A Brief History of Numbers

A Brief History of Numbers

A Brief History of Numbers

A Brief History of Numbers


The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century. Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.


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 . . .

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