I'm currently an American sophomore undergrad and I'm looking into research opportunities at the moment. My problem is that the area of mathematics that interests me the most is mathematical logic and set theory, and even more specifically inconsistent mathematics, but there appear to be no opportunities for undergraduate research in this field. I'm unsure what to do or what would be the most helpful choices for me at this point. I know my college recommends cold-emailing professors if I have trouble finding something, but I'm also worried that I'm narrowing my search down too much. So should broaden my search first, just go ahead and start writing emails, or do both at the same time?

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    I would advise you to stay out of set theory in general - on average less than one set theorist gets hired as a professor per year in all of the US. It's not so much that you are narrowing too much, as that you're narrowing in on a topic that is both fairly rare and that tends to take a lot of time and expertise to achieve any research results. – Alexander Woo Jan 25 at 1:26
  • @AlexanderWoo thanks for the heads up on that. Is there a source I can use to find data like that so that when looking into potential fields I can keep employability in mind? – tox123 Jan 25 at 3:40
  • What is your long-term goal? "Employability" may not be the most important criterion unless you want to join the workforce rather than academia. – Buffy Jan 27 at 16:14
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    @Buffy Given the rarity of lifelong academic jobs, it seems prudent to at least consider employability or at least the suitability of a backup plan entirely outside the area of focus. – Bryan Krause Jan 27 at 16:23
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    @Buffy I'm in a non-professor track in academia. That said, it's problematic to take advice from professors, professional athletes, and famous actors to follow their dreams, etc - too much selection bias in those categories. I don't disagree with you, though, that someone at a young age has plenty of time to flounder in some area yet still have a successful career. I just read your comment as potentially implying "if your goal is academia you can study in any field you want" which isn't entirely true. – Bryan Krause Jan 27 at 16:44

I suggest you greatly broaden your search. There are common features to all research. Perhaps even look at research projects and programs in adjacent areas, like combinatorial research in computer science.

Since you could easily wait until the following summer to get involved in a research project, you can write programs and professors (in the area, or where you might want to visit) and ask about what you might do to prepare for the projects that exists. If you do not know computer programming, perhaps that is a gap needing a fill.

It would be good to be exposed to many areas of mathematics before you decide on what you focus upon in graduate school. I was convinced I wanted to to algebra when I was an undergraduate, but then topology started to be appealing. In graduate school I switched to analysis. Now I mostly do applied math research related to physics.


I'm currently an American sophomore

Not to sound dismissive, but I wouldn't be too focused on one area of math at this stage in your career (note: not a mathematician). Many (most?) sophomores haven't declared a major yet, much less settled on an area for graduate studies. That is to say, don't dismiss opportunities in other areas - you might find that you enjoy research more in those areas, even if you didn't like the classes.

So should broaden my search first, just go ahead and start writing emails, or do both at the same time?

I think most people would agree cold emails are the least successful way of obtaining anything, especially during COVID when professors are even more overworked than they were a year ago. My point is, is if they haven't posted looking for an undergrad, they aren't very likely to have the bandwidth to add one.

So I would strongly recommend finding an open position that at least somewhat interests you, doing good at it, and using that professor to help you find a position closer to your interests (perhaps supervising a bachelor's thesis?). When that set theory position opens; you're going to be more competitive with a year of work behind you than without.

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    You seem to be claiming that the asker should not study their area of interest because they might change their mind about their interests. I disagree. The asker should study their area of interest to help them change their mind, if they are going to change it. – Anonymous Physicist Jan 27 at 21:55
  • Advertised positions might not exist. – Anonymous Physicist Jan 27 at 21:55
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    @AnonymousPhysicist I don't think this answer says "don't study other areas of interest", it says "don't close your mind to other areas of interest". In particular, it's not a choice between "study (specific area)" and "study nothing", especially at this stage. – Bryan Krause Jan 27 at 23:22
  • @Anon No, not at all. I am saying it could be more productive to apply for a similar position that to cold email profs looking for set theory and only set theory (but I really have no idea how broad that is). – Azor Ahai -him- Jan 28 at 1:05
  • Well, your comment is clearer than your answer. – Anonymous Physicist Jan 28 at 2:08

You should do a narrow search first and then a broad search. Treat it as an experiment to see which method works better. You will likely need to try more than once, quite probably over multiple years.

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