Shape

The Hidden Geometry of Information, Biology, Strategy, Democracy, and EverythingElse

By: Jordan Ellenberg

Narrated by: Jordan Ellenberg

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.

Critic reviews

“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.’” —Parul Sehgal, The New York Times

“Ellenberg’s commitment to explanation, his exploration of the humanity of mathematics, and the tour de force of the final chapter in defense of a democracy girded by fairness and science are enough to remind you why he is America’s favorite math professor.” —Daily Beast

“A deeply enjoyable and insightful book.” —The New York Times Book Review

“Containing multitudes as he must, Ellenberg's eyes grow wider and wider, his prose more and more energetic, as he moves from what geometry means to what geometry does in the modern world.” —The Telegraph

“[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


“Math professor Ellenberg (How Not to Be Wrong) shows how challenging mathematics informs real-world problems in this breezy survey . . . Math-minded readers will be rewarded with a greater understanding of the world around them.” —Publishers Weekly

“Shape 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

math is as fun as this book

top favorite for 2021, clever, up to date and funny.
Jordan is well versed with both words and numbers!

Shape's about reason, logic, mathematics & more...

I love the scope of this book; from explaining the rigor of Abraham Lincoln immersing himself "till I could give any propositions in the six books of Euclid at sight" to applying the inherent reasoning and logic of demonstrating proof to far-flung human undertakings.

Ellenberg is a math professor who can write. His speaking style, while forthright, cannot fully contain his enthusiasm for his subject matter. His narration is conversational and reminds me of the best of the Great Lectures books I've enjoyed.

Rational thought and reasoning can be applied to everything from geometry to maps to politics, artificial intelligence to genealogy and biology. The best arguments are "self-evident," and Ellenberg weaves mathematical, cultural and political history into Shape, elucidating great advances in math and other endeavors, from Ancient Greece to the American Revolution; from the thinking of Abraham Lincoln, to gerrymandering today.

Shape will make you think...without making your head hurt too much in the process. What a treat! I'll be up for a second, and perhaps a third listen. And based on Shape, I'm up for trying Ellenberg's other work as well.

Skip to chapter 14

I strongly dislike the structure of this book. The author considers himself a "fun professor" and meanders from topic to topic. This panders to those with short attention spans. And bothers me.

A meaningful potential thesis of the book is the mathematics of gerrymandering. It seems to me the author was afraid this is too boring a topic. Which it's not. There are onion layers to the problem of determining if a district map has been gerrymandered. It's really interesting!

I recommend you skip to chapter 14 titled "How Math Broke Democracy (and Might Still Save It)".

It's the only chapter worth reading.

An Excellent Branching Dive into Geometry

This book is fun, interesting, educational, and entertaining as it explores the geometry and general maths present in a wild variety of subjects, branching from history to games to diseases to politics to artificial intelligence and more. Tickle your brain and get ready for an excellent read.

Wonder and laughter

Shape is absolutely hilarious and breathtakingly impressive. And it makes a great audiobook too. I never got out pencil and paper, and had a great time listening to it. (I might have learned more if I had, but I don’t have free hands while I listen.)