Numerology

My cousin, bound for a top liberal arts college in the fall, was amused when I told her I was reviewing a book about big ideas in mathematics, from the classical to the contemporary. “Don’t they already know everything about math?” she asked. “You know, there’s algebra ... and then calculus ... and that’s it, right?”

Andrew Hodges, a fellow at Oxford and the author of the lively new book “One to Nine,” would have been horrified, but not surprised. My cousin, in his view, is a victim of the pedagogical tradition that presents math as an eternally fixed array of computations, to be memorized and repeatedly executed without motivation or explanation. The result, he writes, is a “legacy of fear and anxiety generated by schools, which leaves most of their victims with a lifetime of mumbling apologetically about ‘my worst subject.’”
“One to Nine” offers a different model for teaching math — discursive rather than linear, topical rather than abstract and remote, and, above all, manically energetic rather than repetitive and plodding. The book is composed of nine chapters, each focused — very, very softly focused — on one of the first nine natural numbers. Chapter Four, for instance, starts out with the observation that four is a perfect square, and from there skips along to the construction of Latin squares, the irrationality of the square root of two, the definition of the logarithm (whose relation to “four” never comes entirely clear), complex numbers, and the even more exotic quaternions (a number system in which “numbers” are actually strings of four integers, and the product of two numbers depends on the order in which you multiply them!), the theory of four-dimensional spacetime and Einstein’s equation E=mc2 (squares again) before finishing with a short and speculative account of the theory of twistors, one of many competing candidates for the universe’s underlying geometry. NYTimes-