The Calculus Worldview Ronnie Mizrachi
“This is just nonsense,” my friend tried convincing me one day in AP Calculus. “Two points can never actually become one, so the concept of a derivative is only abstract,” he cynically remarked. “But think about how profound that is, Marc. By imagining their convergence, we can come up with real results about the actual slope,” I explained to him. But his rolling eyes and unwavering expression of discontent made it clear to me that he was stuck in the rigidity of algebraic manipulation. I related to his skepticism. As a rudimentary mathematics student, I was taught to seek truth by asking questions like “What is the case?” in algebraic equations, and “How do you know?” in geometric proofs. But my experiences in AP Calculus distanced me from those processes of concrete analysis. Calculus’s approach intrigued me because it relied on the preexisting axioms of algebra and geometry, but also searched for mathematical truths by asking “What if?” What if a rectangle could have infinitesimally small width? What if a function could approach infinity? While I noticed that many seemed to fear such abstractions, I felt inspired by the seemingly limitless potential to elaborate on the nuance of what is real and true. In a sense, calculus taught me that delving into abstract gray areas is an integral part of seeking truth and inspiration. I began to find Calculus everywhere. For two summers, I had the privilege of working for my grandfather, “Grandpa Ronnie,” on his Bible commentary, both as a writer and an editor. Much of his commentary focuses on literary elements such as intertextuality, structure, and symbolism, which may be observed only by departing from a simplistic reading of the text. Through his tough criticism, my grandfather taught me the value in questioning and challenging traditionally
84 ~ Snow
