British mathematician Barrow ( Theories of Everything ) here commands an elegant modern style in describing a more classical, structured grammar: that of numbers. This broad history of--and reflection upon--the role of mathematics in the human enterprise of figuring reality spans recorded civilization. Barrow examines hash marks made on bones that date from 9000 B.C., delves into numerology, observes mathematics in the depths of philosophy and the far reaches of cosmology, often utilizing playful headings to introduce substantive material (the section on early mathematics in the Near East is titled "The Counter Culture"). General readers who doubt that "numeracy" is as civilizing a pursuit as literacy will note how utterly human are some of the early-20th-century intuitionists' debates Barrow recounts in "Intuitionism: The Immaculate Construction." He does not justify the culture of mathematics as "fun" or as a separate, mystical realm but characterizes it as the modern manifestation of the oldest and most compelling human instinct.