THE SECRET LIVES OF NUMBERS

A fine history of mathematics that seeks to decouple it from its traditional Eurocentric focus and usually succeeds.

Kitagawa, a leading historian of mathematics, and Revell, a “lapsed mathematician” and U.S. editor for New Scientist, note that the discipline of mathematics began as tallying, the beginning of which is lost in history. However, anthropologists have turned up 20,000-year-old bones covered with regular notches that may or may not indicate that someone was counting. After a quick review of early civilizations—Babylon, Egypt, Assyria, Maya, Greek—the authors devote large sections to China and India from ancient to near-modern times and to the Arab world after the rise of Islam. Until the appearance of decimals, a base-10 number system, and the concept of zero, during the first millennium, all of which make calculation easier, pre-modern mathematicians were limited to simple arithmetic and bookkeeping, but they accomplished amazing things. They could predict eclipses, measure the length of a day within seconds, and determine pi to eight decimal places. The Pythagorean theorem was proven long before Pythagoras, and the concepts behind calculus appeared during India’s golden age. The authors demonstrate that the scientific revolution was not strictly a European invention because science had been advancing throughout history. “Many ideas that turn up in the ‘Scientific Revolution’ had already been explored elsewhere or were the culmination of incremental steps made by others,” they write. What changed was the idea that humans were ignorant and that knowledge would encourage progress and make life better. Ancient cultures assumed that everything important was already known. Pre-modern mathematicians solved practical problems and were considered experts on calendars (essential for religious ceremonies), but mostly mathematics was admired as a mark of superior culture in the same class as poetry and philosophy. No one expected math to change the world; Galileo, Newton, and Einstein did that.

A solid corrective to a host of misunderstandings about math.