Maybe there is a royal road to mathematics, after all. If so, Paulos is motoring on it in the driver's seat with this wide- ranging follow-up to his best-selling Innumeracy (1988). In the course of 320 pages, Paulos introduces the reader to mathematics ancient and modern: from Euclid to chaos, pi to probability theory, the Fibonacci series to fractals. And all in truly short-takes (one or two pages per entry), which, one discovers, are presented in alphabetical order. This makes it easy to use the book as a reference while calming the mathematically anxious who might fear taking longer or deeper plunges into any subject. Yet Paulos does not trivialize. His clearly stated objective is to right the wrongs that drill, formulas, and endless exercises have wrought in high-school classrooms. Mathematics is a language with structure and logic, elegance and beauty. Its interpreters can be purists who deplore finding any use for math or practical-minded thinkers who apply its tools and techniques to physics and engineering. Bridging the two are those mathematical excursions into number theory, set theory, or non-Euclidean geometry that turn out to be models of the natural world-of the way flowers grow, quarks interact, or how the universe is shaped. Paulos tells it all like the gifted teacher he is, combining the mathematical lore with asides on culture and personalities. Galois died at age 21 in a duel over a prostitute; Gîdel died of malnutrition occasioned by ``personality disturbances.'' And so on and on in what one would like to see become an infinite series.