An instant New York Times Bestseller!
“Unreasonably entertaining . . . reveals how geometric thinking can allow for everything from fairer American elections to better pandemic planning.” —The New York Times
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"comes 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.
Math professor Ellenberg (How Not to Be Wrong) shows how challenging mathematics informs real-world problems in this breezy survey. "Geometry," Ellenberg writes, is "at the heart of what's required for real figuring in the world," and in 14 chapters, he covers such questions as why polling works and how artificial intelligence plays chess. In "How Many Holes Does a Straw Have," he uses topology to prove that the answer is one (pants, meanwhile, have two). Especially relevant are his explanations of the math behind Covid-19 case growth and why more testing makes sense, and how geometry plays into politics. On the thorny issue of redistricting, he convincingly argues that there is significant electoral inequality at play and that math can help solve the problem of gerrymandering. Ellenberg digs into the human side of the science by sharing tales of the feuds and disagreements that punctuated the history of the field (such as a rivalry between a chess master and a computer program) and paying tribute to the genius of the mathematicians whose work underlies today's disciplines. Math-minded readers will be rewarded with a greater understanding of the world around them.