One day that September, I found myself leading an awkward impromptu discussion of why we study geometry. Did grown-ups write two-column proofs? Did engineers work in “no calculator” environments? Did personal finance demand heavy use of the rhombus? None of the standard justifications rang true. In the end, my 9th graders settled on “We study math to prove to colleges and employers that we are smart and hardworking.” In this formulation, the math itself didn’t matter. Doing math was a weightlifting stunt, a pointless show of intellectual strength, a protracted exercise in résumé building. This depressed me, but it satisfied them, which depressed me even more.
The students weren’t wrong. Education has a competitive zero-sum aspect, in which math functions as a sorting mechanism. What they were missing—what I was failing to show them—was math’s deeper function.
Why does mathematics underlie everything in life? How does it manage to link disconnected realms—coins and genes, dice and stocks, books and baseball? The reason is that mathematics is a system of thinking, and every problem in the world benefits from thinking.
