Stuart Hollingdale - Makers of Mathematics

Makers of

Mathematics

Makers of

Mathematics

STUART HOLLINGDALE

Dover Publications, Inc., Mineola, New York

Copyright

Copyright 1989, 1991, 1994 by Stuart Hollingdale

All rights reserved.

Bibliographical Note

This Dover edition, first published in 2006, is an unabridged republication of the 1994 printing of the edition published by Penguin Books, London and New York, 1989.

Library of Congress Cataloging-in-Publication Data

Hollingdale, S. H.

Makers of mathematics / Stuart Hollingdale.

p.cm.

Originally published: London ; New York : Penguin Books, 1989.

eISBN-13: 978-0-486-17450-1

1. MathematicsHistory. 2. MathematiciansBiography. I. Title.

QA21.H74 2006
510.9dc22

2005056066

Manufactured in the United States by Courier Corporation
45007404 2014
www.doverpublications.com

The origins of this book are to be found in a number of essays (many of them anniversary tributes) and book reviews which have appeared in the Bulletin of the Institute of Mathematics and its Applications over a period of some ten years from 1976. The articles were written primarily for a specialist readership the Fellows and members of the Institute, the great majority of whom are graduates in mathematics. The material has been edited and reworked to meet the needs of the general reader, which I take to be a broadly educated and lively-minded person whose mathematical knowledge may not extend much beyond that required for the General Certificate of Education at Ordinary Level (or a broadly equivalent standard in the new GCSE). More advanced ideas and procedures are carefully explained and illustrated as they are introduced.

Most of the IMA articles are set in the seventeenth, eighteenth or early nineteenth centuries, so some gaps in the story needed to be filled. Seven chapters () are completely new. Even so, the book is in no sense a balanced history of mathematics, but rather an informal, personal even idiosyncratic attempt to present the main features of a long story through the lives and achievements of some of its great men, from Pythagoras to Einstein. We have recently been celebrating the tercentenary of the publication of Newtons Principia, so it seemed appropriate to accord this unique masterpiece a chapter to itself. Some more specialized and technically demanding material has been placed in five short appendices. For the first of these I am indebted to J.H. Cadwell, a close colleague for more than twenty years who died in 1984.

While writing this book, two objectives have been kept in mind. The first is to convey something of the fascination of mathematics of its austere beauty, intellectual power and infinite variety. The second is to draw attention to the eventful lives and colourful personalities of so many of its leading practitioners. The common view of the mathematician as a desiccated, passionless, cloistered creature of narrow interests, out of touch with the real world, is indeed very far from the truth. In selecting the main characters of the story, I have not attempted to hide my personal preferences. For me, Newton stands alone at the summit, closely flanked by Archimedes, Gauss and Einstein; Eudoxus, Fermat, Euler and Cantor stand not far below. Nor have I sought to disguise my affection for such lesser-known figures as Archytas, Tartaglia, Cotes and dAlembert.

The intense specialization of contemporary mathematics is a fairly recent phenomenon, albeit an inevitable one. Few of our subjects made much, if any, distinction between what Thomas Jefferson, when founding the University of Virginia, called Mathematics, pure and Physico-mathematics. Indeed, the subject of the final chapter, Albert Einstein, was not primarily a mathematician at all, but he is too important a figure to be excluded. In this book the whole of mathematics, together with its many applications, is to be perceived as a seamless robe.

Although there is much biographical information, I have not hesitated to include too a substantial measure of solid mathematics, in particular demonstrations of some of the more historically significant, elegant or unexpected theorems and procedures. Indeed, some readers may find parts of the book heavy going. I hope they will not give up too easily. To follow a chain of reasoning of moderate length and complexity undoubtedly demands persistence and determination, but it can be argued that the exercise of these faculties is one of the pleasures to be obtained from the study of mathematics and hence, it is to be hoped, from reading a book of this kind.

I have not thought it necessary (or indeed desirable) to include scholarly footnotes; the number of individual references to the works quoted has been kept to a minimum. The list of references given at the end has been limited, with a few exceptions, to sources from my own library which I consulted while writing this book. I am much ) has recently been published for the second such course; it is a mine of information and critical comment. I am also indebted to David Nelson for his valuable comments on my draft text. Finally, I would like to express my thanks to Catherine Richards, the Secretary and Registrar of the IMA, and her staff for encouragement, for typing services and for general administrative assistance and, not least, for sending me so many good books to review.

June 1989

A new edition provides a welcome opportunity to correct misprints (how do they get through?), clarify or amplify a few paragraphs and add two new Appendices (). Many of the changes derive from comments made by correspondents and I would like to thank them collectively for their, valuable help. Three of them must, however, be mentioned individually.

Soon after the book was published in September 1989, I received a letter from Dr C. Kenneth Thornhill, an old colleague in the Scientific Civil Service, expressing his surprise at my statement (now deleted) on page 104 that the method used by Leonardo of Pisa to solve the court squares problem was not known. He writes: I know how to obtain his solution and I should think it fairly certain that my way is the same method that Leonardo used. In further correspondence Dr Thornhill communicated several of his methods for solving the generalized squares problem, of which Leonardos court problem is a special case. He then consulted a polymath friend of his, Mr A. Roger Thatcher, who retired a few years ago as Registrar-General after a distinguished career in the Civil Service. He pointed out that Leonardos treatment of the general problem is discussed in detail in .

, which can be savoured by the most non-mathematical reader, tells a remarkable story of mistaken identity in high places: it may be allowed to speak for itself.

Several correspondents from the teaching profession have queried my remark in the 1989 Preface that readers need to have little mathematical knowledge beyond that required for the GCE at ordinary level. To some, indeed, my claim was wildly optimistic. I must plead guilty: I was, I regret to say, showing my age! I had not realized to what extent the classical mathematical content had been reduced since I'd taken the General Schools Certificate (and London Matric) examinations in the 1920s. In those days, Elementary Mathematics, Mathematics (more advanced) and Mechanics could be offered as three separate subjects. The process of emasculation (if that is not too strong a word) appears to have started a few years after the war with the introduction of the GCE and to have been carried further by the recent change to the GCSE. I hope that younger readers will not allow a limited school background to deter them from tackling the book. Some readers will, no doubt, be able to rectify any gaps in their knowledge without too much difficulty as they work through the book. For others, perhaps, some judicious skipping would be appropriate.