My relationship with math over the years has been like many of my other relationships—promising, awkward and ultimately disappointing. (Understand, BTW, that this is from someone who has remained happily married for 37 years, so there have been exceptions.)
After scoring the highest mark in my large high school class on the math section of the SAT (surpassed thirty years later by my son’s perfect score), I chose not to take any math in my senior year of high school or in college. Multiple friends and classmates said, “What a waste!” but I retained an appreciation for the reverence many great thinkers have had for math and its centrality in understanding the world around us.
In his book, Infinite Powers: How Calculus Reveals the Secrets of the Universe, Steven Strogatz quoted Galileo: “This grand book [i.e., the universe]…cannot be understood unless one first learns to comprehend the language and read the letters in which it is composed. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it.”
Over centuries and across cultures, attempts to understand and solve practical problems about things like inheritance law, tax assessment, trade, accounting and interest calculations drove the progression of math from geometry (plane and analytic) to algebra (verbal and symbolic) to calculus (integral and differential). As they were combined and visualized in new and changing ways, the branches of math provided solutions to new problems, enabled new inventions and enriched our understanding of ourselves.
I don’t understand much about calculus, but in many aspects of modern life, Strogatz said, “calculus operates quietly behind the scenes.” I know, as Strogatz said, that calculus has two sides: differential (which divides complex problems into an infinite number of pieces) and integral (which reassembles the pieces to solve the problem). In this way, while geometry deals with things that are static—speed, straight lines, ratios—calculus can address things that change—acceleration, curves, interest rates—by using derivatives to model rates of change and integrals to model the accumulation of change.
Operating “quietly behind the scenes,” calculus enables the functioning of things like GPS, electronic financial transactions, wireless communication, HIV immunotherapy and satellite navigation that we mostly take for granted and depend on every day.
I get pleasure from reading about math not because I understand its highest levels—I don’t—but because it makes me aware of how many ways math can express the nature of the universe and how useful it can be.