Synopses & Reviews
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
"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
"Ifrah's monumental follow-up to From One to Zero goes from one to (almost) infinity as he meticulously reviews the numbers and reckoning systems of countless tribes and cultures in a dazzling scholarly performance....A must for any library and a wonderful gift." Kirkus Reviews
"Monumental...a fascinating journey taking us through many different cultures." The Times
"Ifrah's book amazes and fascinates by the scope of its scholarship. It is nothing less than the history of the human race told through figures." International Herald Tribune
"'A brief history of the metric system,' an introduction (with plentiful pictograms) to Mesopotamian decimal notation, a guide to ways of representing quantities by tying and untying knots in strings and a 70-page 'Dictionary of Indian Numerical Symbols' are just some of the pleasures of The Universal History of Numbers: From Prehistory to the Invention of the Computer. Georges Ifrah's enormous illustrated compendium of essays on mathematics and counting methods in various cultures became an unlikely bestseller in France. This attractive if weighty edition in English required four translators David Bellos, E.F. Harding, Sophie Wood and Ian Monk whose combined efforts are sure to transfix readers who care about the math of the past." Publishers Weekly
"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
Includes bibliographical references (p. 601-615) and index.
About the Author
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.
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.
Index of Names and Subjects.