This is the book that could replace most every textbook used in grade school math. It brings the reader from geometry to differential calculus in an astonishingly smooth progression. Let me say that again because you weren’t paying attention: Lockhart leads you, in plain language, from the most basic concepts of line and shape, all the way to differential ever-loving calculus in a single svelte volume. And this progression is more than a series of lectures, this is a book on Mathematics: each concept leads logically to the next, each answer leads to the next question. And you, the reader, are doing the asking and answering. It feels inevitable and effortless. This is Truth without pretense. Lockhart does not waste time (his or yours) on arbitrary definitions or vocabulary. He knows that understanding a thing is more important than knowing the name of a thing.
This book cultivates, indeed relies upon, the spark of curiosity that drives all children. The spark that gets extinguished so efficiently by what presently passes for education in most American schools. Instead of training you to be a calculator, Lockhart shows you his own passion and curiosity and teaches you how to ask and answer your own questions. This is a book that teaches you how to fish.