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?