SHAPE

A wide-ranging sojourn into geometry and how it can be applied to real-life situations.

Even for the math-averse, there is something indelibly “primal” and useful about geometry, at least of the Euclidean variety. As University of Wisconsin math professor Ellenberg is quick to note, however, “geometry is the cilantro of math. Few are neutral.” As the author shows, it’s a subject on the move, providing new insights and deployments. “We are living in a wild geometric boomtown, global in scope,” writes Ellenberg in this often humorous, anecdotally rich dive into numerous mathematical theories. (His accessible approach carries over from How Not To Be Wrong, his 2014 bestseller.) The author feels that geometry has a lot to do with integrity and honesty, but he doesn’t want to sacrifice intuition at the altar of logical deduction: “We start from our intuitions about shapes in the physical world (where else could we start?), we analyze closely our sense of the way those shapes look and move, so precisely that we can talk about them without relying on our intuition if we need to.” Ellenberg introduces readers to a bevy of relatable mathematical concepts: the “theory of the random walk” and its implications regarding the unpredictable nature of the stock market; “tree geometry” and how it might help you win certain games; the algorithms that work their ways into tennis matches and the World Series as well as some that recall a bunch of monkeys at typewriters, “reducing literary texts to a binary sequence of consonants and vowels.” Also eye-opening are the author’s discussions of pandemics—progression, decay, and the math of herd immunity—and how geometric processes can “model smallpox, scarlet fever, train derailments, and steam boiler explosions.” In the penultimate chapter, “How Math Broke Democracy (and Might Still Save It),” Ellenberg offers an engrossing discussion of how geometry can help in the fight against gerrymandering.

Serious mathematics at its intriguing, transporting best.