I'm not sure if this is an appropriate question for MO, but I figured it couldn't hurt to ask. I'm a second year graduate student, currently gearing up to construct a committee and syllabus for my oral exams, and I'm struggling with some issues regarding the subject(s) I wish to study. In particular, I have found that what I am truly interested in is transcendental number theory and would absolutely love to have this as a primary area of focus for my exams, with the hope of developing a thesis in this area as well.
However, after speaking to some of my professors I now have the impression that the field is not exactly dead, but very, very cold. Not only do the open questions in the field seem to be impossibly difficult, but there are very few mathematicians out there (or so it seems) who focus on transcendence as a primary area of research. In light of these difficulties, I'd like to ask the following:
For graduate students in pure mathematics, do you recommend following your interests despite obvious challenges, or should students temper their passions and pick more fruitful areas of research for their theses? Additionally, for my particular case, where/who do I turn to to discuss transcendence and cultivate a sense for what types of problems (if any) are suitable for a PhD thesis?
Thanks in advance for your responses!