The more famous mathematician's apology is written by British mathematician G.H. Hardy, and he uses the word "apology" in the sense of a formal justification or defense. I'm using the word "apology" today in the other, more common sense, as a plea for forgiveness.
I've always been "decent" at middle school and high school mathematics, but I never found it particularly interesting. Numbers and geometric shapes and basic algebraic manipulations made sense to me and it wasn't too difficult to pick up new concepts, but the number chugging, equation plugging, rote learning brand of mathematics in high school never caught my fancy. Instead, my interest in math developed fairly late, starting late first semester of senior year. I remember officially starting calculus a few weeks before winter break, and mentioning offhandedly to Ms. Connor (a wonderful math teacher at my high school) that I found calculus interesting but the pace of my class too slow. She, being the wonderful, magnanimous teacher that she is, gave me her notes for calculus and sent me on my journey of mathematical discovery. For the next few months, I started reading and studying mathematics on my own time, fanatically going through chapters of calculus, helped along by Ms. Connor. For the first time, I saw how interesting mathematics was, and how astonishing it was that everything just worked. It was beautifully shocking every time I learned a new concept and saw how it just fit. I was convinced that mathematics was art, and happily spent hours learning and appreciating the beauty of mathematics. When I went to college, I was set on studying mathematics, which was what was wanted (W5).
But in venturing forth into what I would describe as "real" mathematics, I started stumbling into some roadblocks. Mathematics was (and rightfully so) no longer the joyous, self-paced journey it was before, and instead made rigorous and competitive by difficult material, constant problem sets, impossible exams, and smarter classmates. Drowned in the feeling that I was bad at math, I slowly began to lose my love of math, and I slowly forgot why I enjoyed mathematics at all. I came in as an intended pure math major, wanting to get a Ph.D. in math, and started second semester in a joint math/computer science major, goals now very far from a math professorship. Worst of all, when people asked me "why do you still do so much math?" I could not find a good answer.
When I began studying for my final in May, all I could think about and worry about was my grade. Math was no longer enjoyable or interesting, but instead an ordeal that I had to get through. The awe and respect I had for mathematics was now replaced by fear and trepidation, and I regarded the final much like a dreaded visit to the dentist's office- painful, yet unavoidable. But once I actually started studying the material, I underwent an amazing change- I once again began to appreciate mathematics. The way in which the material would expand in a wholly unexpected direction, and yet remain undeniable true and verifiable once again drew my awe and fascination. The way Greene's Theorem, Stoke's Theorem, and Gauss's Theorem related made intuitive sense to me, and the picture that was so hard to keep clear slowly lost its fog. By the time I finished studying, I re-found my love of mathematics, but also a deep sense of guilt that I had once forgotten it.
While I still didn't do great on my final (that thing is seriously impossible), I am glad that I remembered why I came into Columbia determined to study math.
So why do I spend so much time on math? Because it is beautiful, and I love it.