Cover image for The universal history of numbers : from prehistory to the invention of the computer
The universal history of numbers : from prehistory to the invention of the computer
Ifrah, Georges.
Personal Author:
Uniform Title:
Histoire universelle des chiffres. English
Publication Information:
New York : J. Wiley, 2000.

Physical Description:
xxii, 633 pages : illustrations ; 24 x 25 cm
General Note:
Originally published: London : Harvill, 1998.
Subject Term:
Format :


Call Number
Material Type
Home Location
Item Holds
QA141.2 .I3613 1998 Adult Non-Fiction Reference material
QA141.2 .I3613 1998 Adult Non-Fiction Central Closed Stacks
QA141.2 .I3613 1998 Adult Non-Fiction Open Shelf

On Order



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

Author Notes

Georges Ifrah is an independent scholar and former math teacher.

David Bellos, the primary translator, is Professor of French at Princeton University.

Sophie Wood, cotranslator, is a specialist in technical translation from French. Ian Monk, cotranslator, has translated the works of Georges Perec and Daniel Pennac.

Reviews 1

Choice Review

In his 1985 book, From One to Zero (CH, Feb'86), independent scholar and mathematics teacher Ifrah proposed a universal history of numbers and succeeded in presenting an engaging and informative story of considerable depth. In this new work, Ifrah has greatly expanded his coverage of the history of numbers and counting to include more of the scholarship that has become available since his earlier work, and a new emphasis on arithmetic devices such as the abacus. The new book restores the original French title and provides a fresh translation by David Bellos, E.F. Harding, Sophie Wood, and Ian Monk. The earlier book told the history of numbers in all its richness and complications; the new one keeps all of the liveliness of the first while serving the role of a "comprehensive, thematic encyclopedia of numbers and counting." The new arrangement of topics adds to the story as well. The number systems of the world represent some of human mankind's greatest strides forward, though they are forgotten as they become part of scientific and economic progress. Ifrah has identified these achievements and reconstructed them for everyone. A great addition to any library. All levels. J. McCleary; Vassar College

Table of Contents

Explaining the Origins: Ethnological and Psychological Approaches to the Sources of Numbers
Base Numbers and the Birth of Number-systems
The Earliest Calculating Machine - The Hand
How Cro-Magnon Man Counted
Tally Sticks: Accounting for Beginners
Numbers on Strings
Number, Value and Money
Numbers of Sumer
The Enigma of the Sexagesimal Base
The Development of Written Numerals in Elam and Mesopotamia
The Decipherment of a Five-Thousand-Year-Old System
How the Sumerians Did Their Sums
Mesopotamian Numbering after the Eclipse of Sumer
The Numbers of Ancient Egypt
Counting in the Times of the Cretan and Hittite Kings
Greek and Roman Numerals
Letters and Numbers
The Invention of Alphabetic Numerals
Other Alphabetic Number-systems
Magic, Mysticism, Divination, and Other Secrets
The Numbers of Chinese Civilisation
The Amazing Achievements of the Maya
The Final Stage of Numerical Notation
Part I Indian Civilisation: The Cradle of Modern Numerals
Part II Dictionary of the Numeral Symbols of Indian Civilisation
Indian Numerals and Calculation in the Islamic World
The Slow Progress of Indo-Arabic Numerals in Western Europe
Beyond Perfection
Index of Names and Subjects