I'll Never Say Failure Again by Andrea

I'll Never Say Failure Again by Andrea - August 2014 Scholarship Essay

When I arrived at Williams College Math Camp, the only figures on the chalkboard were 1, 2, and half of the alphabet. I remained optimistic, but I knew I was in for a challenge. Still, how hard could it be? I thought naively. During our first lecture I took notes diligently and understood most of it well enough, and our practice problems could even be called easy. The second day, however, I could only get through about half of the problems on my own. What I didn’t know was that they were from a 300-level course intended for Math majors, and completing half the problems was pretty good. I was starting to feel overwhelmed. Math had hardly ever challenged me before, and I couldn’t believe I was having trouble. It had to get better.

But better was not meant to be. After the lecture the third day, I was despairing. My understanding of everything from the first two days seemed to crumble around me when we dove deeper. To make matters worse, our professor assigned a proof that I didn’t have a clue how to do. My group spent our entire lab block working on the proof and by the end I was holding back tears, trying not to let on how confused I was. I didn’t know my aim, starting point, or anything in between. Our teaching assistants seemed to realize about an hour and a half in that my group mates and I were trying, but failing to make any progress whatsoever. The TAs pointed us in the right direction, explaining the first step and facilitating some actual progress. But I still had no real grasp on what any of it meant. Later that evening, I came back with some friends to work with the TAs. I wasn’t going to fail this, I couldn’t. So I took what I had already done, put some math I didn’t entirely understand in the middle, and handed it in to be checked. It was quickly returned with a look that said, very clearly, “You really don’t know what you’re doing, do you.”

No, I didn’t. I had the pieces, but I didn’t know how to put them together, and my first attempt had completely failed. Not only had I failed to prove the number of squares mod p for any odd prime n, it seemed I had failed to learn anything that week. But then it finally sank in. I had failed so far, yes, but I had tried. I had the pieces all there! Before Monday morning, I had had no background in Number Theory or modular arithmetic or anything I was doing now.. My education so far had emphasized that learning and succeeding meant answering everything right on the test. Points were lost for things unknown, and things known were simply points saved. But here, what I didn’t yet understand wasn’t a failure. Instead, what I did understand was an accomplishment. I didn’t need to get it all just yet. I was a sophomore fresh out of Algebra II/Trigonometry taking Number Theory 313, and I understood some of it. From that point in my education, my thinking changed. I no longer studied to avoid a grade I didn’t want; I studied in order to learn, to gain knowledge that I hadn’t had before.

So I took the rejected draft of my proof, and faced the facts. I took the pieces that my group mates and other campers had already figured out, and I wrote them down too. And suddenly the puzzle began to take shape, with every piece falling perfectly into place after seeing it again. I did understand; I just needed the realization that a failed attempt is not, in fact, failure. Failure didn’t exist anymore, because something can be gained from every mistake. I needed that “failed” draft to put the pieces together, and I needed to realize my accomplishment in trying. And so I put that proof together and handed it in on Friday morning. It still wasn’t perfect, but it still reminds me every day that our education is in our accomplishments, not our successes or failures on a scale of 100. Failure exists to push us along on our path, because without it, we’ll just stay where we are, content with our current efforts. So as the puzzle pieces of the proof came together, so did these puzzle pieces, and I’ll never say “I failed” again.