First off, I’m being an idiot. Here I am, as a self-proclaimed “math person,” disparaging a fourth of high school mathematics, but I suppose honesty has no bounds. Let me also be clear about Lakeside geometry classes: they’re fantastic — clear, precise, and taught by excellent teachers. This is not a reflection on them, but rather on geometry as a subject.
When I try to describe geometry in one word, my mind gravitates towards a collection of unbecoming descriptors: useless, irrelevant, irritating, useless again. And there’s a reason for it — geometry, unlike algebra or calculus, rarely appears elsewhere. Now yes, I’m aware that formulae like the area of a triangle or rectangle — as well as fields of study like trigonometry and vectors — do come up later in mathematics. But let’s be honest: If you’re going into a high school geometry course, you know the basic facts you need to know. And trigonometry and vectors will follow in precalculus and calculus anyway.
So what else does geometry have to offer? I suppose we have cevians and medians and tridians and symmedians (one of those is fake), but almost no one — sans the mathletes — is going to need to remember the angle bisector theorem any more than most need to remember who the U.S. president was in 1836. Is it a nice fact to know? Sure. Can I search it up? Yes. Am I going to use it more than maybe once a year (outside of competitions)? No. Geometry simply has no bearing on any math that came before it. In high school, we have a beautiful sequence of courses that build on each other: Polynomials in Algebra 2 turn into functions in precalculus, which turn into derivatives and integrals in calculus. And then there’s geometry stuck in the middle. Ignore those quadratics you just learned; let’s learn about orthocenters, circumcenters of triangles, and Heron’s Formula instead!
But what about the mode of thinking learned in geometry classes? It’s where high schoolers usually learn proofs for the first time. Proponents of two-column proofs, the technique often introduced and reproduced countless times in geometry classes, argue that the technique is a great way to segue math students into producing proofs. And yet, two-column proofs are almost never used by mathematicians. I would argue that the way we learn to write history essays is closer to the mode of thinking used in math proofs than the way we learn to write math proofs. The level of detail required in geometry proofs is precisely the wrong amount: it’s too little to call the proof “rigorous logic,” and yet it’s much more detail than most advanced math proofs. In either case, geometry is not the discipline for proof introduction. There are numerous methods of proof that geometry doesn’t cover, hardly making geometry the garden of proofs geometers claim it is.
But maybe learning geometry is still important because of the “pursuit of learning.” I disagree. Geometry is a bamboozling forest of bamboo that students have to bumble through until they find la belle rue. Even though the subject is visual — which is great for most people, including myself — that also makes it all the more irritating. In other fields, you have a sense of direction: whether to solve a problem using derivative rules, the quadratic formula, or systems of equations; in geometry, that all falls away. Your best way to solve any problem is to stare at it until some angles look congruent, some sides look congruent, or you see that one pair of similar triangles that unlocks the remaining steps.
But this is where I must concede one fact to geometry lovers: The subject forces us to imagine — a skill far more important than mathematical knowledge itself. In most high school math courses, creativity and the ability to dream up solutions for ourselves are almost afterthoughts. By its very nature, geometry is special, as proofs are often required — something which doesn’t happen again until multivariable calculus — and problems need outside-the-box solutions. If you want to flex your problem solving skills even more, I’d suggest trying out a math competition. Of course, the irony is that, to succeed in a competition, you do actually need a strong command of geometry. Maybe the subject isn’t that worthless after all.
