Is Math Beautiful

The circle is the simplest shape in the world. No corners, perfectly round; one continuous line. A mathematical examination of the circle reveals that at the heart of this most simple of shapes lies the number pi, and anyone who has taken math knows that pi is the most complex number we have discovered to date. Thus, in one shape, we have the most simple, and the most complex. More than that, pi is indefinite, as a number. Not necessarily infinitely large, but we don’t know how large it is. With math, we are able to understand a number which is, by all rights, impossible to understand. This paradoxical symbiosis between simplicity and complexity that comes from math can be seen everywhere in the world.

Consider a tree: When you look at it once, you see a tree and that’s all. But as you continue to look at it, to stare at it, to follow the trunk up into all the branches into the all the leaves, seeing all the possibilities for growth and change, you begin to realize that a tree is incredibly complex. A mathematical analysis, which considers probability and chaos, increases the complexity to effectively infinite proportions. But this complexity still cannot change the original simplistic conclusion: that you are looking at a tree.

Math is not only seen, it is heard, felt, spoken… In music for instance, we study frequencies, and individual notes, and from these we derive theories on the nature of music: basic music theory, intervals, scales, etc. Then we see and understand patterns: harmony, counterpoint, adding theory to theory, number to number, creating more and more complexity until finally we have the full understanding of what music is. But… How can anyone understand a concept as ambiguous, as complex, as music? Can anyone define music? What, a progression of notes? Organized auditory input interpreted by the brain? Is it really that simple? There is no real way to define music, just as there is no way to define truth. The nature of a concept like music keeps us from understanding it, and yet we seem to be doing just that. To the point where we are beginning to be able to program computers to generate music without human editing. Break down a song into nothing but numbers for a computer to analyze and modify. And this is also true of poetry, and visual art. All art has, as the cornerstone of their understand, math, and the paradox that math creates. Math brings both chaos and order everywhere it is applied; it allows us to delve into everything around us, so that we may simultaneously understand it and render it incomprehensible.

Math, and paradox, is the only way to find a solution where there is none, and make a solution impossible, when it was clear before. They are irrational, and imperfect, and so it only makes sense that they are fundamental, because it does not take long to realize that the universe is imperfect. In fact, it is this very imperfection that allows for growth, development, and evolution. Order evolves from chaos, but there is always a balance between the two that must be maintained, for existence to continue: There must be enough chaos that something as random as the formation and advance of life can take place, but there must also be enough order that the formations can be maintained. Math, paradox, is that balance.

We find math in life, in art, in shapes and colour and worlds and stars, and because of that, we can begin to understand it, to hear music, to read poetry, to look at art and know what it is when we do. You can break a piece of music down into a set of numbers, or you can just press play; either way you can understand what it is. Math allows the simple and the complex, the chaotic and orderly, to come together in all things and that unity, that math, is truly beautiful. The paradox which math brings to life is the driving force behind all truth, and all beauty.