This Handbook explores the history of mathematics under a series of themes which raise new questions about what mathematics has been and what it has meant to practise it. It addresses questions of who creates mathematics, who uses it, and how. A broader understanding of mathematical practitioners naturally leads to a new appreciation of what counts as a historical source. Material and oral evidence is drawn upon as well as an unusual array of textual sources. Further, the ways in which people have chosen to express themselves are as historically meaningful as the contents of the mathematics they have produced. Mathematics is not a fixed and unchanging entity. New questions, contexts, and applications all influence what counts as productive ways of thinking. Because the history of mathematics should interact constructively with other ways of studying the past, the contributors to this book come from a diverse range of intellectual backgrounds in anthropology, archaeology, art history, philosophy, and literature, as well as history of mathematics more traditionally understood. The thirty-six self-contained, multifaceted chapters, each written by a specialist, are arranged under three main headings: 'Geographies and Cultures', 'Peoples and Practices', and 'Interactions and Interpretations'. Together they deal with the mathematics of 5000 years, but without privileging the past three centuries, and an impressive range of periods and places with many points of cross-reference between chapters. The key mathematical cultures of North America, Europe, the Middle East, India, and China are all represented here as well as areas which are not often treated in mainstream history of mathematics, such as Russia, the Balkans, Vietnam, and South America. A vital reference for graduates and researchers in mathematics, historians of science, and general historians.
INTRODUCTION; GEOGRAPHIES AND CULTURES: GLOBAL; 1.1 What was mathematics in the ancient world? Greek and Chinese perspectives; 1.2 Mathematics and authority: a case study in New and Old World accounting; 1.3 Heavenly learning, statecraft, and scholarship: the Jesuits and their mathematics in China; 1.4 The internationalization of mathematics in a world of nations, 1800-1960; GEOGRAPHIES AND CULTURES: REGIONAL; 2.1 The two cultures of mathematics in ancient Greece; 2.2 Tracing mathematical networks in seventeenth-century England; 2.3 Mathematics and mathematics education in traditional Vietnam; 2.4 A Balkan trilogy: mathematics in the Balkans before the First World War; GEOGRAPHIES AND CULTURES: LOCAL; 3.1 Mathematics education in an Old Babylonian scribal school; 3.2 The archaeology of mathematics in an ancient Greek city; 3.3 Engineering the Neapolitan state; 3.4 Observatory mathematics in the nineteenth century; PEOPLE AND PRACTICES: LIVES; 4.1 Patronage of the mathematical sciences in Islamic societies; 4.2 John Aubrey and the 'Lives of our English mathematical writers'; 4.3 Introducing mathematics, building an empire: Russia under Peter I; 4.4 Human computers in eighteenth and nineteenth-century Britain; PEOPLE AND PRACTICES: PRACTICES; 5.1 Mixing, building, and feeding: mathematics and technology in ancient Egypt; 5.2 Siyaq: numerical notation in the Persianate world; 5.3 Learning arithmetic: textbooks and their users in England 1500-1900; 5.4 Algorithms and automation: mathematics and weaving; PEOPLE AND PRACTICES: PRESENTATION; 6.1 The cognitive and cultural foundations of numbers; 6.2 Sanskrit mathematical verse; 6.3 Antiquity, nobility, and utility: picturing the Early Modern mathematical sciences; 6.4 Writing the ultimate mathematical textbook: Nicolas Bourbaki's Elements de mathematique; INTERACTIONS AND INTERPRETATIONS: INTELLECTUAL; 7.1 People and numbers in early imperial China; 7.2 Mathematics in fourteenth-century theology; 7.3 Mathematics, music, and experiment in late seventeenth-century England; 7.4 Modernism in mathematics; INTERACTIONS AND INTERPRETATIONS: MATHEMATICAL; 8.1 The transmission of the Elements to the Latin West: three case studies; 8.2 'Gigantic implements of war': images of Newton as a mathematician; 8.3 From cascades to calculus: Rolle's Theorem; 8.4 Abstraction and application: new contexts, new interpretations in twentieth-century mathematics; INTERACTIONS AND INTERPRETATIONS: HISTORICAL; 9.1 Traditions and myths in the historiography of Egyptian mathematics; 9.2 Reading ancient Greek mathematics; 9.3 Number, shape, and the nature of space: thinking through Islamic art; 9.4 The historiography and history of mathematics in the Third Reich; ABOUT THE CONTRIBUTORS; INDEX
