by Connor Novak, mathematics
I frequently have the following interaction: I meet someone new, who asks what I do. I say to them: “I’m a grad student in math”. They reply: “Wow that’s crazy, I could never do that because I hate math.” These interactions make me sad, but it is not because they don’t like math; everyone has their own interests, and I don’t expect them to align with mine. It makes me sad because they say they “hate math,” but 99.9% of the time, they mean that they hated high school algebra, trigonometry, or calculus. But this isn’t what math really is about.
There are so many amazing things that happen in mathematics that a high school student could understand, which they are never introduced to. In his book Love & Math,1 Edward Frenkel draws a nice analogy: imagine if in art class in school, you were only taught how to paint a fence. You were never shown the art of Van Gogh, da Vinci, or Picasso. Art was purely taught as a means for utility, never for beauty. You would hate art. This is essentially what is the case in mathematics education. For the most part, high school students are shown the boring mathematical concepts that they “have” to know, but they are not shown the fascinating, beautiful ideas which maybe they don’t “have” to know. For instance, most people were probably never shown this picture in a high school math class:
The above image is what’s known as the Mandelbrot Set, and it is an example of what mathematicians refer to as a fractal. What the Mandelbrot set is or what it is used for may not be a reasonable topic for a high school math class, but a teacher could easily take one day of class, maybe at the end of the semester when the course is winding down, to talk about fractals and show some cool examples. Just like how we are shown the art of the old masters in art class, we could be shown some of the clever ideas of great mathematicians of the past, from Gauss and Euler all the way back to the Greeks and Euclid. I believe people would feel differently about math if they were shown that objects like this exist at all, no need to go into the details. In my experience, it really doesn’t take all that much for someone to become inspired by mathematics. Most people I have met who study math developed their love for math because they saw something inspiring one time. Maybe they watched a cool video on youtube, or maybe a high-school teacher showed them something interesting after class. Nobody is inspired to pursue math because of the beauty of factoring cubic polynomials.
Math is inherently captivating, in my opinion, because it underlies the nature of our reality. There is a famous quote from Galileo Galilei:
“Mathematics is the language in which God has written the universe.”
In my experience, doing math makes me feel close to the fundamentals of our existence. It makes you question what it means for something to be true. How do we know that the square root of two is irrational? How do we know that 1 is greater than 0? What is a number? It allows you to consider fundamental ideas such as symmetry, duality, and classification. Most of all, you approach all of this with just your mind. You become close to your intrinsic abilities to perceive, analyze, and deduce.
One thing you might say in response to this could be: “Why should we do this? We don’t need everyone to become mathematicians.” You’re right, we definitely do not want everyone to become a mathematician. However, there is value in pursuing math to some degree for everyone. Math teaches you to become an excellent problem-solver. When solving higher-level math problems, you need to consider many different approaches, and you are often forced to change how you think of a concept to understand the solution. The critical thinking skills you can gain from mathematics are invaluable, and they can help you in whatever field you are in—not just in math. My point is that math has a role in everyone’s life, no matter how small. Letting math into your life will change you for the better in some way. It could make you better at attacking complex problems, it could teach you how to think about some aspect of our world, or it may even show you beauty in a way you never could have expected.
- Frenkel, Edward. Love and Math: The Heart of Hidden Reality. Basic Books, a Member of
the Perseus Books Group, 2014. ↩︎