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Beauty in Mathematics

Eugenia Chan

Roald Hoffman stated in his essay, gThoughts on Aesthetics and Visualization in Chemistryh, that gbeauty is created [and found] c at some tense edge where symmetry and asymmetry, simplicity and complexity, order and chaos, contendh (Hoffman 4). An artist may be able to see the beauty of a portrait, or a landscape in terms of the symmetry, asymmetry, simplicity, complexity, order and chaos that Hoffman speaks of. However, from scientistsf, or perhaps a mathematiciansf point of view, beauty is more than just the first-glace aesthetical perception; it has to do with the ability to manipulate or create a concept and rules by which everyone can communicate with. Science lays in the foundation of mathematics; mathematics is in fact where chemistry, biology, and physics begin. It is then the simplicity of mathematics that makes the world in the eye of a scientist so beautiful. Hoffman suggested that humans have gsomehow evolved to favor simplicityh (Hoffman 3) suggesting that whatever we are able to understand and make sense of, we are able to think of as beautiful. Mathematics is probably the only elanguagef that can be simplified or condensed; it is taking a larger concept of an idea and using symbols to represent that idea in a simpler manner. The number e6f for example, refers to an idea of physically having six different objects. However, through time this symbol has become a universal sign representing the idea of physically having six somethings. The figure itself does not consist of six strokes, nor does it seem like it contains six of anything, but nevertheless it is representational of a larger idea. The mere fact that these seemingly meaningless symbols represent something on a universal scale is even more beautiful. Think about it. There are only a very limited number of languages that are universal and they are all linked to mathematics in one way or another, whether it is pure mathematics or music. Like an artist, the scientists and mathematicians expresses and communicates their gknowledge and emotionh (Hoffman 3) using symbols on paper in an gabstract artistic wayh (Hoffman 3). Communication is what makes us human; humans long to be able to relate, understand, and share with one another. Contrary to popular beliefs, art is not the only gateway for such human contact; science too can also be a humanistic study. Of course, the beauty of mathematics to most mathematicians and scientist is its nature of being purely objective and not subjective. Unlike of the other disciplines, there are no grey areas in mathematics; there are no confusions. Of course, this exactness of mathematics comes at a price of having to learn all of the principles and laws that must be strictly followed for one to experience this regularity and perhaps reliability of mathematics. But one this is certain, mathematics can and does make life simpler- furthermore, it is essential to everyonefs lives. No one really considers or counts the number of times we do esimple-mathf in our heads everyday: it can be in the form of time management, or splitting an order of cheese fries with a friend. Math is essential and important, and something important to us can always be viewed as beautiful. What strikes me as most fascinating is the idea of mathematics being symmetrical, asymmetrical, simple, complex, orderly and chaotic all at once. This improbable occurrence happens all the time in a simple mathematical (or chemical) equation. I am personally not a big fan of mathematics in the classroom; I believe that its function and usefulness is beautiful in a more universal scale, but in itself- I could do without. Math class every Mondays, Wednesdays, Fridays is always a painful experience. However, the motivation and excitement I get from taking the math course is, obviously when I can get the correct answer but also, when I understand and see the steps where something slowly evolves into another thing, how çsin3(5x)cos10(5x)dx could transform itself in a matter of eight steps into (1/5)[(1/13)cos13(5x)-(1/11) cos11(5x)] +C. In a sense, this equation:
çsin3(5x)cos10(5x)dx = (1/5)[(1/13)cos13(5x)-(1/11) cos11(5x)] +C
could be seen as asymmetry since both sides do not physically look like one another. But in the different sense, they are equal, so technically, they are symmetrical, or at least balanced or equal. One of the most wonderful characteristics about mathematics is how one is able to use it, and solve it in so many different ways. Eventually, the answer will be the same (given that it was done correctly). This pseudo-variation (where it seems different but in actuality is not) intrigues me most about mathematics. In mathematics, simplicity can be associated with order. This is not to say in the real world that this holds true, but in the world of mathematics where everything is (essentially) perfect, simplicity = order, and likewise, complexity = chaos. In the beautiful world of mathematics, there IS a cure for chaos; algebraic manipulation, factoring, substitutionc just to name a few. But the real world doesnft have such an easy cure for chaos; there are more problems to deal with, more issues to consider, and most of all, more complications to control and fix. The world of mathematics IS simple in comparison to the real world, it is perfect, and it is flawless. Knowing that a perfect world exists somewhere is a rather satisfying feeling; for once, you do not have to think about not being able to solve a problem. Knowing this about mathematics, in a sense, makes it beautiful and perhaps comforting to me. Without mathematics, the world would not be an uglier place, but it would be an emptier one. Without mathematics and the sciences, the technological world as we know it would not be the same. Nature would be unaffected, but nature is not the only entity we think of as beautiful, as some people stated, they found their possessions (created by technology and ultimately mathematics) beautiful and meaningful to them. The possessions that we consider beautiful are the end products of the beautiful edoingsf of mathematicsc that is awe striking and enough to convince me that mathematics and science is a beautiful thing I could not live without. Walking into math class is still hard for me- I could never appreciate math in its purest form; not by doing hours and hours of problems listed in the oh-so-familiar James Stewartsfs 5th Edition. But after reading Hoffman (and after digesting his words for a few weeks), I was able to see mathematics from his viewpointc and it is actually beautiful.


Roald Hoffman, "Thoughts on Aesthetics and Visualization in Chemistry." Preface to an issue on Aesthetics and Visualization. Hyle.

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