Obtaining academic positions after doing research in logic

Question

Suppose one is starting their math PhD in the US and is considering doing research in logic. Let's roughly split "logic" into "pure logic" and "applied logic".

How hard will it be for them to get academic positions to a math PhD with specialization in logic (given that they don't come from a top logic department, like Berkeley, or even Wisconsin; but from a group I university). Would it be easier if they have a PhD in pure or applied logic? In the latter case, how possible is it to work in two areas? (E.g. if one does applied logic related to computer science/natural language, is it possible to eventually become a professor in both math and computer science/linguistics?)

(I understand that many answers will say that it depends on the research that the PhD did/adviser/connections, etc., but let's just assume that the research if fine (not exceptional), the adviser is a more or less known logician. I just wanted to estimate how hard it is to get academic jobs for a logic person compared to pure mathematicians, as well as if it's possible to work in two areas if one specializes in applied logic.)

Answer 1

The perception, at least within logic, is that finding research positions in logic is even harder than in most specialities in mathematics - most research hiring is restricted to a specialty, and there are rarely new positions created in mathematical logic.

I'm not sure how true that perception is. As far as I can tell, every field perceives hiring as very tight. There are more qualified people than available jobs in all fields of math; there are fewer positions in logic than, say, algebra, but there are also fewer new PhD's in logic, and I don't know of any data on how the actual ratios compare. But it's certainly hard to get an academic position in logic, and every year very good researchers decide to give up pursuing academic positions.

My impression is that logicians do slightly better than the average mathematician at getting positions at schools that are less research oriented - schools that are hiring based mostly on teaching ability, but want their professors to also be doing some research. (Partially, I think, because those schools often want people who can teach a variety of undergrad classes, and many logicians these days are trained to be able to do that.) But that obviously depends on being a very good teacher.

Regarding applied logic, it's very rare these days for someone with a math PhD to get hired to an interdisciplinary position, at least in the US. Someone who's already established can sometimes can an honorary position in another department, but they still have to be hired (and eventually tenured) by their home department. I think that's different in Europe, where there's a lot more mathematical logic going on in CS departments.

Answer 2

Having any narrow specialty narrows the jobs you will be considered for. Many job offers specify a sub field. Often it is to find someone to fit into an existing research group. Given that logic is pretty narrow that will narrow your possibilities. The same would be the case if you specialized in classical real analysis.

But a lot of advertisements leave the field open. But most of your teaching would likely be more general than your specialty. If you are well prepared generally, to teach mathematics, then you will probably be fine. But don't expect to find too many job offers that specify logic, whether pure or applied.

In the best case you will get to teach a logic course or two and find a few students to work with.

But if you are also generally well educated (you mention linguistics), then you may fit well into any program that stresses interdisciplinary work.

Once you have a degree and a position from which to work, the direction of your career is pretty much up to you.