Are postdocs in your own institution frowned upon?

The extent to which it is frowned upon differs greatly by discipline and country. At least having been in different departments/universities is usually beneficial for young scholars. Departments differ quite a bit, so having been in different departments/universities/countries broadens the range of experiences. This is usually taken into account by hiring committees, but again, the extent to which that is the case differs substantially.

Here is a perspective from pure math, which is probably applicable to some but not all other disciplines.

It’s not really about “pursuing” or about “frowning upon”. You “pursue” a postdoc to broaden your mathematical horizons and develop yourself as a researcher in an environment where you are exposed to new ideas. Doing a postdoc at your PhD institution will not achieve those goals, and hence as a secondary effect won’t help you get a tenure track job, since everyone you are competing with will have been working on developing themselves in that way. So, to an almost perfect approximation, no person driven by a rational objective will “pursue” such a thing.

Consequently, no one will need to “frown upon it” either, since there isn’t a problem of fresh PhDs asking to do a postdoc at the departments they graduated from and needing to be frowned at. By and large, almost everyone at that stage knows that what’s best for them is to do a postdoc elsewhere if they want to stay in academia, or to get a much-better-paying-than-a-postdoc, non-academic job right away if they don’t.

In other words, a useful way of thinking about it is that a “postdoc at your PhD department” is (at least in the context of pure math, as I said) a kind of category error. The concept “does not compute”, so to speak.

(Source: personal experience in academia.)

Edit: some people (who are not mathematicians and don’t share my understanding of math research culture) insist on claiming that doing a postdoc at your PhD department is “frowned upon” even according to my own analysis. It seems to me that this is an argument about semantics, and as such, I don’t find it that interesting or essential. But for what it’s worth, I’m willing to concede that one can view it as frowned upon according to a reasonable interpretation (though one that differs from my own) of those words.

Even if that’s the case, that does not affect my main argument, which is that for a mathematician to do a postdoc at their PhD department would be counterproductive from both a career and personal development point of view, and would largely defeat the purpose of doing a postdoc at all and miss the point of what postdocs are for. And this is true to such a large extent that almost no one will be interested in pursuing such a thing, and were they to try, their department would be very unlikely to offer them the opportunity to do it in the first place, except perhaps under very rare sets of circumstances. Call it frowning or whatever else you like, it simply is a thing that doesn’t make a lot of sense.

I think the issue is less about frowning upon post docs at the same institution you graduate from, but rather the missed opportunities.

Working with a different group of people increases the pool of folks you have that are willing to vouch for your abilities. It increases the pool of people you are likely to collaborate closely with.

Moving to a different institution gives you some new perspectives, including different approaches both to academic research and to all the peripheral goings on at a university.

Even just living in different cities might help you decide what things are important or at least relevant to decisions you make about where you want to take a job, both in terms of academic and local culture. Academic jobs tend to be more fixed than industry ones - there are fewer opportunities to move around later.

All these things can be beneficial to your future academic career.