# The Universal History of Numbers: From Prehistory to the Invention of the Computer

## Synopsis

A riveting history of counting and calculating from the time of the cave dwellers to the late twentieth century, The Universal History of Numbers is the first complete account of the invention and evolution of numbers the world over. As different cultures around the globe struggled with problems of harvests, constructing buildings, educating their citizens, and exploring the wonders of science, each civilization created its own unique and wonderful mathematical system.

Dubbed the "Indiana Jones of numbers," Georges Ifrah traveled all over the world for ten years to uncover the little-known details of this amazing story. From India to China, and from Egypt to Chile, Ifrah talked to mathematicians, historians, archaeologists, and philosophers. He deciphered ancient writing on crumbling walls; scrutinized stones, tools, cylinders, and cones; and examined carved bones, elaborately knotted counting strings, and X-rays of the contents of never-opened ancient clay accounting balls. Conveying all the excitement and joy of the process of discovery, Ifrah writes in a delightful storytelling style, recounting a plethora of intriguing and amusing anecdotes along the way.

From the stories of the various ingenious ways in which different early cultures used their bodies to count and perfected the use of the first calculating machine-the hand-to the invention of different styles of tally sticks, up through the creation of alphabetic numbers, the Greek and Roman numeric systems, and the birth of modern numerals in ancient India, we are taken on a marvelous journey through humankind's grand intellectual epic.

We meet those who only count to four-anything more is "a lot"; discover the first uses of counting fingers and toes; learn of the amazing ability of abacus users to calculate with brilliant efficiency; and ponder the intriguing question: How did many cultures manage to calculate for all those centuries without a zero? Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought-and into the ways our understanding of numbers and how they shape our lives has slowly changed and grown over thousands of years.

In this illuminating and entertaining work, you'll learn about:

• The earliest calculating machine--the hand
• Tally sticks--accounting for beginners
• How the Sumerians did their sums
• Greek and Roman numerals
• The invention of alphabetic numerals
• The achievements of the Mayan civilization
• India and the birth of modern numbers
• Indo-Arabic numerals and how they reached the West
• The final stage of numerical notation

Praise for The Universal History of Numbers

"Let us start the year with a bang. Georges Ifrah is the man. This book, quite simply, rules.... It is outstanding, and not least because it has been written from first principles, for people like you and me, curious but by no means expert... a mind-boggling and enriching experience." -The Guardian

"Pursuing the invention of numbers across civilizations, Georges Ifrah has written the grand story of human ingenuity.... His amazing undertaking, describing humankind's relationship with numbers from Paleolithic times to the computer age, spans the world from Mayan ruins to Indian museums, from Egyptian hieroglyphics to Greek philosophers to Chinese libraries." -Le Figaro

"Follow the astonishing path of Georges Ifrah, the Indiana Jones of arithmetic... who decided in 1974 to begin the search for his Grail, the origin of numbers. Journeying over mountains and across valleys, he discovered how-from Mayan to Chinese, from Indian to Egyptian-humankind has juggled numbers." -Express

"Ifrah's book amazes and fascinates... It is nothing less than thehistory of the human race told through figures." -International Herald Tribune

## Excerpt

The main aim of this two-volume work is to provide in simple and accessible terms the full and complete answer to all and any questions that anyone might want to ask about the history of numbers and of counting, from prehistory to the age of computers.

More than ten years ago, an American translation of the predecessor of The Universal History of Numbers appeared under the title From One to Zero, translated by Lowell Bair (Viking, 1985). The present book translated afresh – is many times larger, and seeks not only to provide a historical narrative, but also, and most importantly, to serve as a comprehensive, thematic encyclopaedia of numbers and counting. It can be read as a whole, of course; but it can also be consulted as a source-book on general topics (for example, the Maya, the numbers of Ancient Egypt, Arabic counting, or Greek acrophonics) and on quite specific problems (the proper names of the nine mediaeval apices, the role of Gerbert of Aurillac, how to do a long division on a dust-abacus, and so on).

Two maps are provided in this first volume to help the reader find what he or she might want to know. The Summary Table of Contents above gives a general overview. The Index of names and subjects, from p. 616, provides a more detailed map to this volume.

The bibliography has been divided into two sections:

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