Leo Corry - A Brief History of Numbers

A Brief History of Numbers

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Leo Corry 2015

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First Edition published in 2015

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Library of Congress Control Number: 2015930555

ISBN 9780191007071

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Dedicado a la memoria de la querida Tere

Preface

This book tells the story of the development of the idea of number since the days of the Pythagoreans and up until the turn of the twentieth century. The latter is more or less the time when currently prevailing conceptions about numbers reached their actual state, for all of their complexity (or perhaps we should rather say, for all of their simplicity). This is not the first book to tell a similar story, or, more specifically, to tell a story of roughly the same subject matter. Still, I believe that this book differs essentially from existing ones in content as well as in style. It certainly differs in scope and in the kind of historical material on which it is based.

For the sake of brevity, and given the somewhat informal character of this book, the historical account presented here will be, of necessity, selective. I have not attempted to be either exhaustive or fully balanced in telling this story. Choices had to be made, and I believe that my choices are fair, in terms of the scope and aims that I have pursued in writing the book. I think that the account is comprehensive and representative enough to provide readers with a fair view of the development of the concept of number. Hopefully, readers will also find my choices to be justified, coherent and illuminating.

The story told here focuses mainly on developments related to European mathematics (including ancient Greece). There is also a relatively lengthy chapter on the contributions of the medieval world of Islam. Because of considerations of space, I have left aside entire mathematical cultures such as those of the Far East (China, India, Japan, Korea) and Latin America, each of which came up with their own significant achievements and idiosyncratic conceptions.

This is a book about the historical development of important scientific ideas. Of course, these ideas were created and disseminated by actual persons, who lived and worked in specific historical circumstances. I devote some attention to these lives and circumstances, but only to the extent that they help us understand the ideas in their proper context. Accordingly, neither heroic duels at dawn nor tragic cases of suicide related to the failure in solving a certain problem appear here as part of my narrative. Not that such anecdotes are devoid of interest. But I thought that the intrinsic dynamic of the ideas is dramatic enough to warrant the continued attention of the reader.

In writing the various chapters, I have tried to reflect the most recent and updated, relevant historical scholarship, alongside some of the best classical one. This is a not a monographical text involving original historical research meant to be cited in subsequent works of fellow historians. Rather, it is a work of synthesis meant to provide a broad overview of what historians have written and to direct prospective readers to their works. I do not claim, however, to have reflected all the existing views on all the topics, nor all of the divergent and sometimes opposed interpretations that historians have suggested for the various episodes that I discuss. At the same time, given the style of the book, I did not want to fatigue the reader with a full scholarly apparatus to support each and every one of the claims I have made in the text. Direct references are only to texts that are cited as full paragraphs, or to texts that elaborate in greater detail on issues that I have only mentioned in passing but that, for reasons of space, I have left as brief remarks. Still, I have provided at the end of the book a somewhat detailed list of texts for further reading, organized more or less in accordance with the chapters of the book. This is my way to explicitly acknowledge the works on which I have directly relied for the various issues discussed. This is my way to indicate my great intellectual debt to each of these authors. Readers interested in broadening the scope of my account will find in those texts large amounts of additional illuminating material. The texts also provide direct references to the primary sources, which lend support to the historical claims that I put forward in this book. In fact, in consideration with space limitations, except in cases where I have cited directly, I do not include primary sources in the bibliographical list, in the assumption that interested readers can easily find detailed information either in the secondary sources or collections cited or by Internet search.

One typical reader that I have had in mind when writing the book is an undergraduate student in mathematics. As she is struggling to develop demanding technical skills in the courses that she is now studying, a book like this may help her make further sense, from a perspective that is different from that found in textbooks and in class, of the world of ideas that she is gradually becoming acquainted with. Her apprenticeship, I think, may gain in depth and richness by reading a book like this one. A second, typical kind of reader I have envisaged for the book is a teacher of mathematics. This book, I believe, may contribute to his efforts in bringing to the classroom a broader understanding of his own discipline, with an eye on the long-range historical processes that have been at play in shaping it.

I have also tried to write in such a way as to allow for a wider readership that would include intellectually curious high-school pupils with an inclination for mathematics, professional mathematicians, scientists and engineers, and other educated readers of various kinds. Hence I have tried to strike a natural balance between technicalities and broad historical accounts. In this respect, there are slight differences among the various chapters. Some are more technically demanding, some less so. In all cases, however, I have made my best efforts to write concisely and in a way that will be within the reach of readers of various backgrounds and will elicit their interest.