If the Limit Never Approaches Anything, the Limit Does Not Exist by Danielle

If the Limit Never Approaches Anything, the Limit Does Not Exist by Danielle - July 2026 Scholarship Essay

I stare at the styrofoam tiled ceiling in my third grade class, counting the specks so that I can avoid long division. I lean back on the hind legs of my chair, busying myself with anything other than my teacher or the workbook in front of me.

Just my luck, I came back to focus to Mrs. Lukemeyer and my entire class looking at me expectedly.

I blink, and I’m fifteen years older, but the situation is the same. Except it’s not Mrs. Lukemeyer, it’s Mr. Lerner, and instead of long division, I’m facing parabolas and limits. And I am quickly approaching mine as my AP Calculus AB class stares at me expectantly.

“The limit… does not exist?”

A shake of Mr. Lerner’s head. Eh. A good effort. I click my mechanical pencil and go back to doodling.

My entire life, I’ve never been great at math. I flew through chapter books in kindergarten but found myself stumped when it came to addition and subtraction. It was hard, and because it was hard, I despised it and avoided it. I counted down the minutes until math class was over so that I could shut my laptop, cram my homework to the bottom of my backpack, and forget all about math until the next day. I liked things that came easy to me, where the answers were just a passage away.

Math, unfortunately, is not one of those things. The horrible thing about it is that to get better at it, to learn its rules and ins and outs, you have to spend time with it. Much like a sport or hobby.

In tenth grade, I took the math class that would become the hardest class I’ve ever taken to this day. Pre-calculus. Test after test, I bombed. My graphs were flipped, rotated, mirrored wrong. I felt more defeated each day, and I didn’t know how anyone was passing this class, let alone getting an A. That was until I noticed one of my classmates, Jack, was always at our teacher’s desk.

Big whoop, I thought. He’s probably woefully lost like the rest of us.

That was until I realized Jack was bringing our teacher a new packet each day. Jack was doing the homework and study guides once, twice, three times… and then bringing them to our teacher to look over so that he could be steered in the right path.

I realized, then, that maybe my strategy towards math was all wrong. And I decided to push through the frustration. I started doing my homework, redoing it, and then doing it again. Completing problems frontwards, backwards… getting into the practice of math like I would with anything else. Suddenly, it became easier. I began to learn the parts of the problems like parts of a well-running machine.

Once I stopped avoiding math, I realized that you can’t give an issue on knock and then quit, no matter how frustrating and time consuming it may be. I gained clarity and perseverance over a subject that had been haunting me for years.

Most useful of all, I gained the ability to see things piece by piece and as a whole, to take them apart and then put them back together. A math problem is actually a whole lot like a real problem, which I deal with in my undergraduate majors, Political Science and Public Affairs. Especially in politics and governmental affairs, problems are more complex than they may seem at face value. They may take a long time to solve - from hours to years, but you can’t quit. Once I stopped approaching myself and my mind with the attitude that math was "too hard" or that I'd "never get it," the limit ceased to exist. In the end, my least favorite subject taught me the most valuable lesson.