I was recently approached to write an essay to convince (high school) art students that math is freaking excellent. This was the result:
You can think of the study of mathematics as the study of art. Throughout our childhood schooling, we were mostly taught the mechanics of art: drawing lines, shading, painting techniques. These notions are developed in a technical way without an inherent understanding of aesthetics. Furthermore, without being exposed to art galleries or painting schools, the capacity of these devices to express emotion, people, philosophy and concepts remains unplumbed. It is only after studying artistic techniques, and art from the masters that we begin to appreciate art.
Our first attempts at art are challenging and sloppy. Many a student cannot see the forest for the trees and complains about how pointless art is. Even over the course of high school, most students remain bogged down in the mechanics, and cannot experience the joy of self expression. By and large, the children who quickly grasped the technicalities and were able to freely express themselves through various media are the ones who became talented artists. If you approach a sketch artist drawing a woman, and comment on the difficulty of drawing curved lines, you will probably get a strange look. The artist has transcended individual shapes and sees the bigger picture.
Mathematics comes less naturally than art to most of us: it requires a degree of abstraction that our primate brains have only recently been equipped to handle. As such, many students will continue to study the technicalities and mechanics of math until they are almost done with their math degree. Any mathematical idea you were taught in school or have come across since is most likely a tool akin to spelling or vocabulary. To be honest, the same is probably true for me. However, the junior math major either immediately grasped the mechanics of mathematics, or he learned not to get bogged down by them. When you see a mathematician manipulate some equations, it may appear to you as an exercise in futility. Bear in mind, however, that algebraic manipulation is as trivial to the math major as drawing curved lines is to you. If so, what does the mathematician see behind the equations that makes him love mathematics?
When studying mathematics, the math major sees pure truth in our understanding of everything. When something is proved in mathematics, it is true forever. Mathematics is also completely subject to our imagination, and not at all limited by the the outside world. Math is a language that allows us to speak about concepts and ideas that no language can express. Algebra is not a series of mindless tricks but the study of the idea of structure. Almost anything you can think of that possesses structure (including art), can be modeled using algebra. Analysis is more than taking a complicated derivative. It allows us to describe and understand the very notion of change. Every physicist, economist, chemist, etc. uses calculus to study the world around us, but calculus itself is more than this. Furthermore, not being bogged down by reality, mathematics is capable of arriving at beautiful generalizations where we discover that there are simple yet powerful laws that govern space, structure, change, and quantity.
Art enables us to describe every emotion and experience known to man, but mathematics enables us to understand the laws that govern everything. Art cannot show us something that is not a human experience, for it is limited by the person who uses it. Mathematics, on the other hand, can show as absolute truth realities too grand to be fully understood by the human mind.
At this point, you may appreciate that others love mathematics, but it “isn’t for you.” Before we proceed: what is mathematics, anyway?
When you think of math, you probably think of the tedious stuff that you do when you are forced to add, subtract and multiply long lists of long numbers. However, this isn’t math; this is arithmetic, which is barely a toenail on the huge elegant beast that is mathematics (i.e. arithmetic is only a teeny tiny part of math). Arithmetic isn’t what gets mathematicians up, out of bed, and excited about their jobs. We don’t just sit around doing long division all day.
Math is not about crunching numbers. Sure, that is part of math, but real math is exploring the properties of shapes, patterns, logic, algorithms, programs, and the relationships between all of these things. It’s about finding elegant and beautiful connections that naturally exist both in the real world and in the perfect mathematical one. It’s full of puzzles and mysteries!
Think about some of man’s greatest achievements:
Sending people to the moon and rovers to Mars, and coming up with mathematical models that describe everything from weather patterns to how galaxies and stars form to how the universe began and maybe will end – the glue that holds all of these things together is math. So, as you can see, math isn’t just boring arithmetic or formulas that come from nowhere. The distance formula is derived from the Pythagorean theorem, where the differences in x and y between two points are the lengths of the base and height of a right triangle. The area of a triangle, 1/2*(base)*(height), isn’t something to memorize: it is half of a square or rectangle.
Think about your every day life:
What is the best way to use linear perspective fool the eye’s depth perception? Use math! Alter the image with various linear transformations.
How do you get your sculpture to remain stable while it strikes an uncommon pose? Use physics! Move your sculpture’s center of mass to the appropriate location.
How do you create an eye-catching pattern as a background or an engraving? Use Escher’s symmetrical method or use fractals! There are so many options!
Are you bored in class? Think about all of the math in the room around you! Transform the ceiling tiles into weird diamonds! Imagine graphs of various polynomial functions that you can ride on like a roller coaster!
Math isn’t boring, it’s fascinating, and it allows us to do magnificent things. Do you want to be more creative? Math allows you to draw connections between otherwise unconnected objects. Math is the same in every country. Being fluent in mathematics gives you super powers: the ability to apply universal truths across fields. Are you tired of waiting on the world to change? Go out and change it yourself with your new found superpower.