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

by Paul Lockhart

No mathematician in the world would bother making these senseless distinctions: 2½ is a “mixed number,” while is an “improper fraction.” They’re equal, for crying out loud. They are the exact same numbers, and have the exact same properties. Who uses such words outside of fourth grade? Of course it is far easier to test someone’s knowledge of a pointless definition than to inspire them to create something beautiful and to find their own meaning. Even if we agree that a basic common vocabulary for mathematics is valuable, this isn’t it. How sad that fifth-graders are taught to say “quadrilateral” instead of “four-sided shape,” but are never given a reason to use words like “conjecture” and “counterexample.” High school students must learn to use the secant function, ‘sec x,’ as an abbreviation for the reciprocal of the cosine function, ‘1 / cos x,’ a definition with as much intellectual weight as the decision to use ‘&’ in place of “and.”