There is a humorous, misguided stigma associated with math. Just the mere utterance of the word “math” conjures up, for many, the image of intimidating, arcane equations strewn about blackboards and calculators gone on the fritz. For many, math was a painful experience in grade school (and beyond) -- myself included! In fact, I did not become interested in pursuing a math major until my sophomore year of college. The purpose of this post is not to philosophize on the state of mathematics curriculum in America’s schools, but rather, to explain how I eventually saw meaning beneath the seemingly endless exercises.
Initially, I had planned on studying biology, in particular, genetic engineering. It always intrigued me how our entire being and makeup was largely determined by a sequence of A’s, T’s, C’s, and G’s. Many of my summers were spent playing with the genomics of glow-in-the-dark zebrafish. I became accustomed to testing hypotheses which rang either true or false within a confidence interval. What I mean by this is that the truth of my ideas and notions were never 100% certain. Arriving at answers that were “probably” correct never sat well with me. However, during my sophomore year I enrolled in an honors calculus course which offered an alternative to this paradigm. The class introduced the notion of “proofs.” Theorems and propositions in mathematics are built up from a chain of logical deductions, known as proofs, which result in conclusions that are simply true. Math is built up from a set of initial assumptions about the world we assume to be true, and from them we create and discover complex results. The method by which we establish our answers live within an airtight vacuum with no room for uncertainty. This was a gripping concept to me which quickly developed into a passion for the field of mathematics.
Given my limited exposure to proof and logic in mathematics, my first few semesters taking higher level courses were challenging. However, my professors were inspiring and supportive and this drove me to continue exploring the field. Initially, I saw mathematics simply as a series of methods used to solve rote and laborious problems, but as my education progressed, I was able to discover its broader applications. I encountered theorems and formulae which could describe phenomena ranging from the movement of financial markets (Black-Scholes equation) to the movement of water (Navier-Stokes equations). Much to my delight, things came full circle with my lingering interest in biology when I encountered a set of equations which could predict predator-prey dynamics (Lotka-Volterra equations). Suddenly the “vacuum” within which mathematical theory existed extended to encompass the world around me.
To see ideas which are proven on paper manifest themselves in reality is simultaneously daunting and exciting. Through research, I have been fortunate enough to contribute original theorems of my own. Using my coursework as a means to create novel ideas gave new meaning to my studies. I imagine for many, math may seem esoteric, and my goal as a tutor is to help eliminate this stereotype. As someone who wasn’t interested in mathematics until college, I am glad I chose to explore this field, and hope to share this enthusiasm with the students I teach.
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