A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

by Paul Lockhart

Sometimes I like to imagine a Two-Headed Monster of mathematical criticism. The first head demands a logically airtight explanation, one with absolutely no gaps in the reasoning or any fuzzy “hand-waving.” This head is a stickler, and is utterly merciless. We all hate its constant nagging, but in our hearts we know it is right. The second head wants to see simple beauty and elegance, to be charmed and delighted, to attain not just verification but a deeper level of understanding. Usually this is the more difficult head to satisfy. Anyone can be logical (and in fact, the validity of a deduction can even be checked mechanically) but to produce a real proof requires inspiration and epiphany of the highest order. Similarly, it’s not that hard to draw an accurate portrait. One can develop an eye and master the technique. But to draw a portrait that means something, that conveys emotion and speaks to us—that’s something else entirely. In short, our goal is to appease the Monster.