Is my research statement supposed to lead to papers in top journals?

Question

I'm about to start a 2-year postdoc in math with a possibility to stay a 3rd year. This means I will probably be on the job market in one year. I am planning to apply for tenure-track research positions. As I understand it, to get a tenure-track offer I should try to get at least one paper in a top journal. When I look at my research statement, I don't think I have projects that will lead to papers in, say, the Annals or JAMS or Duke. I listed a few projects that I think can get done quickly but are basically extensions of other people's papers, the idea being that these are "low-hanging fruit." I also listed some long-term ideas but they are speculative and aren't concrete problems. If I follow the research statement I probably won't have a paper in a top journal. Am I doing something wrong?

Edit: I should also add that my letter writers all looked at my research statement (they requested it) and didn't say that anything was off.

Answer 1

You do the best you can do with the ideas you have. Most very good mathematicians can’t come up with a JAMS worthy result every year, and it’s harder when you’re just out of graduate school. You do need to spend some time on some more ambitious ideas as a postdoc, but “more ambitious” doesn’t mean JAMS-worthy and there’s luck in which ideas pay off and when there’s an unexpected connection that turns up when you’re in the middle of a project.

Yes if you want a job at a top place you might need top publications, but all you can do is do your best with the ideas you have the expertise you developed. Most of us only get a couple publications at that level in our life. Aim to be productive and to increase the level of your publications, but thinking about how to get into JAMS or the Annals isn’t helpful.

Answer 2

This is orthogonal to the actual question, I realize. The answer of Noah Snyder is direct and seems correct to me. But I'd like to make a couple of recommendations about what to do during the postdoc so that when you enter the actual job market you are in the best possible position whether or not your research has resulted in completed high level papers.

First, your current backlog seems appropriate with both short and long term projects. You want to maintain and extend that.

The first recommendation is that you keep a research notebook in which you record ideas, as they occur to you, that might be exploited later when you have time. Researchers in large companies like IBM keep a "patent book" in which they record "possibly patentable" ideas when they occur. You can do the same with any sort of research. Periodically review the entries in your notebook to see whether you have additional extensions of them or can now develop them more fully. This notebook can form the basis of your next "research statement" when you are in the job market. Having a good backlog of projects of various difficulty and in various states of development can be an asset. Research in most fields, including, or maybe especially, mathematics can't really be time boxed. The results come when the insights come. But one big insight is knowing what might be possible to develop - and not forgetting it in the heat of other pursuits. Keep a notebook. Update it constantly.

And if you get blocked for some reason on your currently most important project, go to the notebook to see what you can do now while the main project gestates for a while. Have several irons in the fire, some hotter than others.

The other recommendation is to use your time as a postdoc to develop collaborative opportunities. Talk to a lot of people about your and their ideas. Think about whether it is advantageous to work with them. And make sure you capture anything significant (even slightly significant) in your research notebook. But one important benefit of such collaborative relationships is that you might eventually take a job at a small institution that doesn't have a lot of local opportunities. If you have a lot of prior relationships then you can still carry on a rich research program even if you are somewhat isolated. Even a relatively large department can be weak in your particular research area.

The notebook is useful for another reason, actually. It is useful for a new faculty member to have some ideas available for student research. If you have several partly developed ideas, perhaps they can be taken over by students. You already have given them some thought so it is easier to advise and guide them.