Like music or painting, says long-time math teacher (K-12 and college) Lockhart, mathematics is an art-""the art of explanation,"" ""the music of reason""-and its method of instruction in American schools has reduced a ""rich and fascinating adventure of the imagination... to a sterile set of facts to be memorized and procedures to be followed."" With passionate reasoning, Lockhart unveils the creative, flexible, open-minded side of math; an early analogy casting music education in a math instruction model-students must study proper notation for years before attempting to, say, hum a tune-makes a brilliant introduction. Making a clear distinction between ""facts and formulas"" and ""mathematics,"" Lockhart inspires a second look at received wisdom regarding math-that it's necessary to learn (do carpenters use trigonometry? Does anyone balance their checkbook without a calculator?), or that it has any direct connection to reality (""the glory of it is its complete irrelevance to our lives""). Though it features a thorough thrashing of current methods without suggesting how to fix the curriculum, Lockhart's slim volume (based on his widely-circulated essay) provides a fresh way of thinking about math, and education in general, that should inspire practical applications in the classroom and at home.