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I just started my 2nd year of master and it's already time to apply for a PhD in math, deadlines are in ~1+ month.

In most samples, students had a clear idea of what they would like to study. They write that they have studied this and that, and that they would like to be under Prof. X's supervision because they worked on his papers.

As for me, I liked most math topics that I have studied, with very few exceptions. In short, I'm undecided, exactly when I buy an ice cream and I'm facing 20 good flavours.

Most universities, on their application page, offer "undecided" among the options (algebra, number theory, ...). Although they may say "it's totally fine" (because everything is nowadays), what is the truth behind the appearances?

Stories from people who are on admissions committees or from [un]successful applicants who wrote that in their SOP are most welcome.

EDIT: I successfully got admitted to some really good US universities with "undecided" in my SOP

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  • What country is this?
    – Elizabeth Henning
    Commented Oct 27, 2018 at 22:53
  • 1
    @ElizabethHenning USA
    – Thomas
    Commented Oct 27, 2018 at 22:58
  • @cag51 thanks, I couldn't find it. However I would be happy to have more "stories"
    – Thomas
    Commented Oct 27, 2018 at 22:59

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Generally in the US you don't need to choose an advisor when you start Doctoral study. Therefore, having a firm idea about a concentration, research focus, is less important than in some other places. But giving the admissions people some idea will give the a better way to think about how you might fit in.

What I would do, in your case, is to say you are undecided, but currently focused on X and Y, where X and Y are a couple of things you know a lot about. It narrows the focus a bit without limiting you in any way. But, having an MS means that you will want to get started on research pretty soon after arrival and so will need to choose an advisor, unless you want to risk having one chosen for you (a bad idea, generally).

However, taking a deep dive into some narrow subfield of math doesn't limit your choices for ever. You will need to focus until you earn the degree, but then the view can open again for you if you want.

It is probably ok to be a bit undecided as long as you aren't chaotic random.

Note that this is a US specific answer. It wouldn't be the same in some other places.

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    I agree with this, but it's better to leave out the part about being undecided. No one is going to hold you to what you said in your SOP.
    – Elizabeth Henning
    Commented Oct 28, 2018 at 2:00
  • This is peculiar, we lot (engineering related fields) can only apply to the vacant positions in some projects in US universities, and faculty does whatever they can for taking the most specific, fitting candidate. Are you talking about being admitted without any scholarship or RA position? Or this is specific for some fields?
    – user91300
    Commented Oct 28, 2018 at 8:23
  • @user91300: in mathematics in the U.S.
    – paul garrett
    Commented Feb 26, 2019 at 17:00

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