reflections

"When I first participated in the Soifer Math Olympiad, I didn’t know what an olympiad was. I assumed that the problems would be familiar, the ideas would be standard, and the time limit (of four hours) would be unnecessary. Suffice to say, I was unprepared for the difficulty and originality of the problems I encountered.

That Olympiad was four years ago, and many of the details have faded in my memory. But I remember one problem distinctly. It involved a person who could make certain moves on a grid, and it asked whether or not the person could move from a start point to an end point in a certain number of moves. I was immediately stumped. How could I find a path on a grid that was too large to draw? If no path existed, how could I actually prove this? After trying to resolve these questions mentally, I tried a more concrete approach: I drew smaller grids and attempted to construct paths for them. Looking at small cases led me to an insight: I could color the grid! Then, each move would correspond to a predictable change in color, making the overall path much easier to analyze. After several hours attempting various colorings, I found one that, magically, showed that no path was possible.

This problem embodies everything I have come to love about olympiad math. It is accessible to almost everyone. Both the statement and solution are simple and elegant. It appears intractable, but is made clear through perseverance.

My experience at my first Soifer Math Olympiad encouraged me to go further. I began to seriously prepare for proof-based contests. I discovered that every problem has a unique, creative idea that is immensely rewarding to find. By attempting these problems, I developed a genuine appreciation for mathematical beauty.

The most important thing I have gained from participating in the Soifer Olympiad is courage: the courage to struggle through difficult problems, despite not knowing where to begin. This courage was invaluable at the 2022 USA Math Olympiad, where I tried idea after idea for four hours before finding one that worked. This courage was crucial when I attended the Research Science Institute this year, where I worked on open problems for a month with no sense of their difficulty. And I am certain that this courage will help me in the future, as I explore a variety of fields and careers.

I am planning to major in math, and I hope to continue working on open research problems. I am forever grateful to the Soifer Math Olympiad for sparking my initial interest in mathematical problem solving."