THE ART OF MORE

A more or less chronological history and compelling case that advances in mathematics provided the foundation for the advance of civilization.

Quantum physicist Brooks, author of 13 Things That Don’t Make Sense: The Most Baffling Scientific Mysteries of Our Time, points out that numbers do not come naturally to humans. Ancient and remote communities could identify one, two, and three, but everything beyond is simply “many.” This is not stupidity but evolution; larger numbers weren’t necessary for their survival. Matters changed when we began to gather in large numbers and exchange goods; counting became essential. Ancient mathematics was clunky, but humans are good at problem-solving, so they achieved feats such as predicting eclipses, building complex structures, and measuring the Earth. Contrary to popular belief, the Middle Ages was a golden age for numbers, and a fiercely controversial concept—the negative number—entered the mainstream. Greeks and Romans did fine without a zero, but contemporary culture needs it, and eighth-century Persian mathematicians were vital to the development of algebra. Imaginary numbers are not imaginary at all; modern engineers could not calculate without them. Brooks proposes that the acceleration of change began around 1500 with the invention of double-entry bookkeeping, a way of ensuring that no errors crept into accounting. Before that, all trade was personal. Afterward, commerce exploded because there was “no more taking the owner’s word for it, or trusting the family name.” An unabashed lover of mathematics, Brooks refuses to take the traditional pop writer’s pledge to eschew equations. Most readers will follow his description of ancient navigation across the Mediterranean and the birth of linear perspective in Renaissance Italy, but when he turns his attention to calculus, logarithms, statistics, and cryptography, there is no shortage of complex equations. Some readers will flinch, but those who power through will be rewarded.

Not a mathematics-is-fun romp but a serious, persuasive effort to describe how its discoveries paralleled human progress.