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Comprising thirty-six self-contained, multifaceted chapters structured around methodological issues in the history of mathematics, this Handbook aims to be exemplary rather than exhaustive by taking a new look at what mathematics has been in history, and what it means to write history of mathematics. It provides a picture of the discipline that reflects the scholarship of recent decades, stating open problems and thus helping to set agendas forsubsequent research. Aimed at a broad academic audience including mathematicians, historians of science, and general historians, the relevance of each subject to general history is stressed, and specific links made tothe wider academic literature.

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• IntroductionEleanor Robson and Jacqueline Stedall
• 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 The cognitive and cultural foundations of numbers
• 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