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I'll be applying to tier II PhD programs in Mathematics. I've made a switch from another field to Mathematics, and, given that my primary major was not mathematics during my undergraduate, I don't have well-defined research interests. I have some idea that I'd like to work in analysis, but I'm not sure of which field -- differential equations, functional analysis, geometric measure theory etc. I still, at the very least, need to study all these subjects in more depth to be able to make an informed decision. Moreover, I come from a background where I studied multiple subjects in college -- Economics, Physics and Mathematics -- and I consistently realized I'm more interested in the mathematics of all the subjects I have studied thus far. So, right now, I am more interested exploring more mathematics out there, so I can make informed choices about my research interests at a later time.

So, my question is: how do students like myself sell their research interests in the personal statement addressed to graduate admissions commmittee?

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  • Your remark that you consistently realized that you're more interested in the mathematics of all the subjects you studied is a serious indicator of your interest. That, together with your observation that there's no reason to make an ill-informed choice also shows good insight into the reality of the situation.
    – paul garrett
    Oct 31, 2017 at 19:40
  • @paulgarrett Having said that, I feel I don't have anything substantial to write about my research interests? I don't wish to boast about anything on my personal statement, but, as a friend of mine who's a math graduate student at a top 5 school suggested, I shouldn't undersell myself. So, I'm having a very hard time reconciling these thoughts to write something substantial in the 1-2 paragraphs devote to this part in the personal statement.
    – user82261
    Oct 31, 2017 at 19:44
  • You could go into some details about the specific math that occurred in your other courses... and what future math specialization might be motivated by that. E.g., "motivated by subtleties of solutions of partial differential equations appearing in quantum mechanics, I am interested in ..." Yes, don't under-sell, but it's all too easy to look naive in the way one does a selling job. Get advice from faculty about delicate word choices.
    – paul garrett
    Oct 31, 2017 at 20:19
  • In mathematics, many students begin their Ph.D. studies without any real idea of what sort of math they want to do --- or with a real idea that changes afterward. When I started grad school, I thought I wanted to become a topologist, but after a couple of years I switched to logic (though I continued to attend topology courses).
    – Andreas Blass
    Nov 1, 2017 at 3:16

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In mathematics it is common to have little specific idea of what you want to do in a PhD at the point of applying. Unlike in many arts subject, for example, your supervisor will largely choose the research question for you (hopefully with your input). At a graduate open day, we were told that SOPs range from 'I want to do a PhD in pure maths' to 'I want to prove the Riemann Hypothesis'. Indeed, my own loosely said 'this is what I've done, so something a bit like that might be good'. Exactly how much detail you need to give will depend on the structure of the PhD programme, and local rules/funding arrangements.

I think the thing you will need to set out clearly is why you've chosen to switch to mathematics, and how you will achieve the same standard as those who have done a maths undergrad/major.

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    And, repeating a paraphrase of my comment above, it is a good "sell" to explain how you've been irresistibly draw to math even while studying other things... This can be a stronger argument than a relatively passive choice of undergrad math major, and then possibly passive-sounding continuation to grad school (with or without "research").
    – paul garrett
    Oct 31, 2017 at 21:17
  • Hi Jessica, Thank you for kind response. Would you mind having a brief follow up conversation either via email or via messages on this website?
    – user82261
    Nov 2, 2017 at 19:17
  • @paulgarrett Thank you for your responses as well. Would you mind having a brief follow up conversation either via email or via messages on this website?
    – user82261
    Nov 2, 2017 at 19:17
  • @user82261, you can easily find my email and send me a note about this...
    – paul garrett
    Nov 2, 2017 at 21:04
  • @paulgarrett I have sent you an email.
    – user82261
    Nov 11, 2017 at 19:25

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