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In undergrad I did a double major in math and linguistics, and I really fell in love with both fields. To be honest, I can't imagine ever fully giving up either one. I have a strong desire to go into academia, and my ideal situation would be to work at intersection of these two fields to some degree. There is a small body of pure math research that is motivated by questions from linguistics, and there's a larger amount of research that uses applied math in computational linguistics and adjacent subfields. My plan, since finishing undergrad, has basically been to try to pursue a PhD in (pure or applied) math, and then eventually get involved in these math-adjacent areas of linguistics in some capacity down the line. This seemed like a good plan for the general sort of work I was interested in doing.

Anyway, this year I applied to graduate programs in both fields. In math I got into a few masters programs, none especially highly ranked (though certainly not bad schools). No PhD programs. In linguistics, to my extreme surprise, I got into a very prestigious PhD program with full funding. I feel like I'd be a fool not to take the offer. However, I am still somewhat conflicted, because I really do want to be involved with math, and I fear that there is far less permeability across fields in the linguistics -> math direction than in the math -> linguistics direction.

I have talked with the person who would very likely be my advisor at said linguistics program; he works in math adjacent areas, and he told me that there would be opportunities for me to take relevant math classes if that's where I ended up. With this in mind: if my academic credentials say "linguistics" on paper, but I end up with a reasonably strong background in (certain areas of) math as well, will it be prohibitively difficult for me to get involved in mathematics research in some capacity (e.g. publishing in a math journal)? If I take the linguistics offer and then decide I'd really have preferred the math route, what are my options? Etc.

If anyone can speak to any of this in any way it would be hugely helpful. I have to decide by the 15th, so any thoughts or advice as soon as possible are very appreciated!

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    "There is a small body of pure math research that is motivated by questions from linguistics" In my ignorant, opinionated, subjective opinion, I would put it this way: there is a small body of pure math research that claims to be motivated by questions from linguistics, and then there is a truly miniscule body of math research that actually is motivated by questions from linguistics. You need to be aware that a lot of the claims that a certain math problem is "motivated by linguistics" are simply propaganda. There is, however, probably plenty of space for applied math work in linguistics.
    – Adam Přenosil
    Apr 15, 2022 at 1:03
  • @AdamPřenosil, ha! Indeed so. Perfectly true. (But: sooo cynical for a young person. :)
    – paul garrett
    Apr 15, 2022 at 1:10
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    @paulgarrett Well, I should know since I have done the "ritual nod to linguistics in the introduction" myself. I have a brief paper on "pregroups", where we say that they were studied by so-and-so "with linguistic motivations in mind". This is perfectly true, but the paper itself doesn't have the slightest connection with linguistics. The OP should be aware that much the same applies e.g. to a large part of the work on Lambek calculus. (Although certainly not all of it!)
    – Adam Přenosil
    Apr 15, 2022 at 1:25
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    @AdamPřenosil, indeed. :) I'm similarly aware that there are even "more-purely academic" (supposed) applications of math to music... using group theory and/or other things. Knowing a bit about music myself, I view all that stuff as really "purely-academic music theory", in the sense of having no genuine interest or use to music or musicians or audiences... And so on. In fact, in general, people who style themselves as "applied mathematicians" really mean that they're dealing with PDE's... with or without actual applications, and with or without talking to people about applications. :)
    – paul garrett
    Apr 15, 2022 at 1:30
  • I'm doing an interdisciplinary PhD (I've taken graduate level courses in both math and linguistics), and I plan for my dissertation to be about linguistics topic-wise but with ideas/methods from math. Let me know if you want to chat.
    – user557
    Jul 15, 2022 at 20:12

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In the "as soon as possible" vein: in my experience, in the U.S., at R1 state univ for some decades: (Edit: and in math, to be clear...)

Publication in math journals would not be influenced by your degree or departmental affiliation.

But perhaps that's not the salient question. If you got a degree called "linguistics", even "mathematical/statistical/whatever linguistics", so far as I know very few math depts would find you a high priority for postdocs or tenure-track hiring. Especially with the economic problems and tight job markets these days, nearly all math depts in R1 and R2 places would have higher-priority candidates than someone with your background.

There was and is certainly an analogous issue with "mathematical biology" and/or "mathematical neuroscience" and such stuff, but this resistance was overcome by exterior priorities aiming to emphasize and fund the practical importance of the applications. I don't know that any form of linguistics could acquire a comparable sense of urgency...

There certainly is the whole industry of trying to make computers understand and use natural language. This seems mostly not to be in math depts, but in computer science depts.

But/and, again, if you have a job that you like, even if you're not officially "a mathematician", there is no serious obstacle to your publishing mathematics research in refereed journals. Or putting it on arXiv... or on your homepage... :)

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    +1. I suspect the situation is not so different in the math -> linguistics direction too. People with degrees in STEM subjects sometimes seem to think that their STEM subject is "really" hard, that the less rigorous subject like linguistics will be easy in comparison, and that the linguistics community will be overjoyed to hire such a smart person even without much relevant experience. But the reality turns out to be quite different.
    – cag51 ♦
    Apr 18, 2022 at 21:37
  • @cag51, hahaha. Indeed. :)
    – paul garrett
    Apr 18, 2022 at 22:00

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