Many short papers or one big paper for a math postdoc?

Question

As the title says, I am a math postdoc. I am working on a project, which I expect will result in a long paper (60-100+ pages, I am not really sure yet). As I work along the way, I am getting results, which are probably interesting on their own.

I wonder if it would look bad on my resume if I will have many short papers (say, of less then 10-15 pages)? or having many papers at this stage of the career is good for me?

Should I balance between these two approaches? What are you thoughts on this, assuming I am interested in getting a tenure track position at a research university?

Answer 1

This really depends on the situation, and I suggest you consult with some colleagues/mentors/your advisor for your specific case. Here are a few points to keep in mind.

• If these results are completely separate, then it makes absolute sense to break things up into separate parts, then assemble the various needed results for the endgame of your project.
• If you're just continually improving results, it may not be worth while to publish every little improvement, particularly if they will not go into good journals, but you might want to look for natural breaks.
• One great paper is better than many mediocre papers, but at this stage you should equate a few good papers with one great paper.
• There's no general rule for how much you should publish, but a good rule of thumb is to aim to have at least decent 1 paper/year since you graduate. Keep in mind, that papers always take longer than expected, and the refereeing time is generally long in math (particularly more so for longer papers), so the sooner you can submit, the better.

So you should take into account the rest of your publication record, a conservative estimate of how long the project will take, and what quality of journals you can publish in if you break things up in to parts versus keeping it as a whole. If you can break things up and still publish in good journals, then I would say this is the safer way to make you a good candidate for tenure-track/second postdoc positions.

Edit: I just realized I didn't directly address the OP's second paragraph. It's not bad to have many papers at this stage if those are good papers (though it can initially look suspicuous if you have many more papers than your peers, and most don't appear in good journals). In some fields, it is normal to mostly write many short papers (and for certain subjects, all papers under 15 pages would be strange). What's most important is that people think you are doing good research, which will come primarily from letters of recommendations and secondarily your list of publications. So while you should think carefully and seek advice from colleagues on how to publish your papers, but one long paper versus a few short-medium papers will probably not affect your application too much if they're accepted by the time you apply.

Answer 2

One consideration that hasn't come up yet is the issue of the amount of time it takes to get published in mathematics. In my experience, it is not uncommon for papers to be in the review stage for up to a year or more, and the longer the paper, the longer the review period.

Since you are a postdoc, you are going to be coming back onto the job market fairly soon and you'll want to have publications to put on your resume. Writing a 60-100 page treatise is going to have a diminished impact if it has not been accepted to a good journal yet. Assuming a 3 year postdoc and taking into account a 1 year review process, a rule of thumb would be to have at least one paper submitted by the fall of your second year and probably you should have more.

Answer 3

The answer depends on several questions:

Is there a natural way to split the paper? If chapter 1 uses algebra to show that the number of plimps equals the number of glops, chapter 2 uses complex analysis to count glops, and chapter 3 uses this to construct an improved database design, splitting seems possiblee. If you develop one idea over a long time and the reader builds up a general understanding of the topic, splitting looks bad.

Would different parts of the paper address different audiences? If your work is in area A, but has implications to area B, people from B might simply ignore a long paper dealing with stuff they don't understand and don't care about. In this case splitting would be good.

Have you other publications? A 60+ page paper in a serious journal makes a pretty good impression. People will take your smaller papers more seriously. If you have no smaller papers, the benefit of a big one is somewhat diminished. However, if people get the impression that you split papers to increase their numbers, your reputation is lost.

Where do you live? There are countries where the number of publications is seen as an objective measure of quality, there are countries where quality is determined in a formalized way, and there are countries where personal impression and reputation count.