Math Without Numbers

Beckman, a math prodigy who captained the New York City Math team at age 13, debuts with a playful paean to the pleasures of studying higher math. Arguing “that everything—plants, love, music, everything—can (in theory) be understood in terms of math,” he uses analogies, puzzles, and formal logic—but no equations—to tackle intriguing questions from various fields. For example, from topology, “geometry’s looser and trippier cousin,” he asks when two shapes can be considered the same, producing the surprising answer that it’s when one can be transformed “into the other by stretching and squeezing, without any ripping or gluing.” Another question revolves around infinities—namely, are some larger than others? Moving on to dimensions, he considers why structures with more than three, though nonexistent, are both theoretically possible and intellectually useful for mathematicians. Beckman’s conviction that math provides the tools to understand everything gets its best showing when he tackles abstract algebra, explaining, among a blizzard of examples, how modeling, where “math connects to the real world,” can theoretically predict the outcomes of systems like economics. Readers with an abundance of curiosity and the time to puzzle over Beckman’s many examples, riddles, and questions, will make many fascinating discoveries. Agent: Jay Mandel, William Morris Endeavor. (Oct.)