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I'm a fifth year pure mathematics student and after this year I should get a Master degree (I'm from Europe). As you might know, this should be the time I decide (or at least seriously start thinking about) whether I should pursue a PhD or go work in the industry.

My main problem with pursuing a PhD is that I haven't found any topic particularly interesting or passionate about, and I think I have quite a wide mathematical education. I can easily get into some area when I'm studying for exams and such, but nothing more than that. I have to admit that I'm indifferent regarding most stuff in my life. While I was in high school, I had interests in number theory and prime distribution, but that has slowly gone away.

Having said all that, I did somewhat enjoy tutoring/helping younger students and explaining stuff to them. I'd also like to think that I would enjoy doing research in mathematics, but not sure.

So my question is: How should I find out what is the field of my interest (and whether it exists at all)? Is my lack of interest a red flag for pursuing a PhD?

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  • This is actually a question to ask yourself. No one else can answer this for you. You should decide what career path you want and act accordingly :) All the best.
    – user1798812
    Commented Sep 5, 2014 at 3:11
  • Do you have the opportunity to try doing some research before making the decision on whether to do a PhD?
    – Tara B
    Commented Sep 5, 2014 at 9:36
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    @Tara There are no REUs or similar stuff where I live. For my master thesis it'll probably be just going a bit deeper into some area and state/prove its important results. I don't know how long would it take to self study to start doing research, if you meant that, but I do indeed see that as an option.
    – user21473
    Commented Sep 5, 2014 at 13:21

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Is my lack of interest a red flag for pursuing a PhD?

Yes, I think so. PhD programs are for people who are so passionate about an academic subject that they are willing to endure the certainty of a long, hard period of apprenticeship and training for the possibility of a secure, moderately well-paid lifelong career in that subject.

In some academic fields, there is a good shot at parlaying a PhD into a lucrative career in business or industry. (In others, this is really not the case.) However, in the current job market there are few if any fields in which a PhD is a guaranteed paycheck. A student who knows that she wants to take her mathematical skills, for instance, to business/industry, would probably have an easier, more pleasant life by starting work with a bachelor's or a master's degree and building her career sooner rather than later. There are exceptions, but they would be better planned in advance: e.g., if you have a specific job in mind for which you specifically know having a PhD would be necessary or beneficial.

There is absolutely nothing wrong with liking a subject and being good at it but not being passionate about it. You should then find what it is that you are passionate about. It need not be career-oriented: many, many people work to live rather than live to work. Just because you have a master's degree in mathematics does not mean that you need to pursue a career in which you use mathematics in any way! I hope you find your passion...whatever it is.

Finally: one option that you haven't mentioned is to teach mathematics at the pre-university level. In the US, a master's degree in your subject area makes you competitive for very strong high school teaching jobs, e.g. at amazing public high schools in desirable cities or elite private institutions. The difference that an excellent school teacher can make has got to be at least as much as most academics, business people or industrialists. In the unlikely event that Europe has a glut of excellent high school teachers, please consider coming to the United States, as I assure you that we do not.

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  • Thanks for your thoughts, I'll consider teaching, though when I mentioned tutoring I meant explaining linear algebra or real analysis to students year younger than me; I haven't taught high school stuff anyone and I'm not sure whether it would be similar
    – user21473
    Commented Sep 5, 2014 at 7:13
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    It should be noted that in many places in Europe, one can't "just" teach in high school, even with a master's degree. E.g., in Germany and Austria, there is a special gradudate study "Teaching/Maths", which combines maths and pedagogy subjects. A degree in this program is a formal requirement for teaching maths in a public high school (and almost all schools are public around here).
    – xLeitix
    Commented Sep 5, 2014 at 7:45
  • Also, afaik, we actually do have more teachers than teaching jobs where I live. Presumably, because high school teacher is actually a quite well-respected and well-paid profession around here.
    – xLeitix
    Commented Sep 5, 2014 at 7:46
  • @xLeitix Yeah, where I live there is also a special graduate study for teaching maths, and it's usually required if you want a job in high school. I don't though know whether the market is saturated in that regard here.
    – user21473
    Commented Sep 5, 2014 at 13:03
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    I agree with what Pete wrote here, and I've sometimes expressed it in a stronger form: You should aim for a Ph.D. in mathematics only if you can't reasonably imagine yourself doing anything else instead. That might be an overstatement, but I'm convinced that, if you're smart enough to get Ph.D. in mathematics, then you're smart enough for any of a lot of higher-paying careers. Only if all those careers look lousy compared to getting your Ph.D. should you get that Ph.D. You'll need a lot of enthusiasm to carry you past the difficulties that will surely arise in Ph.D. work.
    – Andreas Blass
    Commented Sep 6, 2014 at 13:53
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A lot of the comments and answers I see here are orthogonal to my experience. Subject matter? Career path? Both irrelevant. I entered graduate school with the intention of getting a Master's degree in Computer Science and left with a Ph.D. in Algebraic Geometry. That happened because I met an inspiring professor---he could have been doing almost anything technical and I would have chosen him, not the subject matter. I find my inspiration in people: Number Theory, Fluid Dynamics, Adaptive Algorithms---ist mir wurst, as they would say in Germany (I'm American). Working with a great professor trumps the subject matter.

You have a strong technical education already. If you are looking for direction, take a cue from it: where is your life gradient pointing right now? Mapping out a career path is great for some folks, for others it is the death of serendipity. You never know. I chose my graduate school because my girlfriend attended it. The girlfriend didn't last, but the professor did. And (serendipity) I met my wife there.

Good luck!

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