Stephen Wilson - It All Adds Up - The Story of People and Mathematics

William Collins

An imprint of HarperCollins Publishers

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London SE1 9GF

www.WilliamCollinsBooks.com

This eBook first published in Great Britain by William Collins in 2018

First published in France by Flammarion, as Le grand romans des maths in 2016

Copyright © Mickaël Launay 2016

Translation copyright © Stephen S Wilson 2018

Drawing here by Maurice Bourlon; Image here © IRSNB, Thierry HubinMap here in the public domain, courtesy of Bibliothèque nationale de France, GE BB-565 (A7,10); Image here from Wikimedia Commons; Image here by Stefan Zachow.

Mickaël Launay asserts the moral right to be identified as the author of this work

Stephen S Wilson asserts the moral right to be identified as the translator of this work in accordance with the Copyright, Designs and Patents Act 1988

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

All rights reserved under International and Pan-American Copyright Conventions. By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on-screen. No part of this text may be reproduced, transmitted, down-loaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of HarperCollins

Source ISBN: 9780008283933

Ebook Edition © October 2018 ISBN: 9780008283957

Version: 2018-11-08

Contents

Cover

Title Page

Copyright

Foreword

1. Mathematicians without knowing it

2. And then there were numbers

3. Let no one ignorant of geometry enter

4. The age of theorems

5. A little method

6. Π in the sky

7. Nothing and less than nothing

8. The power of triangles

9. Into the unknown

10. In sequence

11. Imaginary worlds

12. A language for mathematics

13. The world’s alphabet

14. The infinitely small

15. Measuring the future

16. The coming of machines

17. Maths to come

Epilogue

To go further

Footnotes

Bibliography

Index

About the Author

About the Publisher

‘Oh, I’ve never been much good at maths myself!’

I’m getting a little blasé. This must be at least the tenth time I’ve heard that remark today.

But this lady has been here at my stall for a good fifteen minutes, standing with a group of other visitors, listening attentively while I describe various geometrical curiosities. That’s how the conversation started.

‘But what do you do for a living?’ she asked me.

‘I’m a mathematician.’

‘Oh, I’ve never been much good at maths myself!’

‘Really? But you seemed to be interested in what I was just talking about.’

‘Yes … but that’s not really maths … that was understandable.’

I hadn’t heard that one before. Is mathematics, by definition, a discipline that can’t be understood?

It’s the beginning of August, in the Cours Félix Faure in La Flotte-en-Ré, France. In this small summer market, I have a pop-up – there is henna tattooing and afro braids to my right, a mobile-phone accessory stall to my left, and a display of jewels and trinkets of all kinds opposite me. I’ve set up my maths stand in the middle of all this. Holidaymakers stroll peacefully by in the cool of the evening. I particularly like doing maths in unusual places. Where people aren’t expecting it. Where they are not on their guard …

‘Can’t wait to tell my parents I did some maths during the holidays!’ This from a secondary school pupil as he walks past my stall on his way back from the beach.

It’s true – I do catch them slightly unawares. But sometimes you’ve got to do what you’ve got to do. This is one of my favourite moments: observing the expression on the faces of people who thought that they had fallen out with maths for good at the instant when I tell them that they have just been doing maths for fifteen minutes. And my stall is always crowded! I present origami, magic tricks, games, riddles … there’s something for everyone.

No matter how much this amuses me, on balance I find it upsetting. How has it come about that we need to hide from people the fact that they are doing maths before they can take some pleasure in it? Why is the word so frightening? One thing is certain: had I put up a sign above my table proclaiming ‘Mathematics’ as visibly as ‘Jewels and necklaces’, ‘Phones’ or ‘Tattooing’ on the stalls around me, I would not have had a quarter of the same success. People would not have stopped. Perhaps they would even have turned away and averted their gaze.

All the same, the curiosity is there. I observe this every day. Mathematics is scary, yet even more, it is fascinating. Some may not like it, but would like to like it, or at least to be able to peep at will into its murky mysteries. Many think it is inaccessible. But this is not true. It is perfectly possible to love music without being a musician, or to like to share a nice meal without being a great cook. Then why should you have to be a mathematician, or someone exceptionally clever, in order to be open to hearing about mathematics and to enjoy having your imagination tickled by algebra or geometry? It is not necessary to delve into the technical details in order to understand the great ideas and to be able to marvel at them.

Since time out of mind, innumerable artists, creative spirits, inventors, artisans, simple dreamers, or the purely curious, have done maths without being aware of the fact: mathematicians despite themselves. They were the first to ask questions, the first to undertake research, the first to brainstorm. If we want to understand the whys and wherefores of mathematics, we have to set out on their trail, since it all began with them.

The time has come to embark on a journey. Please allow me the space of these few pages to carry you with me into the twists and turns of one of the most fascinating and most astonishing disciplines ever practised by humankind. Let us set off to meet those who have created its story through unexpected discoveries and fabulous ideas.