Why I Recommend Studying Pure Math

When I applied to be a math major, I was convinced applied math was the only option that made sense. It sounded practical. Algorithms, optimization, finance. Things that clearly led somewhere. Pure math, in my mind, was for people who planned to spend their lives in academia.

That wasn't me. I wanted to work. I wanted to build things. So I wrote off pure math.

Then my degree plan forced me into a proof-based class.

I enrolled in Discrete Math with Dr. Zachary Miner. The course followed an inquiry-based learning format, which meant very little lecturing and a lot of student-driven discussion. At first, it felt easy enough. The first two weeks covered logic and standard proof techniques. I thought I understood what I was doing.

I lost that confidence when we moved into more serious theorems.

For homework, Dr. Miner gave us theorems from the textbook to prove. No hints. No roadmaps. During class, students had to present their proofs. Sometimes they worked, sometimes they didn't. On days when nobody in the room could fully prove a theorem, Dr. Miner didn't fill in the gaps. He would point out exactly where the logic failed and moved on. Even in office hours, he refused to give us answers. He only asked questions back. Questions that made it obvious what I didn't understand.

At the time, this was incredibly frustrating. Exams were approaching, homework deadlines were tight, and I would spend hours stuck on a problem without making any progress.

What surprised me was that I signed up for another one of his classes anyway.

Number Theory. Harder content, same teaching style, and same refusal to hand me solutions. I did it because that first class taught me something no other course had. How to sit with uncertainty without panicking. How to be precise when nothing feels obvious. Every other math class I had taken trained me to recognize patterns and apply formulas. Dr. Miner trained me to slow down and reason. When I genuinely didn't know what to do, progress came not from memorizing tricks, but from asking what I actually knew, what I was assuming, and whether those assumptions were justified.

That idea stayed with me.

As I continued through my degree, I took a class taught by Aaron Benda, a math PhD student at UT, focused on what it means to teach undergraduate math. One central question we kept returning to was simple but uncomfortable: what is the purpose of a math education? The answer wasn't producing mathematical prodigies. It was about training people to reason carefully in ambiguous situations. To make arguments that hold up under scrutiny. To stay disciplined when the path forward is unclear.

That reframed everything for me.

Looking back, I realized I had slowly fallen in love with proof writing. Writing proofs forced me to confront my own thinking and often exposed every shortcut I wanted to take, especially moments I was tempted to say “this is obvious” without actually knowing why.

By contrast, many of my applied math courses, at the time, felt mechanical. Memorize the formula and plug in the numbers. Useful, but fundamentally different.

That trajectory eventually led me to Real Analysis with Dr. Alexis Vasseur. Easily the hardest class I have ever taken, and also one of the most meaningful. In that course, nothing was allowed to be taken for granted. We proved things I had assumed were obvious for years. That zero times an integer is zero. That limits and derivatives behave the way calculus claims they do. Entire pages devoted to concepts I once accepted without question.

It was exhausting and humbling, but it changed how I think.

Pure math taught me to stop accepting truths just because they were handed to me. It trained me to ask why, and to demand an answer that actually made sense. That habit has carried far beyond math: questioning whether this algorithm is the right choice before implementing it, evaluating claims I encounter in everyday life, and recognizing when I don't understand something as well as I think I do.

If you want clean answers and fast results, pure math will probably frustrate you. It definitely frustrated me. But if you want to build the rigor and patience to operate when nothing is spelled out, and to develop the habit of asking “why” instead of taking things for granted, I can't recommend it enough. Even when it's stressful. Especially then.