Cover of: The Universal History of Numbers by translated by David Bellos, E. F. Harding, Sophie Wood, and Ian Monk

The Universal History of Numbers

From Prehistory to the Invention of the Computer

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October 18, 2022 | History

The Universal History of Numbers

From Prehistory to the Invention of the Computer

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  • 1 Want to read
  • 1 Currently reading
  • 0 Have read
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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

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Edition Availability
Cover of: Universal History of Numbers
Universal History of Numbers: The Modern Number System
2000, Penguin Random House
in English
Cover of: Universal History of Numbers
Universal History of Numbers: The World's First Number Systems
2000, Penguin Random House
in English
Cover of: The Universal History of Numbers
The Universal History of Numbers: From Prehistory to the Invention of the Computer
2000, John Wiley & Sons Inc

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Book Details

Published in

New York, USA

Table of Contents

Foreward v
List of Abbreviations vi
Introduction - Where "Numbers" Come From xv
Chapter 1 - Explaining the Origins: Ethnological and Psychological Approaches to the Sources of Numbers 3
Chapter 2 - Base Numbers and the Birth of Number-systems 23
Chapter 3 - The Earliest Calculating Machine - The Hand 47
Chapter 4 - How Cro-Magnon Man Counted 62
Chapter 5 - Tally Sticks: Accounting for Beginners 64
Chapter 6 - Numbers on Strings 68
Chapter 7 - Number, Value and Money 72
Chapter 8 - Numbers of Sumer 77
Chapter 9 - The Enigma of the Sexagesimal Base 91
Chapter 10 - The Development of Written Numerals in Elam and Mesopotamia 96
Chapter 11 - The Decipherment of a Five-thousand-year-old System 109
Chapter 12 - How the Sumerians Did Their Sums 121
Chapter 13 - Mesopotamian Numbering after the Eclipse of Sumer 134
Chapter 14 - The Numbers of Ancient Egypt 162
Chapter 15 - Counting in the Times of the Cretan and Hittite Kings 178
Chapter 16 - Greek and Roman Numerals 182
Chapter 17 - Letters and Numbers 212
Chapter 18 - The Invention of Alphabetic Numerals 227
Chapter 19 - Other Alphabetic Number-systems 240
Chapter 20 - Magic, Mysticism, Divination, and Other Secrets 248
Chapter 21 - The Numbers of Chinese Civilisation 263
Chapter 22 - The Amazing Achievements of the Maya 297
Chapter 23 - The Final State of Numerical Notation 323
Chapter 24 - Part I - Indian Civilisation: the Cradle of Modern Numerals 356
Chapter 24 - Part II - Dictionary of the Numeral Symbols of Indian Civilisation 440
Chapter 25 - Indian Numerals and Calculation in the Islamic World 511
Chapter 26 - The Slow Progress of Indo-Arabic Numerals in Western Europe 577
Chapter 27 - Beyond Perfection 592
Bibliography 601
Index of Names and Subjects 616

Edition Notes

Copyright Date
1981, 1994, 1998
Translation Of
Histoire universelle des chiffres


Library of Congress
QA141 .I3713 2000, QA141.I3713 2000

The Physical Object

Number of pages

ID Numbers

Open Library
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