I have never been to grad school, but I have several publications, in good journals, as well as planned future projects. Some very prominent experts know me and think well of my work. In this case, should I apply for postdoc or just go to grad school?

If it matters, I am working in a subfield of mathematics.

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    I cant be sure, but I would think that most, if not everyone, interpret a Post Doctoral Position as one that requires a Doctoral Degree first. – user-2147482637 Dec 25 '14 at 9:47
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    Can you elaborate how those publications and projects came to be without you getting a PhD along the way? – Wrzlprmft Dec 25 '14 at 9:55
  • I read or heard (I go to conferences) about open problems, occasionally had an idea as how to solve them, and wrote up the solutions. – sam Dec 25 '14 at 10:04
  • OK, and what official qualifications do you have? Also: Why do you want to have a postdoc position? In my field and country, the main difference between a PhD position and a postdoc position is that the latter has a better pay. – Wrzlprmft Dec 25 '14 at 10:10
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    Generally, something called "post-X" necessarily comes after X. – JeffE Dec 25 '14 at 19:25

At this point in time, a Ph.D. is generally a non-negotiable requirement for a postdoc position. If you are already carrying out independent research, however, then it might be possible for you to obtain a Ph.D. in graduate school in a significantly shorter period of time than normal.

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    Even skipping graduate school altogether and just writing up a Ph.D. thesis might be an option if the OP can find a professor willing to be his promotor. – Michiel Dec 25 '14 at 14:20
  • You should consider writing a cumulative thesis to obtain your phd. this cumulative thesis would "simply" consist of the publications you already have. typically you should write an overarching introduction chapter which states how the publications relate to each other, but it should be fine. i am not sure, but in computer science this gets more and more common. maybe also in your field. you need to check with your university and/or supervisor. – beta May 19 '16 at 21:35

What are you hoping to get out of a postdoc? Typically postdocs offer a chance to enhance your research credentials and capabilities before moving on to a more permanent position either in academia or a serious research institution. If you do not have a PhD and wish to follow this career path, the best way to enhance your credentials and capabilities would be to pursue a PhD. A very capable PhD student can certainly do work of equal quality to postdoctoral researchers while also gaining a degree in the process. The only drawbacks to a PhD position compared to a postdoc seem to be somewhat lower pay and receiving slightly less individual credit for your work (in some fields anyway).

To more directly answer your question: Given enough funding flexibility, it's not unheard of for a professor to fill an advertised postdoctoral position with a very capable grad student. It would be very uncommon for a non-PhD, non-grad student to hold such a position.

As an aside, by definition you cannot hold a postdoctoral position without having a doctorate. The term literally means "after doctorate" and therefore requiress first gaining a doctorate. Any position you hold before obtaining a doctorate is by definition a pre-doctoral position.

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  • I upvoted this answer, and I agree completely that the OP should not try to do a postdoc in mathematics before a PhD. I wanted to mention: "The only drawbacks to a PhD position compared to a postdoc seem to be somewhat lower pay and receiving slightly less individual credit for your work (in some fields anyway)." Most American PhD students in mathematics make $15K-$30K per year; most American postdocs in mathematics make $45K-$60K per year. I wouldn't describe "probably about half as much" as "somewhat less".... – Pete L. Clark May 19 '16 at 16:52
  • ...In (pure) mathematics, most PhD students will already be doing their own work, not helping with their advisor's project: a very small percentage of such students are supported from their advisor's grant, and even if they are the expectations are no different. On the contrary, being a PhD student in math means you get substantial research assistance from your advisor. Most postdocs get less assistance unless they are collaborating with their advisor. That you get much less help in your work is one of the biggest differences between being an advanced PhD student and a postdoc. – Pete L. Clark May 19 '16 at 16:57
  • Agreed. The "somewhat lower pay" is understating the situation in most cases. I think math is different than most engineering fields in that the larger effort/projects in engineering tend to be a long-term focus of the PI and his lab whereas mathematics PhD tend to more completely take ownership of their project. – Doug Lipinski May 19 '16 at 17:53

You should certainly apply for grad school!

If your credentials are as you say, you will probably have the opportunity to go to one of the very best universities. Is there anyone whose work you have always admired? You now possibly have the chance to study under him or her. Take advantage of it!

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There are some research assistant positions that might fit into your qualifications. Some of the RA positions may only require a masters degree.

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    Could you provide specific examples? I have never heard of such in mathematics. – Tobias Kildetoft May 19 '16 at 18:14

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