My Thoughts on the Beauty of Mathematics

Math has always been one of those things that comes naturally to me. My whole family, really. We used to sit around the dinner table, and after eating, my dad would conjure up math problems for my sisters and I to solve. I could not have been much older than 8 or 9 when he started to give me algebra problems to do. I would sit there and solve for x in my head, not really comprehending the significance of what I was doing.

One thing I've never understood is that people assume that because I'm good at math, I must be really smart. I've got news for you people, math is about the only thing I'm good at. I am horrendous musically, I have the literacy of a third grader, and I barely remember what I had for breakfast ten minutes ago, let alone any sort of important fact from world history. But if you put an integral in front of me, it's a language I can speak. An art that I can perform. People knock math around all the time. I cannot tell you how many people I know who hate math. I know kids at school who are engineering, econ and physics majors, all mathematically based subjects, who hate doing calculations. I truly believe that in a largely ugly world, mathematics is beautiful.

Have you ever read a proof? I'm not talking about one of those crappy three liners we wrote in freshman geometry, but a truly detailed proof? Maybe the proof of the Fundamental Theorem of Calculus? Or the one of the Fundamental Theorem of Finite Abelian Groups? Although you may not understand what is going on, there is a subtle elegance to it. Any logical argument can be constructed to sound correct. Darwin's theory of evolution is a perfect example. It makes complete sense, and anyone with a brain is confident in its truth (If you don't, odds are you are not reading this - very few creationists are concerned with what a 21 year old kid from Massachusetts has to say about math). However, the arguments depicted in this theory are not facts. It is not the same as a mathematical proof.

A true proof is so incredible because it is not something that can be refuted. Obviously creationism is an argument against evolution, but there is really no way to refute that if the average speed along a closed interval is c, then at some point the instantaneous speed along the interval is also equal to c (this is the mean value theorem - I have omitted the proof for two reasons: 1) I don't fully remember it and 2) it is quite complex. This does not negate the fact that it is true. No matter who you are, where you're from, what you believe in, etc.) I think that's the biggest reason I've always been drawn to math. It really is one of the only complete and total truths in the world.

Math is a language common to all walks of life. Probability distributions have the same functions whether you live in the US or in Turkey, whether you speak Spanish or Russian, whether you are Jewish or worship Satan. Math is constant regardless of race, creed, ethnicity, nationality, social background, religion, language, IQ, or really any other feature that defines each individual. In a world full of division (pun intended), math is one of the few things that is common among us all.

If you're still reading this, you either really enjoy my writing (doubtful, let's face it, writing is not my greatest strength) or you really enjoy math. If the latter is true, then I applaud you. Very few of us exist and I think loving math is something to be proud of. I don't believe it makes us better or smarter than anybody else, but it means we can do things that other people cannot. While I do not believe math is necessarily the most glorious subject, for me, it is the most rewarding.