Table Of ContentA New Year’s Present from a
Mathematician
ii
A New Year’s Present from a
Mathematician
By
Snezana Lawrence
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487- 2742
© 2020 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid- free paper
International Standard Book Number- 13: 978- 0- 367- 21936- 9 (Paperback)
International Standard Book Number-13: 978- 0- 367- 21937- 6 (Hardback)
This book contains information obtained from authentic and highly regarded sources. Reasonable
efforts have been made to publish reliable data and information, but the author and publisher cannot
assume responsibility for the validity of all materials or the consequences of their use. The authors and
publishers have attempted to trace the copyright holders of all material reproduced in this publication
and apologize to copyright holders if permission to publish in this form has not been obtained. If any
copyright material has not been acknowledged please write and let us know so we may rectify in any
future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or
hereafter invented, including photocopying, microfilming, and recording, or in any information
storage or retrieval system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-7 50- 8400. CCC is a not- for- profit organization that provides licenses
and registration for a variety of users. For organizations that have been granted a photocopy license by
the CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and
are used only for identification and explanation without intent to infringe.
Visit the Taylor & Francis Web site at
www.taylorandfrancis.com
and the CRC Press Web site at
www.crcpress.com
To my Kit, who is constantly mathematizing
Contents
List of Figures, xi
Preface, xvii
Acknowledgments, xix
About the Author, xxi
Introduction 1
TWELVE DROPS OF MATHEMATICAL WISDOM 1
LET’S CREATE OUR MAP 4
WHY THE DESERT? 6
IS MATHEMATICS FOR YOU, OR ARE YOU FOR
MATHEMATICS? 6
Chapter 1 ◾ January 9
MATHEMATICAL TRIBES 9
I WROTE YOU A POEM 11
NEWTON’S INFINITELY IMPORTANT AND INFINITELY
SMALL QUANTITIES 13
THE SEARCH FOR THE PHILOSOPHER’S STONE 18
THAT DIVINE CLOCK 19
FRIENDS IN NEED 21
Chapter 2 ◾ February 31
THE HOLY MONTH OF WISDOM 31
GOING BACK TO THALES 35
ISIDORE, THE MILESIAN 40
vii
viii Contents
◾
APPROXIMATIONS IN MATHEMATICS,
ARCHITECTURE, AND LIFE 40
Chapter 3 ◾ March 45
HIDDEN DOMES AND HEAVENLY IDEAS 45
THE HANGING CHAIN CURVE 49
WREN AND OTHER CURVED SHAPES 51
BEAUTY IS IN THE EYE OF THE BEHOLDER – OR IN
MATHEMATICS? 52
SOME OTHER INTERESTING CURVES 53
Chapter 4 ◾ April 59
AN IDEAL AND EMMY 59
NOETHER’S ABSTRACT ART OF MATHEMATICS 60
NOETHER SET DOWN THE LAW 63
WHAT ABOUT THE IDEAL AND EMMY? 65
Chapter 5 ◾ May 69
THE WITCH THAT TURNED 69
NEWTON FOR, AND BY, LADIES 71
THE BOOK 71
THE SPECTACLE OF NEWTONIANISM 72
AGNESI AND THE WITCH 74
AND, BY A TURN IN THE STORYLINE… 76
Chapter 6 ◾ June 79
MATHEMATICS IS LIKE… A TRANSLUCENT OBJECT
FLOATING IN SPACE 79
SOLIDS NAMED AFTER A GREEK PHILOSOPHER 81
THE STRUCTURE OF THE FIFTH ELEMENT 85
THE TRANSLUCENT OBJECT FLOATING IN SPACE 89
Chapter 7 ◾ July 95
THE POWER OF (MATHEMATICAL) BOOKS 95
THE MATHEMATICAL PREFACE 98
BURNING BOOKS 99
AND THEN, ACROSS THE POND 100
Contents ix
◾
Chapter 8 ◾ August 105
REVOLUTIONARY MATHEMATICS 105
THE REAL BIRTHDAY OF IMAGINARY BOURBAKI 107
THE MODERN ELEMENTS 108
THE ETERNAL APPEAL OF PYTHAGORAS 109
DANGEROUS BENDS 111
BOURBAKI’S THEOREM – EN FIN 112
Chapter 9 ◾ September 115
THE MATHEMATICAL TRAVELER IS AT HOME
EVERYWHERE 115
THE NUMBER THAT BEARS YOUR NAME 116
CAN I IMAGINE AN EVEN BIGGER NUMBER? 118
BIG NUMBERS IN ANTIQUITY 118
ERDŐS AND HIS MATHEMATICAL FRIENDS’ NUMBERS 120
A FAMOUS MISTAKE AND THE VALUE OF BIG NUMBERS 124
Chapter 10 ◾ October 127
THE ROUNDED LIFE AND MUSIC OF VIBRATING
STRINGS 127
THE FOURTH DIMENSION 129
THOUGHT EXPERIMENTS 130
SOME MORE DIFFICULT MATHS 132
A FULL CIRCLE BACK TO LE ROND AND HIS WAY OF
FINDING HAPPINESS 134
Chapter 11 ◾ November 137
WE MAY BE FRIENDS, BUT I STILL HAVE TO CHECK
WHETHER WHAT YOU ARE SAYING IS TRUE 137
NEW WORLDS ON THE HORIZON 139
THE BOOLE FAMILY AND THEIR FRIENDS 140
AS MATHEMATICAL FAMILIES GO… 141
THE LEGACY FOR THE FUTURE 145
Chapter 12 ◾ December 149
WHAT CAN A MATHEMATICIAN GIVE TO
THEIR FRIEND AS A NEW YEAR’S PRESENT? 149
