I'm extremely and equally interested in a subset of cognitive psychology (a research question pertaining to individual differences in attentional control) and in Lie algebras/representation theory. Unfortunately these are disparate topics that aren't conducive to being tied together via interdisciplinary work.

I'm currently in a postbac program and will be applying to PhD programs this coming winter. (I'm familiar with both research "lifestyles" and don't feel that taking additional courses or doing further independent research would significantly elevate one interest over another.) Given that academic jobs are fiercely competitive, which path (e.g. apply to math PhDs and try to do a psych master's, apply to psych PhDs and try to do a math masters, or some other path) would maximize my chances of ultimately being able to productively research both topics alongside one another?

Some factors I'm aware of (but am struggling to coalesce into a decision). Please correct me if I'm wrong on any of these:

  • Jobs in academia are limited and competition is fierce, but it seems there are fewer jobs and greater competition in cog psych than math. In other words, the probability of obtaining a faculty job is significantly greater for math grads than for psych grads. Math 1 Psych 0
  • Math is primarily a pen and paper field (and collaboration appears to be relatively easy to make happen, contingent on usefulness), whereas cog psych research requires funding (equipment/software) and resources (subject pools). It would be possible for a cognitive psychologist to work on Lie theory as a hobby, but the reverse would be very difficult to impossible. Math 0 Psych 1

  • It's much easier to teach yourself math and how to do math research than it is to teach yourself cog psych and how to do cog psych research - the latter is heavily dependent on learning from experienced others and hands-on practice. Math 0 Psych 1

  • I am, at the moment, able to piece together a stronger application to math PhD programs than to psych PhD programs - and this difference is amplified by the fact that most departments have a bunch of faculty working on Lie algebras/rep theory, whereas there are currently fewer than five people in the US doing research on that sub-sub-topic of cog psych (or at least fewer than five people that I'm aware of, but I've done my research). I could try to piece together a stronger application to my top choice psych programs (or rather, advisors), but it would either be risky and expensive or risky and financially unethical. Math 1 Psych 0

If anyone is familiar with this type of situation, could you offer advice on which academic path one should take to maximize their chances of doing research in two nonintersecting fields, particularly given the factors listed above? What kinds of PhD programs should one focus on applying to? (I realize this question is similar to another that's been asked, but most of the answers to that question involved tying together the two fields, which isn't an option in this case :)

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    Given the difficult job market, one question you might ask yourself: what jobs, other than academia, do people who earn these degrees often end up taking? Of these jobs, do any of them appeal to you? – Anonymous Oct 16 '17 at 2:47
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    Related: Is doing two PhDs a good path?. While not the same question, many of the answers there discuss the problems associated with doing research in two fields. May be worth a read. – ff524 Oct 16 '17 at 4:17
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    What kind of academic position do you see yourself having that would encourage you to publish in a completely disjoint field? The point of pursuing a PhD is to specialize. If you become a professor in a psych department, they are likely to view you publishing articles on Lie theory as a distraction. – Morgan Rodgers Oct 16 '17 at 4:17
  • Also, once you finish a PhD, you should not then go and do a Masters in another subject. You will need to right away start a postdoc, applying to positions, etc. If you waste the two years after PhD getting another degree in a different topic, think about where that puts you when you start applying for jobs. – Morgan Rodgers Oct 16 '17 at 4:26
  • I meant doing a master's concurrently while enrolled in a PhD program. – genericity Oct 16 '17 at 4:50