If you believe mathematics offers little of practical use, Stewart is back to show you the error of your ways.

In the latest of his numerous books on his favorite subject, the acclaimed mathematics popularizer writes for an audience prepared to pay attention to ingenious yet undoubtedly complex insights. He begins by pointing out that scientists and engineers depend on math, but this is no less true of politicians. “One of the curious features of democracy,” he writes, “is that politicians who claim to be devoted to the idea that decisions should be made by ‘the People’ regularly go out of their way to ensure that this doesn’t happen.” Most readers know about gerrymandering, but this turns out to be the tip of the iceberg as Stewart describes many other ways to pervert voting, all revealed and disproved by mathematics. The author then moves on to the larger question of election fairness. America’s winner-takes-all system seems reasonable, but if one candidate is defeated, 100% of his or her supporter’s votes are wasted. In nations with proportional voting systems, minority voters elect a minority of representatives, so their votes are not wasted. This is fairer—in some ways. In fact, mathematicians have proven that a completely fair voting system is impossible. “Dictatorships are so much simpler,” writes Stewart. “One dictator, one vote.” Regarding our most pressing contemporary issue, climate change, Stewart explains that physicists have found that the growth of melting ponds over Arctic ice bears a striking resemblance to other phase transitions, and sea levels are rising faster than predicted. In other sections, the author offers the revealing (but not simple) explanation of the mathematical background of a GPS system, explains the data compression that vastly increases a computer’s power, and delves into the genuinely weird: how a puzzle with no solution—proven by a great mathematician—increases the ease of kidney transplantation.

Richly informative for careful readers who enjoy math.