History By Numbers

Fully updated and carefully revised, this new 2nd edition of History by Numbers still stands alone as the only textbook on quantitative methods suitable for students of history. Even the numerically challenged will find inspiration. Taking a problem-solving approach and using authentic historical data, it describes each method in turn, including its origin, purpose, usefulness and associated pitfalls. The problems are developed gradually and with narrative skill, allowing readers to experience the moment of discovery for each of the interpretative outcomes. Quantitative methods are essential for the modern historian, and this lively and accessible text will prove an invaluable guide for anyone entering the discipline.

The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the mathematics of the 18th to the early 20th century. Focusing on both foundational debates and practical use numbers, and showing how the story of numbers is intimately linked to that of the idea of equation, this book provides a valuable insight to numbers for undergraduate students, teachers, engineers, professional mathematicians, and anyone with an interest in the history of mathematics.

"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

Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." — Choice.

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.

Numbers: A Cultural History provides students with a compelling interdisciplinary view of the development of mathematics and its relationship to world cultures over 4,500 years of human history. Mathematics is often referred to as a "universal language," and that is a fitting description. Many cultures have contributed to mathematics in fascinating ways, but despite its "universal" character, mathematics is also a human endeavor. It has played pivotal roles in societies at particular times; and it has influenced, and been influenced by, a wide range of ideas and institutions, from commerce to philosophy. Ancient Egyptian views of mathematics, for example, are tied closely to engineering and agriculture. Some European Renaissance views, on the other hand, relate the study of number to that of the natural world. Numbers, A Cultural History seeks to place the history of mathematics into a broad cultural context. While it treats mathematical material in detail, it also relates that material to other subject matter: science, philosophy, navigation, commerce, religion, art, and architecture. It examines how mathematical thinking grows in specific cultural settings and how it has shaped those settings in turn. It also explores the movement of ideas between cultures and the evolution of modern mathematics and the quantitative, data-driven world in which we live.

"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.

Most of us hardly ever think about those ubiquitous things that hang—along with wreaths, light fixtures, and the occasional delivery attempt notice—at our front door: house numbers, our address. Taken for granted in the hustle and bustle of everyday life, house numbers have the crucial burden of organizing the places of the world—and they do it with zero fanfare or appreciation. In this unique illustrated history, Anton Tantner pays long-overdue tribute to those unassuming combinations of digits, showing that house numbers haven’t always existed, and that they have their own interesting history, one he spells out with vivid images from around the world. As Tantner shows, house numbers started their lives in a gray area between the military, tax authorities, and early police forces. With an engaging style, he moves from the introduction of house numbers in European towns in the eighteenth century, through the spread of the numbering system in the nineteenth century, and on into its global adoption today. He uncovers a contentious past, telling the stories of the many people who have resisted having their homes so systematically ordered. Along the way, his visual journey showcases a surprising diversity of house number displays, visiting historic addresses from the London house on Strand-on-the-Green that is numbered “Nought” to 1819 Ruston, Louisiana. The result is a story that will forever change the way you see a city, one that elevates the seemingly insignificant house number to an important place in the history of urban planning.