Opinion: You’ve Been Lied To Your Entire Life About Math

Life as a junior at Reed typically takes the form of a later season of a sitcom, with recurring, comfortable characters that I tend to know quite well, people in my classes I’ve seen time and time again, and familiar faces every corner I turn, but occasionally I put myself out of my comfort zone and meet someone new. Unfortunately, I tend to slide into the default option for small talk, and I usually end up in the all-too-familiar conversation of “Hi, what’s your name? What year are you in?” before getting to the grand finale of “what’s your major?” At this point, I know exactly how the conversation is going to go. “Math–Physics,” I tell them. “Oh, I was never very good at math,” is what I hear a lot. “Numbers aren’t really my thing,” they tell me. At this point, I never really know how to continue the conversation. Do I try to even the score by saying I never really got the hang of anthropology or economics? Tell them that I struggle sometimes with writing a good essay? But why would I try to further a binary divide and allow it to define myself within one of two well-sorted academic houses? 

I’m not an expert in the humanities, but I know what it’s like to be human, to work with language, to feel emotions and feel inspired to put those emotions into art that can be interpreted, understood, and misunderstood. I’m not an expert in political science, but I have to live under the same systems of governance as the rest of us, and want to know how to organize and build a better system. These things can be studied, but they can also be felt and talked about by anyone without requiring a prerequisite course or jargon lesson. Why are math and science any different? 

You’ll often hear people try to prescribe disciplines into one of the two categories to make a point about their inherent quality, value, or jurisdiction. Someone might call biology “an art” if they want to describe the certain je ne sais quoi of the chlorophyll production process in a plant cell. Someone might call economics “a science” if they want to create an allure around free-market capitalism to argue that it is analyzable, equipped with axioms, and thus, unemotional. After all, who could have feelings about a number, a statistic, or a model? The STEM/Humanities divide is not just inaccurate, it’s an ideological weapon.

If I had to pick a point where this ideology enters the average person’s life, it would be the third grade times table tests. Many of us can recall having to sit down, with a clock ticking above our heads, as we were forced to remember that six times five is 30, eight times eight is 64, and seven times nine is… and then the timer was up and we had to retake the test again the next week. We were told that this is math: that math is about learning facts, figures, numbers, and rules, then doing the problems quickly and efficiently. This is as much of a primary school lie as the first Thanksgiving.

This is not what math is, in the same way that agriculture is not the act of finding the most profitable way to get your weeds pulled, but the act of understanding why they grow in the first place. The names of numbers, theorems, and formulas are not the entirety of what math is, but instead a colonization of an invisible landscape that is accessible to anyone. There’s a reason that the hypotenuse of a right triangle is found by what we call the “Pythagorean Theorem,” but the method for determining unknown quantities involving a value scaled by its own magnitude is known as the “quadratic formula” and not “the method of Muhammad al-Khwārizmī.” The shapes that compose the universe are a boundless resource available to us all, but they have been named, standardized, packaged, and sold by those in power, who will continue to do so until we stop treating math as a gift given to the fortunate and start treating it as one of the many revelations of consciousness that connects us all.

I’ve spent a decent amount of time explaining what math isn’t, but now I’d like to give you an understanding of what math is, by tackling one of the most difficult problems from the dark depths of the notorious course that is Real Analysis. Behind its terrifying logic symbols and theorems named after 19th-century Italians, Real Analysis is, at its core, the study of distance.

I want you to find an empty room. Sit somewhere in the room, stretch your arms out, and feel the space around you. First, notice the existence of things. Your head is the thing you are looking at the rest of the room with, but your hands are somehow different things connected to the rest of your body by arms. 

Next, realize the existence of distance, that there exists distance between your eyes and your hands, there exists distance between yourself and the walls, there exists space everywhere in all directions. What is this distance? Does it really exist or is it just in your mind? What are things you know about this distance? You did not bring a ruler with you, and in fact, you don’t need one. You can learn three things about this distance completely on your own. First, you know that distance cannot take on any value: you know that your hand has no distance from itself, it is, in fact, exactly where it is. Second, you know that distances can be equal: as an easy example, you know that the distance from your left hand to your right hand is the same as the distance from your right hand to your left hand. 

The last thing you know is that some distances are larger than others, even if you can’t measure them. You know that if you first traced the distance between your eyes and your left hand, and then kept going from your left hand to the door handle, this distance would be no shorter than if we went directly to the door handle. Somehow, if we add a detour along the way, our notion of distance must either get larger or stay the same. Now that we live in a room with distance, we can learn so much more about the room. Now it is no longer just a space, but something a mathematician would call a metric space. However, you can call it whatever you want. Again, you are the only one in this room.

However, this just leads to more questions. How close can you get to the walls in this room without touching them? How many different points in space are there in the room? Could one add any more? Something about this room feels very claustrophobic now that we think about it, everything seems so…close together, inescapable, compact. But what does this mean? 

Suppose you wandered around in this room for an infinite amount of time. At every second, a camera on the wall took a picture of your position in this room. Suppose you took up very little space and were very fast, so that you could be at any singular location in space in the room at any point in time. You want to see if you can really truly thoroughly explore this space, and not linger around in the same place for too long. Every infinitely long wander you take, however, the perverted being who took photos of you for eternity takes the stack of photos in order, tossing out most of them but still leaving an infinite amount of photos left. This being shows you these remaining photos, which show you getting closer and closer to a single point in space, eventually appearing to stand still. This happens every time, no matter what path you take.

It turns out that this property of the room makes it a wonderful laboratory for all sorts of other experiments. Understanding it plays a part (through the field of study known as functional analysis) in allowing the mechanics of math to be wielded by physicists who want to answer questions about the nature of the universe, about gravity and the smallest particles, and about chaotic movements through space and time. It can be developed just starting with our three simple axioms of distance. 

However, while we can try our best to build a language that puts all the pieces of the universe together, not everything fits together so nicely. Two of the discoveries of 20th century physics, standardizing every particle in existence and understanding how matter curves space and time, still have yet to fit together perfectly. Maybe we are all “not very good at math.” Or maybe we’re all just trying to make sense of the short experience we get with consciousness, with everything we perceive: shapes, thoughts, structure, disarray, beauty, distance, suffering, warmth, motion, change, all in one amorphous blob of existence that cannot be cut down the middle, but can be experienced by all.