Beyond Infinity: An Expedition to the Outer Limits of Mathematics

by Eugenia Cheng

Overview

How one powerful concept reveals the biggest (and smallest) mathematical truths

How big is the universe? How many numbers are there? And is infinity + 1 is the same as 1 + infinity? Such questions occur to young children and our greatest minds. And they are all the same question: What is infinity? In Beyond Infinity, Eugenia Cheng takes us on a staggering journey from elemental math to its loftiest abstractions. Along the way, she considers how to use a chessboard to plan a worldwide dinner party, how to make a chicken-sandwich sandwich, and how to create infinite cookies from a finite ball of dough. Beyond Infinity shows how one little symbol holds the biggest idea of all.

Product Details

ISBN-13:	9781541644137
Publisher:	Basic Books
Publication date:	05/01/2018
Edition description:	Reprint
Pages:	304
Sales rank:	286,477
Product dimensions:	5.30(w) x 8.10(h) x 1.00(d)

About the Author

Eugenia Cheng is Scientist in Residence at the School of the Art Institute of Chicago and an Honorary Visiting Fellow at City, University of London. She has authored numerous titles, including How to Bake Pi, Beyond Infinity, The Art of Logic, and x + y. Cheng lives in Chicago, Illinois.

Table of Contents

Prologue ix

Part 1 The Journey

1 What is Infinity? 3

2 Playing with infinity 12

3 What Infinity Is Not 28

4 Infinity Slips Away from Us Again 39

5 Counting Up to Infinity 55

6 Some Things Are More Infinite than Others 78

7 Counting Beyond Infinity 94

8 Comparing Infinities 108

9 What Infinity Is 124

Part 2 The Sights

10 Where Is Infinity? 141

11 Things That Are Nearly Infinity 147

12 Infinite Dimensions 159

13 Infinite-Dimensional Categories 179

14 The Infinitesimally Small 197

15 When Infinity Nearly Caused Mathematics to Fall Apart (and Maybe Also Your Brain) 211

16 Weirdness 246

17 Where Infinity Is 271

Acknowledgments 279

Index 281

Editorial Reviews

09/11/2017
Cheng (How to Bake π), a scientist in residence at the School of the Art Institute of Chicago and honorary fellow at Sheffield University, tackles some difficult concepts in this superb study of the mathematics of infinity. Beginning with the definition of infinity, Cheng moves through myriad mind-bending inquiries, including what the smallest infinity is, how to compare different infinities, whether you can subtract from infinity, and whether you can make an infinite number of cookies with a finite amount of dough. For each, she provides the mathematics behind the often counterintuitive answers. Cheng works hard at making these concepts accessible, employing menus and music playlists, among other things, to frame the challenging mathematical proofs. Acknowledging the difficulties the proofs present, Cheng wisely provides readers with reasonably accessible equations, useful graphics, and entertaining and straightforward explanations. Contemplating infinity is not trivial, even when following the lead of a writer as talented as Cheng, and readers will have to stop and wrestle with such recondite concepts as surjective and injective functions, harmonics, and factorials. Cheng’s enthusiasm for mathematics is infectious and readers curious about the mathematics of infinity will find her to be a worthy guide. Agent: George Lucas, Inkwell. (Mar.)

Publishers Weekly

"Ms. Cheng's chatty tone keeps things fresh. She has a knack for folksy analogies, and at different points in the book she illuminates different properties of infinity by discussing Legos, the iPod Shuffle, snorkeling, Battenberg cakes and Winnie-the-Pooh... she does a great service by showing us non-mathematician schlubs how real mathematical creativity works."
—Wall Street Journal

"Our minds cannot truly grasp the concept of infinity, but Eugenia Cheng takes us on a wild journey to help us in our search for it. It's a small, unassuming symbol, but it holds a giant idea. Cheng helps us understand the basics of infinity and then takes us on a ride to see its most lofty applications. From the practical to the entirely theoretical, this is a book to watch for."
—Paste Magazine

"The idea of infinity is one of the most perplexing things in mathematics, and the most fun. Eugenia Cheng's Beyond Infinity is a spirited and friendly guide—appealingly down to earth about math that's extremely far out."—JordanEllenberg, author of How Not to Be Wrong and professor ofmathematics at University of Wisconsin-Madison

"Beyond Infinity is witty, charming, and crystal clear. Eugenia Cheng's enthusiasm and carefully chosen metaphors and analogies carry us effortlessly through the mathematical landscape of the infinite. A brilliant book!"—IanStewart, author of Calculating the Cosmos

PRAISE FOR EUGENIA CHENG

"[Cheng] conveys the spirit of inventiveness and creativity in math... Refreshing is the word that keeps coming to mind."—StevenStrogatz, as quoted in the New York Times

"Dr. Cheng...has a knack for brushing aside conventions and edicts, like so many pie crumbs from a cutting board."—NatalieAngier, New York Times

"[Eugenia Cheng's] tone is clear, clever and friendly. Even at her most whimsical she is rigorous and insightful... [She is] a lucid and nimble expositor."—AlexBellos, New York Times Book Review

From the Publisher