Finding a field of interest for my PhD 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?
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.