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Is it better to indicate 3 interests rather than one? Does it affect who looks at my file or affect my chances of acceptance in any way? For example, suppose I'm mainly interested in combinatorics but also am interested in algebraic topology. If I just put down combinatorics as my primary interest and nobody in the department does combinatorics, will that make the file worse than if I had put down 2 interests?

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When I, as a faculty member, go to MathJobs to evaluate postdoc applications, the first thing I do is to click a link that sorts the applications by research area. That way, I can efficiently go through the applications in my field without having to scroll through the whole database. As far as I can tell, the sorting is done on the basis of the applicant's primary interest. So the answer to your title is yes, your choice of primary interest definitely matters.

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    Yes, the sorting is done based on primary interest. You can also do searches that include secondary interests. E.g., sometimes when I look at postdoc candidates, I search for candidates with "number theory" listed as one of their interests, though I imagine this is the less common way to "sort" postdoc candidates. Thus adding secondary interests can also make some difference in getting your application seen.
    – Kimball
    Commented Jan 28, 2019 at 1:02
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If the job has a heavy teaching component then a variety of interests is probably valued. For a primarily research job, however, having interests that are aligned in some way with current faculty will be helpful as it adds synergy. In such a case, specialization would likely be valued over generalization.

Do your homework and find out what are the needs of the department you would be joining. I assume that for a post-doc, research is the more important thing, but it should also be compatible with current faculty interests.

However, if you are in a particularly hot/new area, then being unique in a department might be an advantage, especially if other members of the faculty were interested in moving in your direction. That would be more likely in a regular position, of course.

For the MathJobs database, you have a delicate balance, depending on the job you seek. If you want a research position, don't give the impression that you are a dabbler in many fields, but that you are focused on your primary area. You can also, perhaps, say that you have secondary interests, especially if the support your main focus in some way.

But, be honest in all things. It is a mistake to "oversell" yourself. Be sure that you are competent in any field you claim as your own.

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  • In my research statement I said I was interested in fields X and Y. But in the MathJobs online application I sometimes just put X as my primary interest and didn't list Y as my secondary interest. Does this matter?
    – user74089
    Commented Jan 27, 2019 at 14:38
  • For a general statement, list more, I think. But when applying for a specific job, tailor it to that position. Every application can be unique.
    – Buffy
    Commented Jan 27, 2019 at 14:40
  • My original reading was "math jobs" not "MathJobs", so my first answer was probably a bit too general. See the update.
    – Buffy
    Commented Jan 27, 2019 at 15:00
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    Teaching positions generally involve mainly undergrad classes. Mathematicians can generally teach many, many undergraduate classes that are not in their primary fields of interest. When applying on Mathjobs, you should be honest. If you say that one of your secondary interests is number theory, say, and it comes out in the interview that you know relatively little about number theory, you have just shot yourself in the foot. If your primary interest is combinatorics, you should probably also list algebraic topology only if you know enough about it to write a paper in it.
    – Peter Shor
    Commented Jan 28, 2019 at 0:16

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