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Contents
Introduction
CHAPTER ONE
Every Number Tells a Story
In which the author examines the feelings we have for numbers. He
discovers why 11 is more interesting than 10, why 24 is more hygienic
than 31, and why 7 is so lucky.
CHAPTER TWO
The Long Tail of the Law
In which the author investigates universal laws of numbers. He discovers
numerical patterns wherever he looks, including in these very pages.
CHAPTER THREE
Love Triangles
In which the author looks at triangles. The shadowy world of Greek
geometry leads him down a well, and up the highest mountain in the
world.
CHAPTER FOUR
Coneheads
In which the author shines his torchlight on the cone, and sees its
reflection in rockets, planets and towers. He learns about the joy of
rolling balls—either dipped in ink in Renaissance Italy or bouncing off
the cushion in upstate New York.
CHAPTER FIVE
Bring on the Revolution
In which the author investigates rotation. He rolls, and spins, the wheel.
He swings the pendulum, bounces the spring and pings the tuning fork.
CHAPTER SIX
All About e
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In which the author explores proportional growth. He gets feedback
from a YouTube celebrity in Colorado, and provides a biography of the
special number behind capitalism, matchmaking and Catalan
architecture.
CHAPTER SEVEN
The Positive Power of Negative Thinking
In which the author goes sub-zero. Minus times minus equals plus, the
reasons for this he needs to discuss. He fails to keep it real and plunges
down Seahorse Valley.
CHAPTER EIGHT
Professor Calculus
In which the author tackles calculus. He takes a roller-coaster ride with
Archimedes and Newton, and asks why the French have a “je ne sais
quoi” when it comes to mathematical thinking.
CHAPTER NINE
The Titl of This Chapter Contains Three Erors
In which the author looks at mathematical proof. He laughs at logical
deduction and meets an anonymous member of a secret mathematical
sect.
CHAPTER TEN
Cell Mates
In which the author voyages into the realm of the cellular automaton. He
explores the meaning of Life and speaks to the man looking for
universes in his basement.
GLOSSARY
APPENDIXES
ACKNOWLEDGMENTS
PICTURE CREDITS
A NOTE ON THE AUTHOR
ASSUMPTIONS, CLARIFICATIONS, REFERENCES AND NOTES
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INDEX
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For Nat
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Introduction
Mathematics is a joke.
I’m not being funny.
You need to “get” a joke just as you need to “get” math.
The mental process is the same.
Think about it. Jokes are stories with a setup and a punch line. You
follow them carefully until the payoff, which makes you smile.
A piece of math is also a story with a setup and a punch line. It’s a
different type of story, of course, in which the protagonists are numbers,
shapes, symbols and patterns. We’d usually call a mathematical story a
“proof,” and the punch line a “theorem.”
You follow the proof until you reach the payoff. Whoosh! You get it!
Neurons go wild! A rush of intellectual satisfaction justifies the initial
confusion, and you smile.
The ha-ha! in the case of a joke and the aha! in the case of math
describe the same experience, and this is one of the reasons why
understanding mathematics can be so enjoyable and addictive.
Like the funniest punch lines, the finest theorems reveal something you
are not expecting. They present a new idea, a new perspective. With jokes,
you laugh. With math, you gasp in awe. It was precisely this element of
surprise that made me fall in love with math as a child. No other subject so
consistently challenged my preconceptions.
The aim of this book is to surprise you, too. In it, I embark on a tour of
my favorite mathematical concepts, and explore their presence in our lives.
I want you to appreciate the beauty, utility and playfulness of logical
thought.
–––
My previous book, Here's Looking at Euclid, was a journey into
mathematical abstraction. This time I come down to earth: my concern is as
much the real world, reflected in the mirror of math, as it is the abstract
one, inspired by our physical experiences.
First, I put humans on the couch. What are the feelings we have for
numbers, and what triggers these feelings? Then I put numbers on the couch,
individually and as a group. Each number has its own issues. When we
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engage with them en masse, however, we see fascinating behavior: they
conduct themselves like a well-organized crowd.
We depend on numbers to make sense of the world, and have done so
ever since we started to count. In fact, perhaps the most surprising feature
of mathematics is how extraordinarily successful it has been, and continues
to be, in enabling us to understand our surroundings. Civilization has
progressed as far as it has thanks to discoveries about simple shapes like
circles and triangles, expressed pictorially at first, and later in the
vernacular of equations.
Math, I would argue, is the most impressive and longest-running
collective enterprise in human history. In the following pages I follow the
torch of discovery from the Pyramids to Mount Everest, from Prague to
Guangzhou, and from the Victorian drawing room to a digital universe of
self-replicating creatures. We will meet swashbuckling intellects, including
familiar names from antiquity and less familiar names from the present day.
Our cast includes a cravat-wearing celebrity in India, a gun-toting private
investigator in the United States, a member of a secret society in France,
and a spaceship engineer who lives near my London flat.
As we roam across physical and abstract worlds, we will probe well-
known concepts, like pi and negative numbers, and encounter more
enigmatic ones, which will become our confidants. We will marvel at
concrete applications of mathematical ideas, including some that actually
are made of concrete.
–––
You don’t need to be a math whiz to read this book. It’s aimed at the general
reader. Each chapter introduces a new mathematical concept, and assumes
no previous knowledge. Inevitably, however, some concepts are more
stretching than others. The level sometimes reaches that of an
undergraduate degree, and, depending on your mathematical proficiency,
there may be moments of bewilderment. In these cases, skip to the
beginning of the next chapter, where I reset the level to elementary. The
material might make you feel a bit dizzy at first, especially if it is new to
you, but that’s the point. I want you to see life differently. Sometimes the
aha! takes time.
If all this sounds a bit serious, it isn’t. The emphasis on surprise has
made math the most playful of all intellectual disciplines. Numbers have
always been toys, as much as they have been tools.
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Not only does math help you understand the world better, it helps you
enjoy it more, too.
Alex Bellos
January 2014
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Description:From the bestselling author of Here’s Looking at Euclid, a dazzling new book that turns even the most complex math into a brilliantly entertaining narrative. From triangles, rotations and power laws, to cones, curves and the dreaded calculus, Alex takes you on a journey of mathematical discovery w
