From the New York Times-bestselling author of How Not to Be Wrong—himself a world-class geometer—a far-ranging exploration of the power of geometry, which turns out to help us think better about practically everything

How should a democracy choose its representatives? How can you stop a pandemic from sweeping the world? How do computers learn to play Go, and why is learning Go so much easier for them than learning to read a sentence? Can ancient Greek proportions predict the stock market? (Sorry, no.) What should your kids learn in school if they really want to learn to think? All these are questions about geometry. For real.

If you're like most people, geometry is a sterile and dimly remembered exercise you gladly left behind in the dust of ninth grade, along with your braces and active romantic interest in pop singers. If you recall any of it, it's plodding through a series of miniscule steps only to prove some fact about triangles that was obvious to you in the first place. That's not geometry. Okay, it is geometry, but only a tiny part, which has as much to do with geometry in all its flush modern richness as conjugating a verb has to do with a great novel.

Shape reveals the geometry underneath some of the most important scientific, political, and philosophical problems we face. Geometry asks: Where are things? Which things are near each other? How can you get from one thing to another thing? Those are important questions. The word "geometry," from the Greek for "measuring the world." If anything, that's an undersell. Geometry doesn't just measure the world—it explains it. Shape shows us how.

* This audiobook includes a downloadable PDF of images and shapes.
“Unreasonably entertaining new book . . . Shape makes geometry entertaining. Really, it does . . . For all Ellenberg’s wit and play (and his rightful admiration of some excellent 19th-century beards), the real work of Shape is in codifying that geometry on the page . . . To Ellenberg, geometry is not a reprieve from life but a force in it — and one that can be used for good, ill and for pleasures of its own. It binds and expands our notions of the world, the web of the real and the abstract. ‘I prove a theorem,’ the poet Rita Dove wrote, ‘and the house expands.’” New York Times

“[Jordan Ellenberg] is up to the engaging standard of his prior book . . . almost anyone is likely to enjoy Ellenberg’s prose, and mind.” Harvard Magazine

“Serious mathematics at its intriguing, transporting best . . . [a] humorous, anecdotally rich dive into numerous mathematical theories.” —Kirkus

is a triumph of mathematical exposition, exposing profound truths—from the nature of distance to the predictability of randomness—as well as profound mistakes—from historical misattributions to Supreme Court justice hardheadedness—with eloquence and hilarious wit. Ellenberg's evident affection for both his subject and his reader makes us feel like the lucky ones who get to hear him hold forth in an intimate setting about his favorite subject, mathematics.” —Cathy O’Neil, author of Weapons of Math Destruction