Papers published during undergraduate degree: can they form the basis to a PhD? 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?
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 &quot;papers&quot; 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.