Jonathan Rueffer
Most of us have sat in a math class and wondered “When am I ever going to use this?” Beyond its undeniable validity, the question reveals a larger issue: math is solely viewed in terms of its usefulness in application. Teaching math through this narrow lens obscures its true nature, creating a reputation that undermines the discipline’s creativity and beauty. I am not trying to argue that everyone should become math majors; I am arguing that math’s reputation is misleading, and that it’s worthwhile to uncover what the subject actually is.
I wasn’t interested in studying math when I came to Wooster. Initially, I treated it as a practical complement to my computer science major. But over several years of challenging math, including a semester abroad focused entirely on it, I began to appreciate the subject for what it is.
So, what is math? I’ve found it useful to think of math as a language—a language of logic that humans created to understand patterns in the world and communicate ideas with absolute unambiguity. Math itself begins with a shared set of assumptions that we agree to accept as true, called axioms. From those simple starting points, the entire structure unfolds: definitions, theorems and logical frameworks that connect them. The “plug and chug” process that most people remember from school are just grammatical exercises, not the language itself.
What fascinates me is the depth of this vast and interconnected structure. Its complexity and beauty stems from a collaborative, centuries‑long conversation between mathematicians thinking carefully and creatively.
“Doing” math isn’t really about manipulating numbers. It is about proving that a statement must be true. A proof is a lot like an argumentative essay, with the final sentence acting as the thesis: “therefore, the statement is true.” The introduction identifies the key elements. The body is a sequence of logical steps, each justified by the earlier, building towards the final conclusion. And just like with writing, you have to be mindful of your audience. How much detail do they need? What background can you assume?
To get a sense of how proof writing works, consider a simple example. Suppose we want to prove the statement: an odd number cannot be divisible by two. Assume, for contradiction, that an odd number is divisible by two. If it were divisible by two, then by definition, it would have to be even. But odd numbers aren’t even—a clear contradiction. Since our initial assumption leads to an impossibility, the only thing that can be wrong is the assumption itself. So, we conclude that an odd number cannot be divisible by two.
Being a math major is not about quick mental multiplications or memorizing formulas. It is about learning to construct clear, logically sound arguments, and that is a skill that transfers to virtually any context.
An example of a small yet surprisingly powerful mathematical idea is the Pigeonhole Principle. The principle states that if you have more items (pigeons) than containers (pigeonholes) to hold them, at least one container must have more than one item. This straightforward observation leads to compelling conclusions. For instance, if you have 13 people in a room, it is guaranteed that at least two people will share a birth month since 13 is greater than 12.
I hope that I have shown that math is not the boring, mechanical subject you may remember, but a human way of thinking that deserves a second chance.