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.

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.

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.

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.

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.

"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.

Every day in the United States, people test their luck in numerous lotteries, from state-run games to massive programs like Powerball and Mega Millions. Yet few are aware that the origins of today’s lotteries can be found in an African American gambling economy that flourished in urban communities in the mid-twentieth century. In Running the Numbers, Matthew Vaz reveals how the politics of gambling became enmeshed in disputes over racial justice and police legitimacy. As Vaz highlights, early urban gamblers favored low-stakes games built around combinations of winning numbers. When these games became one of the largest economic engines in nonwhite areas like Harlem and Chicago’s south side, police took notice of the illegal business—and took advantage of new opportunities to benefit from graft and other corrupt practices. Eventually, governments found an unusual solution to the problems of illicit gambling and abusive police tactics: coopting the market through legal state-run lotteries, which could offer larger jackpots than any underground game. By tracing this process and the tensions and conflicts that propelled it, Vaz brilliantly calls attention to the fact that, much like education and housing in twentieth-century America, the gambling economy has also been a form of disputed terrain upon which racial power has been expressed, resisted, and reworked.