The Oxford Handbook of the History of Mathematics

by Robson, Eleanor; Stedall, Jacqueline

• ISBN13: 9780199603190
• ISBN10: 0199603197
• Edition: Reprint
• Format: Paperback
• Copyright: 2011-04-01
• Publisher: Oxford University Press

Summary

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 practice 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.

Author Biography

Eleanor Robson is Reader in Ancient Middle Eastern Science in the Department of History and Philosophy of Science at the University of Cambridge. Jacqueline Stedall is a Senior Research Fellow in History of Mathematics at the Mathematical Institute, Oxford, and Fellow of The Queen's College, Oxford.

Table of Contents

Introduction	p. 1
Geographies and Cultures	p. 5
Global
What was mathematics in the ancient world? Greek and Chinese Perspectives	p. 7
Mathematics and authority: a case study in Old and New World accounting	p. 27
Heavenly learning, statecraft, and scholarship: the Jesuits and their mathematics in China	p. 57
The internationalization of mathematics in a world of nations, 1800-1960	p. 85
Regional
The two cultures of mathematics in ancient Greece	p. 107
Tracing mathematical networks in seventeenth-century England	p. 133
Mathematics and mathematics education in traditional Vietnam	p. 153
A Balkan trilogy: mathematics in the Balkans before World War I	p. 177
Local
Mathematics education in an Old Babylonian scribal school	p. 199
The archaeology of mathematics in an ancient Greek city	p. 229
Engineering the Neapolitan state	p. 253
Observatory mathematics in the nineteenth century	p. 273
People and Practices	p. 299
Lives
Patronage of the mathematical sciences in Islamic societies	p. 301
John Aubrey and the 'Lives of our English mathematical writers'	p. 329
Introducing mathematics, building an empire: Russia under Peter I	p. 353
Human computers in eighteenth - and nineteenth-century Britain	p. 375
Practices
Mixing, building, and feeding: mathematics and technology in ancient Egypt	p. 407
Siyaq: numerical notation and numeracy in the Persianate world	p. 429
Learning arithmetic: textbooks and their users in England 1500-1900	p. 448
Algorithms and automation: the production of mathematics and textiles	p. 468
Presentation
The cognitive and cultural foundations of numbers	p. 495
Sanskrit mathematical verse	p. 519
Antiquity, nobility, and utility: picturing the Early Modern mathematical sciences	p. 537
Writing the ultimate mathematical textbook: Nicolas Bourbaki's Éléments de mathématique	p. 565
Interactions and Interpretations	p. 589
Intellectual
People and numbers in early imperial China	p. 591
Mathematics in fourteenth-century theology	p. 619
Mathematics, music, and experiment in late seventeenth-century England	p. 639
Modernism in mathematics	p. 663
Mathematical
The transmission of the Elements to the Latin West: three case studies	p. 687
'Gigantic implements of war': images of Newton as a mathematician	p. 707
From cascades to calculus: Rolle's theorem	p. 737
Abstraction and application: new contexts, new interpretations in twentieth-century mathematics	p. 755
Historical
Traditions and myths in the historiography of Egyptian mathematics	p. 781
Reading ancient Greek mathematics	p. 801
Number, shape, and the nature of space: thinking through Islamic art	p. 827
The historiography and history of mathematics in the Third Reich	p. 853
About the contributors	p. 881
Index	p. 891
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