How can I be competitive in pure math research if I don't get a postdoc?

Question

I want to do good work, but I don't have the benefit of a postdoc advisor to bounce ideas off of. I applied for postdocs but didn't get any offers. Now I'm just reading papers in my room on my own and trying to generate stuff, but I end up with "observations." At this rate I'll never publish in a top journal. And I'll be competing with postdocs who have the advantage of working with postdoc supervisors who give them projects to work on that will get published in good journals. What should I do?

Here's a concrete example. I was reading two papers, both on similar things. I wondered if it was possible to extend one of the results using ideas from another paper. At first I didn't have a good understanding of either paper, because I hadn't read them carefully. Then once I really understood what was going on, I realized that it's actually very easy and the proof can be given in a few lines. So I still prove things, but it's without any guidance and the result I get ends up being an "observation." Not an Inventiones paper. At this rate, all I will end up with is minor results that aren't publishable in good journals. What do I do?

I know I can do math. But I'm not in a situation that will lead me to be competitive and I want every advantage I can get.

Answer 1

The good news is that you don’t need an Inventiones-level paper to get a tenure track position. Most people who get a position at my department do not have such a paper. That is even true at departments that are better ranked than mine.

The bad news is that you have correctly diagnosed that not having a postdoctoral position puts you at a significant disadvantage. I’ll go even further: if you cannot get a postdoctoral position with a reasonably good mentor who can help you advance in your research, you will not be able to have an academic career.

So, your focus should be on making yourself attractive enough so that someone will want to offer you a postdoctoral position. That means writing up and publishing whatever results you have that are not yet published. And it means networking, through your adviser and other connections, to identify opportunities. And, of course, applying to whatever positions you can find that seem like even remotely realistic prospects.

As for getting new publishable results all by yourself: this can be an extremely difficult thing to do for someone at your career stage, and for some people it will be impossible. So, it’s worth trying fir sure, but don’t neglect other approaches, such as collaborating with your adviser or other people you got to know during your PhD. It may well be the case that the best use of your time right now is not to try to do new research, but to publish the work you have already done and to promote yourself with the goal of securing a postdoctoral position, which will set you up for continued success.

Good luck!

Answer 2

Times may have changed, but when I had a postdoc in pure math it did not occur to me to ask my supervisor for a project. My supervisors supported me in many other ways, like snagging me invitations to conferences and helping me interpret referee reports. That said, I got advice from a lot a mathematicians at that time, including from supervisors. I still got advice from my former PhD advisor. I also talked to mathematicians I met at conferences. This was before the internet, so I imagine it is a lot easier to met other mathematicians these days.

I found it easier to keep up with math topics when there was a local seminar. One can then present your results and get an idea of what confuses others prior to sending the paper to a journal.

The main benefit one gets from a good pure math postdoc is reduced teaching and travel funds. That is, time and money to devote to research. You need to seek resources for one or both of these. This seems to have gotten harder than in the past.

You told us you did not get a postdoc position, but not what position you did get. If you are unemployed and hungry you need to ignore this advice and focus on food and shelter. I am writing this assuming you have something like a visiting professorship with a full teaching load.

Since riding a supervisor's coat-tails is not an option, I suggest you start developing your own areas of research and cultivating your own list of collaborators. These days you need not ever met someone in person to write a paper together. Instead of sending a small observation to a modest journal, consider discussing your observation with some mathematicians that you know and see if you can develop a joint project. If you don't know a dozen early career mathematicians in your area, you need to met some.

Answer 3

Most math Ph.D.s (who remain in academia) end up at an institution with lower reputation than their Ph.D. institution. So look for a position at such a place.

If you are near a research math department, they will likely be happy to let you attend talks given there. Or even let you hang around at a departmental tea. Probably you should just listen for a few weeks before you try to discuss your interests with them.

Answer 4

Not an answer, but too long for a comment.

You have asked several questions here about your academic career that suggest it has not been going as well as you hoped and asking how you could fix that.

Try to think more about how your career might evolve in broader terms than wanting to be "competitive in math research".

You have earned (or are about to earn) a doctorate in mathematics, so you have proved some theorems. Write them up and submit them to appropriate journals - places where people who work in your area will find them. Work at getting your mathematics out into the world rather than about the rankings of the journals. Find coauthors who share your interests, independent of their prestige.

Look for a job at a where you can enjoy the work at level appropriate to your abilities. That may be at a place that values teaching along with research.