A stimulating, wide-ranging look at how the Greek mathematician and philosopher’s key insights have been at the heart of an enormous range of subsequent thought.

Mention Pythagoras and most people think of the geometrical theorem that bears his name. Science writer Ferguson (*Tycho & Kepler*, 2003, etc.) shows how much more his ideas have meant to both science and philosophy. Biographical data is sparse: Pythagoras was probably born around 570 BCE on the Aegean isle Samos, studied in Asia and possibly Egypt and settled in Croton, a Greek colony in southern Italy. There he founded a school of philosophy based on mathematics. A key discovery was that a vibrating string produces pleasing harmonies when divided into simple ratios. From this insight, the Pythagoreans posited that numbers lie behind all of nature. In particular, they believed in the music of the spheres, caused by the movement of the planets. They were also vegetarians and believed in reincarnation. Ferguson traces the ways in which later philosophers drew on their central ideas. Plato, who met some of Pythagoras’s disciples during a visit to Italy, used a geometrical proof in one of his dialogues and was thought by his successors to have drawn heavily on Pythagorean doctrines. Plato’s pervasive influence on later philosophers meant that Pythagorean ideas concerning mathematics were transmitted down the ages and can be found not only in philosophy, but in astronomy and the other exact sciences. This holds especially true for the music of the spheres, which was taken literally by no less a scientist than Kepler and served as an important metaphor for major poets into the 19th century. The Pythagorean faith in the mathematical foundation and ultimate comprehensibility of the universe played a key role in physics, from Newton through Einstein right up to today’s string theories.

Ferguson shows the main currents clearly, without complicated math, although readers with some knowledge of geometry and music theory are most likely to enjoy the book.