Let me begin with some background: I used to enjoy mathematics immensely in school, and wanted to pursue higher studies. However, everyone around me at that time told me it was a stupid area (that I should focus on earning as soon as possible), and so instead I opted for an engineering degree. While in college, I used to find myself fascinated by higher math and other stuff, and used to score near-perfect all the time (but only in mathematics!). I must make it clear that I don't have an extraordinary talent for math; it's just that I enjoy exploring it very much, and then describing it to others in interesting ways. Anyway, it so happened that I went on changing job after job and was never satisfied. Now at the age of 27, I'm sitting home and realizing that I should have given mathematics a thought. So I'm thinking of taking up a graduate course and picking up where I left off.
HOWEVER . . .
I dream of becoming a teacher cum researcher some day, even if it's at school-level only. Before my graduate course begins (in 2-3 months), I've started reviewing math from my school books. Now the point is that I expect myself to be much more mature and smarter by now. That means I should be able to solve any problem and prove any theorem given in school math. But I can't, and it's shattering me. I mean, if I can't even prove basic theorems related to Euclid's geometry, how can I ever hope to do some authentic research like the mathematicians I so admire? This makes me wonder if I’ll ever be fit for teaching. If, at the age of 27, I can’t even master basic school mathematics with certainty, how can I ever hope to tackle problems in calculus and polynomials that students bring me tomorrow? It’s as if I’m cheating myself and those who’ll come to me for instruction.
Am I being too hard on myself? Am I expecting too much too soon? Does there come a point in a person’s math studies when he is able to discern properties and theorems all on his own? Or are all students of mathematics struggling and hiding their weaknesses? Or I really have no talent for math and it’s just an idle indulgence of mine. I mean, I’m not sure “how good” I’m supposed to be in order to feel confident that I can pull it off. In general, I find myself wondering how much do the others know math. Do all the teachers have perfect knowledge of, say, geometry, and can tackle every problem? If not, what gives them the right to call themselves teachers?
I have a feeling most of these questions are absurd, but I’ll be very thankful if someone can put me out of my misery.