An expansive overview of numbers and figures, and those who find them irresistible.

Though he has an Oxford degree in math, former *Guardian *reporter Bellos (*Futebol: Soccer: The Brazilian Way*, 2002) approaches the subject as an enthusiastic amateur. He begins at the most basic level, with the concept of number itself, looking at the ways children, tribal cultures and animals deal with the idea of quantity. Perhaps not surprisingly, an ability to recognize which of two trees bears the most fruit seems to predate the ability to count. Cultural differences appear even in mathematically advanced societies, and the conventional system of base ten math is only one of several ways to break up the number system, with binary math probably the best known alternative. For arithmetic, Bellos looks at Japanese abacus experts, who can add columns of numbers faster than a calculator, and the Vedic math promoted by an Indian sect, which offers advanced algorithms for multiplication and other troublesome operations. Geometry also provides plenty of material, from the Pythagorean theorem to origami to the “golden ratio” beloved by architects and artists. A chapter on logarithms leads to a discussion of slide rules, the first choice for scientists and technicians requiring a quick answer until the pocket calculator drove it out of favor. Another chapter provides a lucid discussion of statistics and the famous bell curve. Recreational math gets its due, as well, with nods to Sudoku, Rubik’s Cube and the master puzzler Martin Gardner. The final chapter examines infinities and non-Euclidean geometry. Bellos maintains focus on the people who have created math and who have used it creatively, from the famous Greeks to Renaissance figures like Descartes and Fermat, and 19th-century giants like Gauss and Poincaré. Readers desiring more will find online appendices that treat the concepts more rigorously, with proofs where relevant. However, most readers who remember high-school math can follow the clear and entertaining accounts.

A smorgasbord for math fans of all abilities.