I’m finally able to verbalize another big reason that grad school was definitely the best choice for me.  I am fascinated by the fine line between the known and the unknown.  I am extremely impressed by mathematicians that are not only aware of this line, but walk it in their careers.

A major concern I’ve had as I move through grad school is that I’m so far removed from research (I haven’t done any since between sophomore and junior years of college) and I don’t have any idea about what’s an open question and what’s already known in any given field of math.  Feeling this far away from real math research sometimes makes me worried that I’ll never find a good dissertation topic, or even know where to look for one.  But recently I’ve been going to presentations/talks in the department and talking to faculty in the department, and it’s helped me get some idea of where some areas of research stand.  The vast knowledge base of professional mathematicians, and their sensitivity to the line between the known and the unknown, is so exciting to me.  I often don’t understand what they’re saying, because the math is way above my head, but when someone says “Here is a bunch of background” and then “Here is a recent result” (that they discovered personally or that they’re just aware of in the field) and then they talk about next steps to find answers to questions for which no one in the history of mankind knows the answers, I find it exhilarating.

I want to get to that point.  I want to become such an expert at something, that I am completely aware of its current limitations, and be an active participant in expanding the category of “things humans know.”  People continue to ask me what I want to do once I graduate with a PhD in math.  I’ve considered the possibility of going back into industry, in a place like where I did my internship as an undergraduate, but in a position more suited to my abilities.  Now that I’m actually aware of how important and exciting research is to me, though, I don’t know if I could do that.  I think I’d have to still be involved in research after I get my degree, either in academia, or in a position that still allows me to continue research in theoretical mathematics.  The farther I get into my PhD program, the closer I’ll get to being an expert in some niche topic.  If after graduation I left that to do something else entirely, I think I would miss that feeling of being cutting-edge.

It’s still early, so it’s hard to tell what I’ll be when I grow up.  🙂  And in the past few weeks, I’ve thought more about how I might get bored with teaching after a while.  But, if teaching a few classes every semester is the price I have to pay to still be heavily involved in something I really do love, then I don’t think that would be too bad.  I guess we shall see…