What's the use? How mathematics shapes everyday life

"It would be easy to conclude that mathematics has become outdated," but modern life would "fall apart" without it, argues mathematician Stewart (Does God Play Dice) in this straightforward survey. With 13 examples that cover movie animation, internet traffic, medicine, photography, and navigation apps, Stewart explains the ways math makes modern life possible. He ties the math of airline routing to the classic "traveling salesman problem" (a way to make a route the most efficient), and explains that GPS users employ Einstein's theory of relativity each time they plan a trip. Graph theory, meanwhile, is used to match organ donors with recipients, and computer-generated imagery is built on 175-year-old math. He also describes how various mathematical concepts were developed, which, taken together, provide a thumbnail history of mathematics. Stewart goes incredibly deep into the difficult math that informs his examples, a choice that will undoubtedly stretch even the most mathematically inclined readers (pseudorandom number generators, he writes, are "generally based on abstract algebra, such as polynomials over finite fields, or number theory, such as integers to some modulus"). But those who stay the course will find that Stewart succeeds in conveying his wonder at the power math has to shape the world. (Aug.)

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. Copyright (c) Kirkus Reviews, used with permission.