How feasible is a remote postdoc in Mathematics? I will be graduating this year with a PhD in mathematics.  My research background is in analysis in a top 20 program in the US.  However, my family situation is such that I can't uproot my family any more than I already have, and I am thus geographically limited in our &quot;in-person&quot; options.  There are several universities and liberal arts schools in my native region, but these days it is increasingly rare to get a tenure track position straight out of the PhD, even for non R1-institutions.
So here is my question.  How open are math departments/potential mentors  to the idea of a remote research postdoc, assuming I can make trips to the host institution, say, two or three times a year? I'm looking both at postdocs in the US and abroad.
On one hand, COVID has made online work more a possibility. And if I stick to research postdocs, I don't have to be in-person for additional tasks (I might also teach online courses in other cases, but I don't want to bank on the continuation of this pandemic, which would just be, well, awful).  Additionally, as a mother I already do most of my research from home, and I have figured out to a large extent how to balance my personal life with my professional life under the flexible time schedules allowed by academia.  My CV and research activity, as far as I know, is decently strong (two published papers, one in a good journal, two submitted papers, one to a top journal, and several more research projects along the way, several talks, including some invited ones), and both I and my advisor had correspondences with some of the researchers in potential institutions, some of who also know I have a child, so they might be more understanding (or not).
On the other hand, I fear a remote option request might be read at best as a lack of commitment to my research, and at worst an insult to the department.  I know personally this isn't the case for me in terms of my productivity (it's been my default for a few years now), but there might be prior assumptions in play.  I also know that generally, math research is increasingly social and collaborative.  There are some advantages to being able to stop by an office next door and ask a math-related/ research question. I also recognize that universities are going to want additional teaching experience if I am applying to tenure track positions afterwards. My limitation to research postdocs also makes it that the total number of postdocs I'm looking at is less than most PhD's numbers of applications.
Should this not work out, I am also applying to non-academic positions as a back-up plan (gotta put food in the table), but I really do enjoy research in pure math and do not want stop doing it.
I’ll only address the US in this answer. Some of this may not be applicable to other countries.
The large majority of US pure math postdocs are mixed teaching and research positions, typically with a three year term. Even though teaching is happening remotely at many schools nowadays, you are asking how departments view the idea of a remote postdoc; well, from a practical point of view, if one is making decisions three years into the future, one cannot assume that teaching is going to continue to be done remotely that far ahead. So, my guess is that you getting such a position as a remote-only postdoc is a non-starter.
That leaves the fairly small number of postdocs that don’t have a teaching component. These come in two flavors. The first is grant-funded and controlled by a specific researcher or research group. These seem to me to be vanishingly rare in pure math these days, but if you are lucky enough to be doing research precisely in an area someone with funding for a postdoc is interested in, you may have a chance. At the very least, it seems more plausible for an individual researcher to be receptive to your suggestion than for a department, committee, fellowship, or other institutional sort of entity.
The other type of positions without teaching are prestigious research postdocs funded by well-known fellowships such as the Miller and Clay. There are only a handful of such fellowships and they are ultra-competitive and extremely difficult to get for anyone, let alone someone who insists on doing a remote postdoc; so getting one of them cannot be thought of as a reliable career plan. But if you’re good enough to be considered seriously for one of those, I can imagine at least a theoretical chance that they might allow you to do the postdoc remotely. You’ll have to check.
The bottom line is that the job market for math postdocs in the US is unfortunately not very friendly towards people in a situation like yours who have geographical location constraints. In any case, good luck!