Marcus Sautoy - The Number Mysteries - A Mathematical Odyssey through Everyday Life

A Mathematical Odyssey Through

Every Day Life

MARCUS DU SAUTOY

Fourth Estate

An imprint of HarperCollins Publishers Ltd. 1 London Bridge Street London SE1 9GF

www.harpercollins.co.uk

First published in Great Britain in 2010

Copyright © Marcus du Sautoy

The right of Marcus du Sautoy to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988

A catalogue record for this book is available from the British Library

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Source ISBN: 9780007278626

Ebook Edition © SEPTEMBER 2010 ISBN: 9780007362561

Version: 2017-08-22

For Shani

Cover

Title Page THE NUMBER MYSTERIES A Mathematical Odyssey Through Every Day Life MARCUS DU SAUTOY

Copyright

Dedication For Shani

Introduction

One - The Curious Incident of the Never-ending Primes

Two - The Story of the Elusive Shape

Three - The Secret of the Winning Streak

Four - The Case of the Uncrackable Code

Five - The Quest to Predict the Future

Picture Credits

Keep Reading

A Note on Websites

Index

Acknowledgements

About the Author

Also by Marcus du Sautoy

About the Publisher

Is climate change a reality? Will the solar system suddenly fly apart? Is it safe to send your credit card number over the Internet? How can I beat the casino?

Ever since we’ve been able to communicate, we’ve been asking questions—trying to make predictions about what the future holds, negotiating the environment around us. The most powerful tool that humans have created to navigate the wild and complex world we live in is mathematics.

From predicting the trajectory of a football to charting the population of lemmings, from cracking codes to winning at Monopoly, mathematics has provided the secret language to unlock nature’s mysteries. But mathematicians don’t have all the answers. There are many deep and fundamental questions we are still struggling to crack.

In each chapter of The Number Mysteries I want to take you on a journey through the big themes of mathematics, and at the end of each chapter I will reveal a mathematical mystery that no one has yet been able to solve. These are some of the great unsolved problems of all time.

But solving one of these conundrums won’t just bring you mathematical fame—it will also bring you an astronomical fortune. An America businessman, Landon Clay, has offered a prize of a million dollars for the solution to each of these mathematical mysteries. You might think it strange that a businessman should want to hand out such big prizes for solving mathematical puzzles. But he knows that the whole of science, technology, the economy and even the future of our planet relies on mathematics.

Each of the five chapters of this book introduces you to one of these million-dollar puzzles.

Chapter 1, The Curious Incident of the Never Ending Primes, takes as its theme the most basic object of mathematics: number. I will introduce you to the primes, the most important numbers in mathematics but also the most enigmatic. A mathematical million awaits the person who can unravel their secrets.

In Chapter 2, The Story of the Elusive Shape, we take a journey through nature’s weird and wonderful shapes: from dice to bubbles, from tea bags to snowflakes. Ultimately we tackle the biggest challenge of them all—what shape is our universe?

Chapter 3, The Secret of the Winning Streak, will show you how the mathematics of logic and probability can give you the edge when it comes to playing games. Whether you like playing with Monopoly money or gambling with real cash, mathematics is often the secret to coming out on top. But there are some simple games that still fox even the greatest minds.

Cryptography is the subject of Chapter 4, The Case of the Uncrackable Code. Mathematics has often been the key to unscrambling secret messages. But I will reveal how you can use clever mathematics to create new codes that let you communicate securely across the Internet, send messages through space and even read your friend’s mind.

Chapter 5is about what we would all love to able to do: The Quest to Predict the Future. I will explain how the equations of mathematics are the best fortune-tellers. They predict eclipses, explain why boomerangs come back and ultimately tell us what the future holds for our planet. But some of these equations we still can’t solve. The chapter ends with the problem of turbulence, which affects everything from David Beckham’s free-kicks to the flight of an aeroplane, yet it is still one of mathematics’ greatest mysteries.

The mathematics I present ranges from the easy to the difficult. The unsolved problems that conclude each chapter are so difficult that no one knows how to solve them. But I am a great believer in exposing people to the big ideas of mathematics. We get excited about literature when we encounter Shakespeare or Steinbeck. Music comes alive the first time we hear Mozart or Miles Davis. Playing Mozart yourself is tough; Shakespeare can often be challenging, even for the experienced reader. But that doesn’t mean that we should reserve the work of these great thinkers for the cognoscenti. Mathematics is just the same. So if some of the mathematics feels tough, enjoy what you can and remember the feeling of reading Shakespeare for the first time.

At school we are taught that mathematics is fundamental to everything we do. In these five chapters I want to bring mathematics to life, to show you some of the great mathematics we have discovered to date. But I also want to give you the chance to test yourself against the biggest brains in history, as we look at some of the problems that remain unsolved. By the end, I hope you will understand that mathematics really is at the heart of all that we see and everything we do.