The Spark that Ignited My Journey into Mathematics: My AMC Story

By Bryan Nevarez (Queens College, City University of New York; Think & Write)

Bryan Nevarez

As a freshman in high school, the only thing that the initials AMC meant to me was the popular nation-wide chain of theaters. So when I was informed by my high school, seemingly out of nowhere, that I was selected to take a mathematics competition alongside my peers, I was intrigued, surprised and, in retrospect, way over my head. I came into the library that day of the exam without any background knowledge or information about the (Mathematical Association of America’s American Mathematics Competition) AMC 10. I just knew that it was a mathematics exam that would test the top performers from my high school’s mathematics classes, so I was glad to have made the cut and to be considered worthy to be a part of this selective group. As I had scored above 90% on math exams and maintained a high average for my math classes up to that point, I presumed that I would perform in a similar fashion on this 25-multiple-choice-question AMC exam. Of course there was a time constraint, but there was no need to show any work since there were no free-response questions. I thought that this shouldn’t be too bad. Boy, I was wrong.

I was completely thrown off guard after skimming through the first few problems. Quickly did I realize that I was out of my league. I only answered the first five questions, and even those answers were chosen with a dubiousness that I had rarely experienced before on a mathematics exam. As I perused through the later portions of the AMC 10, I quickly felt intimidated and lost because I had no clue as to what the questions were asking. I truly felt like I was grasping for straws in a futile attempt to not only understand what the problem was asking, but also to know where to even start.

I remember how, after the time for the exam had elapsed, I sheepishly handed in my exam with the answer sheet that had only five answers bubbled in. I then spoke to a few of my classmates who had taken the same AMC 10 exam: many experienced the same feelings that I had in terms of the level of difficulty of the problems. I recall how one of my classmates, considered by many as one the smartest kids in our grade, belittled the importance of his performance on the exam because he recognized that he had never learned the material so his own poor performance did not matter. Many others that took the exam felt the same way as he did and quickly moved on as if they never took it. However, I was not dismissive of the humbling realization that I did not know how to solve everything. Ironically, my dismal performance on the AMC was the very moment when my acute interest in mathematics emerged.

Directly after finishing the exam I felt a sense of inadequacy, but when I learned that my high school’s mathematics department would have a set of solutions for the exam, my gloom turned into hope and I was instantly intrigued to see how the problems were solved. Upon reading the solutions booklet, I was completely in awe of how clever and elegant the solutions were. It was an experience that revealed to me the high level of critical thinking and creativity needed to solve sophisticated mathematical problems. I realized that there was a whole mathematical world I had yet to explore outside of the mathematics presented in my high school classes. And I wanted to learn more.

From then on, I knew that I would pursue mathematics as my undergraduate major. In addition, I was certain that if I were to continue with my graduate studies that it would also be in mathematics. The AMC raised my level of expectation for my own performance and understanding of mathematics. I saw how mathematics problems could be categorized as “interesting,” “good,” and even “fun.” I found true delight in figuring out the solution to a problem —a quintessential joy for many math enthusiasts. Solving mathematics problems does not necessarily depend upon the knowledge that one possesses but rather on applying key insights to a previous base of knowledge in novel ways. This drove me to learn the why and how instead of just the what of mathematics. And this drive to learn mathematics with a more intuitive perspective led me to choose a career in mathematics.

Fast forward fifteen years from my first encounter with the AMC. I now have found my way onto the Editorial Board of the AMC 8. Being on the other side of the AMC—shifting from a student to an editor—really brings things full circle for me. I liken solving these mathematical competition problems to picking locks under a stress-filled time constraint, whereas the creation of mathematical problems is like the work of a locksmith whose expertise presumably surpasses those who are trying to solve them. Now, my mathematical interest has evolved from solving mathematical problems to creating them. I find that the process of creating good mathematical problems is orders of magnitude more difficult than the creation of a solution to a problem. And my appreciation for cleverly constructed problems has ballooned as a result of this editorial role I currently hold.

I have tremendous gratitude and respect for the MAA and the AMC. Due to my experience with this competition as a high schooler, my appetite for mathematics was both piqued and whetted. I remember reading the mission statement of the AMC back then, and I vaguely remember it stating that the nonroutine problems on the AMC serve to foster interest in mathematics. And this mission of theirs was fulfilled with me. This one exam has left such an indelible mark upon my journey that I am still recounting this experience many years later. Ultimately, I have come to realize that the competition is less among the students who take the exam and more about the competition between each student and the problem itself with the goal of overcoming the difficulty that the problem presents. And my competitive drive has only grown over the years.

I have learned that studying mathematics is truly a journey that requires mental grit and perseverance with the rewards being quite gratifying. The ability to do mathematics is not dependent upon one’s performance on any particular exam. As one of my favorite college professors once said, the two real prerequisites to learn mathematics are “the intellectual curiosity to learn” and the “willingness to think.” I would like for anyone reading this to know that as long as you have the curiosity and willingness to think, you, too, can learn and do mathematics. We in the mathematical community know and accept that mathematics is hard! There is no denying nor hiding this reality. Nonetheless, we accept the struggle as part of the journey to grow as an individual and human being. And we are here to help one another achieve heights that we personally may not fathom reaching. I hope that my story can help anyone begin or continue on their own journey!

Bryan Nevarez is currently an adjunct lecturer at Queens College (CUNY), a mathematics instructor at Think & Write, and serves on the Editorial Board for AMC 8. He majored in mathematics at Macaulay Honors College (Queens College) and earned an MS in Applied & Interdisciplinary Mathematics from the University of Michigan, Ann Arbor.