Pearl
She trembles with excitement and anticipation. She recently turned sixteen, and today she is to be married. There would be no other possible time. At her birth, astrologers predicted that she would never marry. Her father, known as the Learned One, was no
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Masters of Mathematics The Problems They Solved, Why These Are Important, and What You Should Know about Them
Robert A. Nowlan Southern Connecticut State University, New Haven, USA
A C.I.P. record for this book is available from the Library of Congress.
ISBN: 978-94-6300-891-4 (paperback) ISBN: 978-94-6300-892-1 (hardback) ISBN: 978-94-6300-893-8 (e-book)
Published by: Sense Publishers, P.O. Box 21858, 3001 AW Rotterdam, The Netherlands https://www.sensepublishers.com/
All chapters in this book have undergone peer review.
Every effort has been made to contact the copyright holders of the figures which have been reproduced from other sources. Anyone with a copyright claim who has not been properly credited is requested to contact the publishers, so that due acknowledgements may be made in subsequent editions.
Printed on acid-free paper
All Rights Reserved © 2017 Sense Publishers No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.
To all my partners in learning mathematics, my students. To my children and their spouses. To my grandchildren. And, most especially, to my best friend and wife, Wendy.
LIST OF CONTENTS
Prefacexv Acknowledgmentsxix Introductionxxi Chapter 1: Mathematics as a Labor-Saving Device
1
The Problem An Aside: Who Are Masters of Mathematics?
1 9
Chapter 2: All about ‘e’ (Well, Almost All) An Aside: Hanging
19 31
Chapter 3: What Else Did Euler Do? Bridges The Problem The Solution An Aside: The Importance of Curiosity to Mathematical Literacy Chapter 4: No Mathematical Work Is Ever Wasted: Knots The Problem An Experiment Partial Solution to the Problem Biographic Information Applications of Knot Theory An Aside: Mathematics of Golf
35 35 37 43 51 51 53 56 58 59 61
Chapter 5: I Have Never Done Anything Like Others: Roughness The Problem Biographic Information The Problem Biographic Information An Aside: Mathematics at the Movies & on TV Chapter 6: Doing the Impossible
69 69 74 75 85 89 97
The Butterfly Effect Goal of Chaos Theory An Aside: Writing Mathematics and Problem Solving
vii
100 102 106
TABLE OF CONTENTS
Chapter 7: “Mathematics Is a Genderless World” – Karen Uhlenbeck
115
The Problem 115 Pagan116 Biographic Information 121 An Aside: Ancient Greek Women Mathematicians 122 Chapter 8: The Reluctant Mathematician
127
Biographic Information 127 An Aside: The Newton – Leibniz Controversy 133 6accdae13eff7i3l9n4o4qrr4s8t12ux134 Chapter 9: Programmer The Problem Meet the Problem Solver Biographic Information The Binary System Other Computer Pioneers An Aside: Enigma & Turing Machines Chapter 10: Rabbits & Patterns Biographic Information Back to the Problem Pascal’s Trian
