe. – Buffy Mar 11 '21 at 19:33
  • Hmm, that is something I should consider. I have the option, under a government scheme, to follow a Masters (taught or by research), at zero cost at my local university. I know on paper this is a no brainer, but there are certain personal matters due to which I wish to move away, at least for some time. Need to weigh this option well. – vertex Mar 11 '21 at 19:37
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    If you follow up on that, you should also make some applications to doctoral programs. There is and advantage to moving and getting exposure to the ideas of a wider range of people. I'd recommend directly joining a doctorate if you can find a good one. – Buffy Mar 11 '21 at 19:48