Guest Review by Janna Levin
Janna Levin is a Professor of Astronomy and Physics at Barnard College of Columbia University. She has contributed to an understanding of black holes, the cosmology of extra dimensions, and gravitational waves in the shape of space time. She is the author of the popular-science book, How the Universe Got Its Spots and a novel, A Madman Dreams of Turing Machines, which won the PEN/Bingham prize. Janna was recently named a Guggenheim Fellow (2012).
I loved this beautiful book from the first page.
Mathematicians are in a peculiar predicament. Mathematical beauty is patent to them. And in the perception of that beauty is pleasure, is joy. But that pleasure is not easily shared. Mathematical beauty eludes many others, or even most others.
Steven Strogatz wants to share that joy. He sees the beauty of pi and 0 and infinity. But he doesn’t want to impose his impressions on you or to report on the view from his privileged perspective. He wants you to see it too. He doesn’t want to argue that mathematics is creative and beautiful. He wants you to experience the visceral pleasure for yourself.
To that end, he disassembles mathematics as a discipline, both feared and revered, and reassembles mathematics as a world, both accessible and magical.
If you have never braved this grand world, put away your math anxiety, your preconceptions. This book is the most welcoming entree to mathematical thinking that I know of.
If you have braved this grand world, you will find a collection of gems, new ways of inhabiting the domain. Strogatz links historical anecdotes to new insights, as though the math itself is sculptural, composed of forms that are simultaneously familiar and ethereal. The logic seems effortless so that each module snaps into its complement with a gratifying click.
This book is a rebuttal to the accusation that mathematical abstraction is cold or inhuman. Mathematics is no more intrinsically cold or inhuman than language. And Strogatz lends a warmth and humanity to both.
The Joy of x is, well, a joy.
Review
"A delightful exploration of the beauty and fun of mathematics, in the best tradition of Lewis Carroll, George Gamow, and Martin Gardner. The Joy of x will entertain you, amaze you, and make you smarter."
— Steven Pinker, Harvard College Professor of Psychology, Harvard University, and author of How the Mind Works and The Language Instinct
"Steven Strogatz should do for math what Julia Child did for cookery. He shows that this stuff really matters, and he shows that it can nourish us."
— James Gleick, author of The Information: A History, a Theory, a Flood and Chaos
"This joyous book will remind you just how beautiful and mesmerizing math can be. Steve Strogatz is the teacher we all wish we had."
— Joshua Foer, author of Moonwalking with Einstein
"I loved this beautiful book from the first page. With his unique ingenuity and affable charm, Strogatz disassembles mathematics as a subject, both feared and revered, and reassembles it as a world, both accessible and magical. The Joy of x is, well, a joy."
— Janna Levin, Professor of Physics and Astronomy, Barnard College, Columbia University, and author of How the Universe Got Its Spots and A Madman Dreams of Turing Machines
"Amazingly, mathematicians can see patterns in the universe that the rest of us are usually blind to. With clarity and dry wit, The Joy of x opens a window onto this hidden world with its landscapes of beauty and wonder."
— Alan Alda
"This book is, simply put, fantastic. It introduces the reader to the underlying concepts of mathematics — presenting reasons for its unfamiliar language and explaining conceptual frameworks that do in fact make understanding complex problems easier. In a world where mathematics is essential but, largely, poorly understood, Steve Strogatz's teaching skills and deft writing style are an important contribution."
— Lisa Randall, Frank B. Baird, Jr., Professor of Science, Harvard University, and author of Warped Passages and Knocking on Heaven's Door
"Strogatz has discovered a magical function that transforms 'math' into 'joy,' page after wonderful page. He takes everything that every mystified you about math and makes it better than clear — he makes it wondrous, delicious, and amazing."
— Daniel Gilbert, Professor of Psychology, Harvard University, and author of Stumbling on Happiness
"Strogatz may be the only person alive with the skill to pied piper me into the murky abyss of set theory. I literally learned something on every page, despite my innumerate brain. This is a fantastic book, conveyed with clarity, technical mastery, and infectious joy."
— Jad Abumrad, host of Radiolab
"Strogatz's graceful prose is perfectly pitched for a popular math book: authoritative without being patronizing, friendly without being whimsical, and always clear and accessible. His x marks the spot — and hits it."
— Alex Bellos, author of Here's Looking at Euclid
"Even the most math-phobic readers might forget their dread after just a few pages of Strogatz’s (The Calculus of Friendship) latest. The author, a Cornell professor of applied mathematics, begins with arithmetic, by way of Sesame Street, then explores algebra, geometry, and, finally, the wonders of calculus—all done cheerfully, with many a wry turn of phrase. From addition and subtraction, with a glimpse into negative numbers and 'the black art of borrowing,' it’s a quick step into the hardcore detective work of algebra’s search for the unknown x, with algorithms like the quadratic equation, 'the Rodney Dangerfield of algebra' ('it don’t get no respect'). Strogatz rhapsodizes over geometry, which he sees as a marriage of logic and intuition that teaches how to build arguments, step by rigorous step, and geometry’s 'loosey-goosey' offshoot, topology. Brisk chapters on prime numbers, basic statistics, and probability are all enlightening without being intimidating. Most impressive is Strogatz’s coverage of calculus, the math used to figure out everything from how fast epidemics spread to the trajectory of a curveball. Readers will appreciate this lighthearted and thoroughly entertaining book."
— Publishers Weekly"Strogatz, an applied mathematician at Cornell University and author of Sync, has compiled his immensely popular series of New York Times columns and added new material. The Joy of X's six parts, each divided into several short chapters, move from number basics through algebra, geometry, calculus and statistics to the frontiers of math, where conjectures about prime numbers are still floating around unsolved. The goal is a second chance at learning the math that might have passed you by—this time from an adult perspective. The tone is light and conversational, with delightful narratives about lonely numbers and the Tony Soprano psyche of math itself—outwardly tough but inwardly wracked with insecurity. The easily digestible chapters include plenty of helpful examples and illustrations. You'll never forget the Pythagorean theorem again!"
—Scientific American
About the Author
Steven Strogatz is a professor of applied mathematics at Cornell University. A renowned teacher and one of the worlds most highly cited mathematicians, he blogs about math for the New York Times and been a frequent guest on National Public Radios RadioLab. In 2007 he received the Communications Award, a lifetime achievement award for the communication of mathematics to the general public. He lives in Ithaca, New York with his wife and two daughters.
Excerpt. © Reprinted by permission. All rights reserved.
PREFACE
I have a friend who gets a tremendous kick out of science, even though he’s an artist. Whenever we get together all he wants to do is chat about the latest thing in psychology or quantum mechanics. But when it comes to math, he feels at sea, and it saddens him. The strange symbols keep him out. He says he doesn’t even know how to pronounce them.
In fact, his alienation runs a lot deeper. He’s not sure what mathematicians do all day, or what they mean when they say a proof is elegant. Sometimes we joke that I should just sit him down and teach him everything, starting with 1 + 1 = 2 and going as far as we can.
Crazy as it sounds, that’s what I’ll be trying to do in this book. It’s a guided tour through the elements of math, from preschool to grad school, for anyone out there who’d like to have a second chance at the subject—but this time from an adult perspective. It’s not intended to be remedial. The goal is to give you a better feeling for what math is all about and why it’s so enthralling to those who get it.
We’ll discover how Michael Jordan’s dunks can help explain the fundamentals of calculus. I’ll show you a simple—and mind-blowing—way to understand that staple of geometry, the Pythagorean theorem. We’ll try to get to the bottom of some of life’s mysteries, big and small: Did O.J. do it? How should you flip your mattress to get the maximum wear out of it? How many people should you date before settling down? And we’ll see why some infinities are bigger than others.
Math is everywhere, if you know where to look. We’ll spot sine waves in zebra stripes, hear echoes of Euclid in the Declaration of Independence, and recognize signs of negative numbers in the run-up to World War I. And we’ll see how our lives today are being touched by new kinds of math, as we search for restaurants online and try to understand—not to mention survive—the frightening swings in the stock market.
By a coincidence that seems only fitting for a book about numbers, this one was born on the day I turned fifty. David Shipley, who was then the editor of the op-ed page for the New York Times, had invited me to lunch on the big day (unaware of its semicentennial significance) and asked if I would ever consider writing a series about math for his readers. I loved the thought of sharing the pleasures of math with an audience beyond my inquisitive artist friend.
“The Elements of Math” appeared online in late January 2010 and ran for fifteen weeks. In response, letters and comments poured in from readers of all ages. Many who wrote were students and teachers. Others were curious people who, for whatever reason, had fallen off the track somewhere in their math education but sensed they were missing something worthwhile and wanted to try again. Especially gratifying were the notes I received from parents thanking me for helping them explain math to their kids and, in the process, to themselves. Even my colleagues and fellow math aficionados seemed to enjoy the pieces—when they weren’t suggesting improvements (or perhaps especially then!).
All in all, the experience convinced me that there’s a profound but little-recognized hunger for math among the general public. Despite everything we hear about math phobia, many people want to understand the subject a little better. And once they do, they find it addictive.
The Joy of x is an introduction to math’s most compelling and far-reaching ideas. The chapters—some from the original Times series—are bite-size and largely independent, so feel free to snack wherever you like. If you want to wade deeper into anything, the notes at the end of the book provide additional details and suggestions for further reading.
For the benefit of readers who prefer a step-by-step approach, I’ve arranged the material into six main parts, following the lines of the traditional curriculum.
Part 1, “Numbers,” begins our journey with kindergarten and grade-school arithmetic, stressing how helpful numbers can be and how uncannily effective they are at describing the world.
Part 2, “Relationships,” generalizes from working with numbers to working with relationships between numbers. These are the ideas at the heart of algebra. What makes them so crucial is that they provide the first tools for describing how one thing affects another, through cause and effect, supply and demand, dose and response, and so on—the kinds of relationships that make the world complicated and rich.
Part 3, “Shapes,” turns from numbers and symbols to shapes and space—the province of geometry and trigonometry. Along with characterizing all things visual, these subjects raise math to new levels of rigor through logic and proof.
In part 4, “Change,” we come to calculus, the most penetrating and fruitful branch of math. Calculus made it possible to predict the motions of the planets, the rhythm of the tides, and virtually every other form of continuous change in the universe and ourselves. A supporting theme in this part is the role of infinity. The domestication of infinity was the breakthrough that made calculus work. By harnessing the awesome power of the infinite, calculus could finally solve many long-standing problems that had defied the ancients, and that ultimately led to the scientific revolution and the modern world.
Part 5, “Data,” deals with probability, statistics, networks, and data mining, all relatively young subjects inspired by the messy side of life: chance and luck, uncertainty, risk, volatility, randomness, interconnectivity. With the right kinds of math, and the right kinds of data, we’ll see how to pull meaning from the maelstrom.
As we near the end of our journey in part 6, “Frontiers,” we approach the edge of mathematical knowledge, the borderland between what’s known and what remains elusive. The sequence of chapters follows the familiar structure we’ve used throughout—numbers, relationships, shapes, change, and infinity—but each of these topics is now revisited more deeply, and in its modern incarnation.
I hope that all of the ideas ahead will provide joy—and a good number of Aha! moments. But any journey needs to begin at the beginning, so let’s start with the simple, magical act of counting.
