"Georges Ifrah is the man. This book, quite simply, rules. . . . It is outstanding . . . a mind-boggling and enriching experience." –The Guardian (London) "Monumental. . . . a fascinating journey taking us through many different cultures."–The Times (London)"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 Now in paperback, here is Georges Ifrah’s landmark international bestseller–the first complete, universal study of the invention and evolution of numbers the world over. A riveting history of counting and calculating, from the time of the cave dwellers to the twentieth century, this fascinating volume brings numbers to thrilling life, explaining their development in human terms, the intriguing situations that made them necessary, and the brilliant achievements in human thought that they made possible. It takes us through the numbers story from Europe to China, via ancient Greece and Rome, Mesopotamia, Latin America, India, and the Arabic countries. Exploring the many ways civilizations developed and changed their mathematical systems, Ifrah imparts a unique insight into the nature of human thought–and into how our understanding of numbers and the ways they shape our lives have changed and grown over thousands of years. "Dazzling."–Kirkus Reviews "Sure to transfix readers."–PublishersWeekly

Numbers Are One Of Two Creations (The Other Being The Alphabet) Of The Human Spirit Which Have Given Us Today S World. The Three Volumes Of The Universal History Of Numbers Are Probably The First Comprehensive History Of Numbers And Of Counting From Prehistory To The Modern Age. They Are Also The Story Of How The Human Race Has Learnt To Think Logically. In Volume 2, Georges Ifrah Continues The Story Of The Invention Of The Modern Number-System By Telling Us How Indian Civilization Became The Cradle Of Modern Numerals With The Invention Of The Place Value System And Of Zero. Twenty-One Geographically Different Indian Numerical Notations Of The Nine Numerals And The Zero Are Explained Individually With Illustrations. A Detailed Dictionary Of Indian Numerical Symbols, Recorded Alphabetically, Gives The Reader A Better Idea Of The Subtle And Complicated World Of Numbers Which Derived From The Genius Of Indian Mathematicians Working In The Late Middle Ages. It Was Arab Scholars Who Brought The System To The West. If Western Mathematical Progress Today Looks Dazzling, It Is Because It Stands On A Solid Non-Western Foundation. Amazing, Captivating And Enriching, The Universal History Of Numbers Is A Must Read Not Only For Specialists And Academics, But Also For The Average Reader Who Is Interested In The Development Of Civilization.

"Traces the development of numerical systems in Sumerian, Egyptian, Greek, Roman, Chinese, Babylonian, and Mayan cultures, and examines the origins of the Hindu-Arabic numerals we use today"--Back cover.

The book explores the science of numeration as it has developed all over the world, from Europe to China, via the Classical World, Mesopotamia, South America and, above all, India and the Arab lands.

Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

“A fascinating book.” —James Ryerson, New York Times Book Review A Smithsonian Best Science Book of the Year Winner of the PROSE Award for Best Book in Language & Linguistics Carved into our past and woven into our present, numbers shape our perceptions of the world far more than we think. In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture, Caleb Everett draws on new discoveries in psychology, anthropology, and linguistics to reveal the many things made possible by numbers, from the concept of time to writing, agriculture, and commerce. Numbers are a tool, like the wheel, developed and refined over millennia. They allow us to grasp quantities precisely, but recent research confirms that they are not innate—and without numbers, we could not fully grasp quantities greater than three. Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians. “This is bold, heady stuff... The breadth of research Everett covers is impressive, and allows him to develop a narrative that is both global and compelling... Numbers is eye-opening, even eye-popping.” —New Scientist “A powerful and convincing case for Everett’s main thesis: that numbers are neither natural nor innate to humans.” —Wall Street Journal

Numbers Are One Of Two Creations (The Other Being The Alphabet) Of The Human Spirit Which Have Given Us Today S World. The Three Volumes Of The Universal History Of Numbers Are Probably The First Comprehensive History Of Numbers And Of Counting From Prehistory To The Modern Age. They Are Also The Story Of How The Human Race Has Learnt To Think Logically. In Volume 1, Georges Ifrah Leads The Reader Through The Whole Art And Science Of Numeration As It Has Developed All Over The World, From The Court Sages Of Mesopotamia And Egypt To The Priests And Astronomers Who Perfected The Mayan Calendar. We Meet Those Who Count To Four Anything More Is Lots ; We Discover The First Use Of Fingers And Toes For Counting; We Follow The Sequence Of Trial And Error That Chose A Number Of Bases For Counting Until Base 10, The Metric System, Was Put In Place. In The Far East They Perfected Many Centuries Ago A Method Of Counting With The Abacus That Remains Astonishing In Its Speed And Sophistication. Yet It Still Begs The Intriguing Question: How Did They Manage For All Those Hundreds Of Years Without The Zero? Amazing, Captivating And Enriching, The Universal History Of Numbers Is A Must Read Not Only For Specialists And Academics, But Also For The Average Reader Who Is Interested In The Development Of Civilization.