Is Math Real? How Simple Questions Lead Us to Mathematics’ Deepest Truths

“Math might seem like it’s about getting the right answers, but really it’s about the process of discovering,” according to this invigorating philosophical take on the field. Mathematician Cheng (The Joy of Abstraction) explores how such questions as “how many sides does a circle have?” and “why does –(–1)=1?” reveal surprising profundities about math. She suggests that situations in which one plus one does not equal two (one pile of sand placed on another makes for one pile) shows how numbers are ways of abstracting and simplifying the world that require individuals to decide what to count (piles of sand) and what to ignore (the individual grains in each pile). Classrooms, she laments, typically shun such modes of inquiry in favor of instilling “rigidly imposed rules,” contrary to the “point of math,” which, she argues, is “learning how to decide what counts as a good answer when there is no answer key.” Cheng has a talent for making mathematical discussions accessible, and her wide-ranging analysis leads to some surprisingly weighty conclusions, as when she argues that expecting students to accept mathematical rules without question sends the message that truth comes from authority, making it nigh impossible to reason with students “because their beliefs aren’t based on reason; they’re based on authority.” It adds up to a stellar meditation on the nature of knowledge and math. (Aug.)