Tell me if this sounds familiar: You’re sitting in your math class and you’re bored out of your mind. The professor is going over a bunch of formulas that you don’t care about. You’re copying each one of them into your notebook only because you will need them for the next exam.
I have seen my friend David go through this experience during a calculus lecture. There was no creativity, no engagement — but learning math doesn’t need to be this dull. I’ve once seen David have a much different attitude towards math, one full of excitement and curiosity.
One day, I challenged David to figure out how to add infinitely many numbers: something known as an infinite series. The first series I discussed with David was the following:
The numbers go on forever, with each being half of the previous. It might not be intuitive at first glance that it is possible to add an infinite set of numbers, but you only need to look at it a certain way.
Here’s an analogy David came up with: Imagine eating half a cake, then eating a quarter of the original cake, then eating an eighth of it, and so on. As you continue eating slices, the cake remaining becomes smaller and smaller while the total proportion of the cake you have eaten approaches 1. If you look at it like that, it makes sense to say that our sum is equal to 1.
Using a similar visual method, we can find the sum of some other series. For example, what do you think this sum is equal to?
David and I both had a lot of fun as I let them discover how to make sense of infinite series. Instead of lecturing, I asked questions and let David do most of the thinking, allowing them to try different things and come up with solutions on their own. I wanted them to feel as if they had personally discovered these facts. This is what learning math should be like: an engaging exploration of problems using only your imagination, along with the satisfaction of coming up with solutions.
As Paul Lockhart describes in his essay “A Mathematician’s Lament,” mathematics is about exploring problems, trying different things and discovering patterns. Yet the mathematics that is typically taught in schools and colleges is nothing like this.
In most math classes, students memorize rules and repeatedly perform uninteresting computations instead of exploring the elegant patterns behind math. It’s like trying to learn piano without ever getting to press the keys. It should not be surprising that this form of education leads to unengaged and underperforming students. UTD is a prime example of this: many students at UTD are struggling in their math courses. According to data from UTD Trends, between the fall 2023 and spring 2025 semesters, the median grade in Integral Calculus is a C+, with over 27% of students receiving a D+ or below. This “D+ or below” rate is over 25% for Differential Calculus and over 23% for Linear Algebra.
Most math classes are focused on performing computations rather than conceptual understanding. Knowing how to perform computations can be useful for some students. But this shouldn’t be the only thing math classes teach; they should also focus on the process of problem solving, the way these formulas were derived in the first place. This doesn’t have to be in the form of formal proof; intuitive explanations are valuable as well. Many formulas have beautiful and intuitive ideas behind them that most students never see.
Despite the issues with math education, we can still improve students’ learning experiences. When we’re helping students with math, we can go beyond computations and formulas and explain the underlying concepts in more depth. My exercise with David is just one example of this approach — one that lets students have a greater role in their learning, allowing them to discover important facts for themselves rather than simply telling them the results. This makes mathematics feel like an engaging puzzle rather than a list of facts and procedures to memorize — a way to discover surprising relationships between ideas and solve some of humanity’s most interesting abstract problems.
We as students have the power to share the beauty of mathematics with each other. Many students hate math not because the subject is inherently tedious and meaningless, but because they’ve never seen math presented in an engaging way. If you know someone who feels this way, you can change this.
Before you say “I’m not good enough at math to help others,” think for a moment about what mathematics is to you. Do you see mathematics as a set of rules and procedures to be memorized, or do you see it as the creative art of discovering abstract patterns and solving problems using them? Are you actually bad at math, or are you just uninspired by how it is taught?
Students aren’t the only ones who can make math more interesting. To increase student engagement, professors can add short interactive sessions at the start of lectures where students get a chance to interact with the concepts and make discoveries themselves.
Any subject could seem dull if taught incorrectly. Imagine an art class where you never get the chance to create your own works, or a music class where you never listen to any pieces. Mathematics is beautiful and culturally important, and we should treat it not just as a science but also as an art. Every student deserves the chance to discover the wonders of mathematics.