#### QED - Math is a Beautiful Thing

by HyunGu Kang

My littlest sister once compared math to "a wicked, multi-purpose Swiss Army knife." I laughed at the time, but the more I consider her words, the more truth I see in the comparison. In its own way, math is a compact, reliable, and relentlessly practical multi-purpose tool. It is flexible, honest, and, at times, even elegant in its simplicity. Math is beautiful, math is productive, but, most importantly, math is the most human alternate reality that I know.

I describe the math world as an alternate reality because, even though it exists only in our collective consciousness, it is vast enough to contain a theoretical model of the universe. Although it may not seem evident at first, math consists of the same kind of matter and energy that the universe does, albeit in idealized mathematical form.

The universe is populated by matter, anti-matter, and other particles that we are just beginning to detect. It develops through the interactions between four principal forces: gravity, the electromagnetic force, the strong nuclear force, and the weak nuclear force. The evidence that we have collected thus far indicates that our universe is expanding, and that it originated during a spontaneous explosion of energy that we call the Big Bang.

Similarly, the math world is populated by numbers. There are natural numbers, integers, real numbers, rational numbers, and complex numbers that exist, not on a number line, but on a Cartesian plane. While the physical universe is limited to four forces, the math world is acted upon by several operations, best encapsulated by the elementary school acronym: BEDMAS. BEDMAS stands for: brackets, exponents, division, multiplication, addition, and subtraction. Unlike the physical forces, the mathematical operations of BEDMAS correspond perfectly to the dimensions of the math world. Addition, the simplest operation in math, is math's first dimension. Multiplication, a function that measures the amount of times a number is added to itself, is the second dimension of math. Exponents measure the amount of times a number is multiplied by itself, and they constitute the third dimension of the math world.

Another way in which math surpasses our physical universe is in the number and variety of parallel universes contained within mathematics. Just as biology, physics, and chemistry are different branches of science, trigonometry, algebra, statistics, probability, and functions are distinct disciplines of math, complete with their own units of measurement, preferred variables, and strategies for successful navigation.

Math owes much of its intrinsic beauty to the interplay between these parallel universes. Each mini math world is distinct, but far from self-sufficient. Algebra is used to find the roots of polynomial functions. Sinusoidal functions are visual translations of common trigonometric relations. The intricate co-dependence of the math universes, like the network of microscopic cells that make up a human body, is mesmerizingly beautiful for both its seemingly impossible complexity and its truly remarkable originality. By weaving the independent math universes into a cohesive mathematical world, humans have created a mind-bogglingly expansive, sophisticated, and beautiful alternate reality that accurately represents the patterns of the physical universe.

In addition to beauty, math has the added advantage of practically unlimited productivity. From math comes a plethora of diverse, independent expressions of the human experience, including: music, dance, architecture, and technology. I was lucky enough to have received a musical education when I was small, and I remember the amazement I felt when sight-reading Beethoven's "Für Elise." The only reason we can experience classical music today is that it has been notated for us. The only reason that music has been notated is that composers made the connection between the numerical organization of math and the hierarchical order of sound. By applying mathematical principles to the world of tone and rhythm, musicians like Bach were able to preserve their art for centuries. This is just one example of the ways in which humans use math as a tool to create innovative fields in art and science. Math is the ultimate multi-purpose cognitive tool because it is flexible, reliable, and universally understood.

Why is the math world universally understood?

I claimed earlier that math is the most human alternate reality that I have ever encountered. Most people find this statement as ridiculous as my sister's comparison of math to a Swiss army knife, but I find truth in both points of view.

Math is beautiful, productive, and universal because, of all the alternate realities that exist in the collective consciousness, the math world is most innate. Math is the expression of the logical framework within which humans experience, manipulate, and manage to survive in the world. This is why math is taught in every country, why math can be understood in every language, and why every human on the planet understands that 1 + 1 = 2, not 11.

One piece of evidence for this perspective on mathematics is that math is the only theoretical reality that is independent of social change. It is unique because it is consistent: no change in culture or history could ever negate the fact that 1 + 1 = 2. In contrast, literature, music, science, religion, and the arts ebb and flow in response to changing values, environments, and mentalities. They change when the social milieu changes, which suggests that they are derived, not from the human, but from the social, cultural and historical environments that surround the human. Math alone is immune to such paradigm shifts. Math is our world, and the rest is commentary.

This, of course, is not entirely true. Science also seeks to accurately represent the world around us. Science, like math, is populated in part by numbers. The main difference between the two disciplines is that science is based on the imperfect workings of the natural world, whereas math is grounded in the purely theoretical alternate reality that I have called the math world. Math is a 100 percent human construct: it is an exploration of human logic, rationality, and psychology that rarely corresponds to physical reality. Science is the labour of applying math to the physical universe. It is less than 100 percent human because its purpose is to illuminate the mystery of natural processes that are alien to human understanding, not to define the workings of a world populated by human ideas.

As for art, art really is commentary. The purpose behind great art is to promote thoughtful discussion by confronting audiences with a warped reality. Milton's *Paradise Lost*, for example, is a groundbreaking poem that challenges audiences to justify the Judeo-Christian moral universe. Unlike math, art is a fluid experience: *Paradise Lost* communicates different messages to different people at different stages of their lives. The various twisted realities conveyed through art are not always logical. If anything, great works of art are more meaningful for the strangeness of their perspective: by immersing audiences in an unusual and even unpleasant point of view, art challenges people to think critically about the social and cultural mechanisms that often go unnoticed in day-to-day life. Milton's magnum opus immerses audiences in a vivid depiction of Hell. By forcing audiences to acknowledge the parallels between Milton's Satan and the archetypal tragic hero of Greek mythology, *Paradise Lost* gives people the opportunity to seriously consider their individual response towards the moral universe of the church. In many ways, the impact of great art is the opposite of the impact of math: art isolates audiences by forcing them to think critically about the world, while math provides a universally accessible way for people to quantify their common experience.

I happen to like science, art, and math, but I've always believed that math is the most integral and the most human of the three. Science is valuable because it satiates our natural curiousity. Art is valuable because it gives us the ability and the responsibility to become self-aware. But math is invaluable because it encapsulates the fundamental ideas of the human experience. It displays the unique logic that governs the human mind, it flexes the cognitive faculties that have allowed us to become so successful as a species, and it continues to be used and developed in the day-to-day life of the nine billion human beings who are alive today.

So, math really is "a wicked multi-purpose Swiss Army knife."

Quod

Erat

Demonstrandum