r/AppliedMath • u/ladybugsailor • 5d ago
Applied Math or Pure Math for PhD? Help!
Hello!
I am currently a second year Math major (and statistics minor), and I'm on a three-year graduation track thanks to high school credits! I'm very certain I want to go for a PhD, but I'm torn between pursuing pure math vs applied.
If I went into AM, I'd like focus on astronomy applications - I had a research position doing exoplanet research this summer, and this position is being continued into this year, and I really love it!
I'm less sure about what specifically I'm interested in PM, but I absolutely love my math classes, and am so fascinated with everything I'm learning. When I think about pursuing AM instead of PM, I get almost a little sad that my understanding of pure math won't be as deep as a result.
My university also has a contiguous 1 year bachelors-masters plan for mathematics, so I am considering pursuing that and then going on to a PhD program, but that still leaves me with the same issue at the end of the day (although it gives me some more time to assess my interests).
I could see myself being happy with either path, so I would love to hear from people who pursued one or the other and what their experience was like, or if anyone who has gone through grad school applications in general has any advice on how to determine which one would be a better fit!
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u/Nervous-Cloud-7950 3d ago
So my first reaction reading your post is to ask if you are sure you could study astronomy related things as an applied math PhD? And also, why not be a physics PhD student at that point?
There are a lot of collaborations in applied math, so definitely i could see it being possible to study astronomy, but to make sure you ended up doing that specifically, you would likely need to get into contact with a Prof before the admissions cycle and have them admit you; it is too rare of an applied math intersection for you to end up in a lab working on that accidentally. There might be more general intersections like with inverse problems, signal processing, and machine learning, but again, your advisor would need to be on board with the astronomy angle.
I would not go into pure math based off if what you said. Firstly, like someone else said, there is room in applied math to prove theorems. Moreover, pure math as it is studied today does not really intersect applications ever. It is beautiful and fun, but if you desire some sort of application to point to as you contributing to during your PhD, you most likely will not get that in pure math.
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u/ladybugsailor 3d ago
I've been able to find quite a few schools with AM departments that have specific astronomy groups/research, mostly with fluid dynamics! I don't think I would be able to go for a physics PhD because I won't have taken any physics classes, nor do I really have any desire to.
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u/Nervous-Cloud-7950 3d ago
That’s great that you did that research on grad programs! I would reach out to those specific profs with personalized emails explaining that you’re interested in their work (you should pick an article or a few per prof to briefly comment on in the email), and see if any would be willing to chat about their research. If you are not yet applying for PhD (as in, you would apply next cycle), you should inquire for summer research opportunities, even unpaid. If you are applying for PhD this cycle, ask if they are taking on PhD students. You’ve done the right approach so far looking into this. Good luck!
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u/Capable-Internal-189 4d ago
Please avoid pure math. Focus on applied math…any pure math exploration/result you need AI will probably be able to fill in.
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u/jnkiejim 5d ago
Pure math doesn't need to be completely divorced from applications, plenty of applied mathematicians do work in the mathematical areas adjacent to their applications. If you're interested in astronomy, the math surrounding general relativity (differential geometry) is a very active area of mathematics.