The Oxford Handbook of the History of Mathematics (Oxford Handbooks)

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. 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. The Thirty-six Chapters Are Arranged Under Three Main Headings: 'geographies And Cultures', 'peoples And Practices', And 'interactions And Interpretations'. They Deal With The Mathematics Of 5000 Years. The Key Mathematical Cultures Of North America, Europe, The Middle East, India, And China Are All Represented Here As Well As Areas Such As Russia, The Balkans, Vietnam, And South America.--from Publisher Description. Introduction -- Geographies And Cultures -- 1. Global -- What Was Mathematics In The Ancient World? Greek And Chinese Perspectives / G E R Lloyd -- Mathematics And Authority: A Case Study In And Old And New World Accounting / Gary Urton -- Heavenly Learning, Statecraft, And Scholarship: The Jesuits And Their Mathematics In China / Catherine Jami -- The Internationalization Of Mathematics In A World Of Nations, 1800-1960 / Karen Hunger Parshall -- 2. Regional -- The Two Cultures Of Mathematics In Ancient Greece / Markus Asper -- Tracing Mathematical Networks In Seventeenth-century England / Jacqueline Stedall -- Mathematics And Mathematics Education In Traditional Vietnam / Alexei Volkov -- A Balkan Trilogy: Mathematics In The Balkans Before World War I / Snezana Lawrence -- 3. Local -- Mathematics Education In An Old Babylonian Scribal School / Eleanor Robson -- The Archaeology Of Mathematics In An Ancient Greek City / David Gilman Romano -- Engineering The Neapolitan State / Massimo Mazzotti -- Observatory Mathematics In The Nineteenth Century / David Aubin. People And Practices -- 4. Lives -- Patronage Of The Mathematical Sciences In Islamic Societies / Sonja Brentjes -- John Aubrey And The 'lives Of Our English Mathematical Writers' / Kate Bennett -- Introducing Mathematics, Building An Empire: Russia Under Peter I / Irina Gouzevitch And Dmitri Gouzevitch -- Human Computers In Eighteenth And Nineteenth-century Britain / Mary Croarken -- 5. Practices -- Mixing, Building, And Feeding: Mathematics And Technology In Ancient Egypt / Corinna Rossi -- Siyaq: Numerical Notation And Numeracy In The Persianate World / Brian Spooner And William Hanaway -- Learning Arithmetic: Textbooks And Their Users In England 1500-1900 / John Denniss -- Algorithms And Automation: The Production Of Mathematics And Textiles / Carrie Brezine -- 6. Presentation -- The Cognitive And Cultural Foundations Of Numbers / Stephen Chrisomalis -- Sanskrit Mathematical Verse / Kim Plofker -- Antiquity, Nobility, And Utility: Picturing The Early Modern Mathematical Sciences / Volker R. Remmert -- Writing The Ultimate Mathematical Textbook: Nicolas Bourbaki's Elements De Mathematique / Leo Corry. Interactions And Interpretations -- 7. Intellectual -- People And Numbers In Early Imperial China / Christopher Cullen -- Mathematics In Fourteenth-century Theology / Mark Thakkar -- Mathematics, Music, And Experiment In Late Seventeenth-century England / Benjamin Wardhaugh -- Modernism In Mathematics / Jeremy Gray -- 8. Mathematical -- The Transmission Of The Elements To The Latin West: Three Case Studies / Sabine Rommevaux -- 'gigantic Implements Of War': Images Of Newton As A Mathematician / Niccolò Guicciardini -- From Cascades To Calculus: Rolle's Theorem / June Barrow-green -- Abstraction And Application: New Contexts, New Interpretations In Twentieth-century Mathematics / Tinne Hoff Kjeldsen -- 9. Historical -- Traditions And Myths In The Historiography Of Egyptian Mathematics / Annette Imhausen -- Reading Ancient Greek Mathematics / Ken Saito -- Number, Shape, And The Nature Of Space: Thinking Through Islamic Art / Carol Bier -- The Historiography And History Of Mathematics In The Third Reich / Reinhard Siegmund-schultze. Edited By Eleanor Robson And Jacqueline Stedall. Includes Bibliographical References (p. 875-879) And Index. Table of Contents......Page 6 Introduction......Page 10 1. Global......Page 14 1.1 What was mathematics in the ancient world? Greek and Chinese perspectives......Page 16 1.2 Mathematics and authority: a case study in Old and New World accounting......Page 36 1.3 Heavenly learning, statecraft, and scholarship: the Jesuits and their mathematics in China......Page 66 1.4 The internationalization of mathematics in a world of nations, 1800–1960......Page 94 2. Regional......Page 114 2.1 The two cultures of mathematics in ancient Greece......Page 116 2.2 Tracing mathematical networks in seventeenth-century England......Page 142 2.3 Mathematics and mathematics education in traditional Vietnam......Page 162 2.4 A Balkan trilogy: mathematics in the Balkans before World War I......Page 186 3. Local......Page 206 3.1 Mathematics education in an Old Babylonian scribal school......Page 208 3.2 The archaeology of mathematics in an ancient Greek city......Page 238 3.3 Engineering the Neapolitan state......Page 262 3.4 Observatory mathematics in the nineteenth century......Page 282 4. Lives......Page 308 4.1 Patronage of the mathematical sciences in Islamic societies......Page 310 4.2 John Aubrey and the 'Lives of our English mathematical writers'......Page 338 4.3 Introducing mathematics, building an empire: Russia under Peter I......Page 362 4.4 Human computers in eighteenth- and nineteenth-century Britain......Page 384 5. Practices......Page 414 5.1 Mixing, building, and feeding: mathematics and technology in ancient Egypt......Page 416 5.2 Siyaq: numerical notation and numeracy in the Persianate world......Page 438 5.3 Learning arithmetic: textbooks and their users in England 1500–1900......Page 457 5.4 Algorithms and automation: the production of mathematics and textiles......Page 477 6. Presentation......Page 502 6.1 The cognitive and cultural foundations of numbers......Page 504 6.2 Sanskrit mathematical verse......Page 528 6.3 Antiquity, nobility, and utility: picturing the Early Modern mathematical sciences......Page 546 6.4 Writing the ultimate mathematical textbook: Nicolas Bourbaki's......Page 574 7. Intellectual......Page 598 7.1 People and numbers in early imperial China......Page 600 7.2 Mathematics in fourteenth-century theology......Page 628 7.3 Mathematics, music, and experiment in late seventeenth-century England......Page 648 7.4 Modernism in mathematics......Page 672 8. Mathematical......Page 694 8.1 The transmission of the Elements to the Latin West: three case studies......Page 696 8.2 'Gigantic implements of war': images of Newton as a mathematician......Page 716 8.3 From cascades to calculus: Rolle's theorem......Page 746 8.4 Abstraction and application: new contexts, new interpretations in twentieth-century mathematics......Page 764 9. Historical......Page 788 9.1 Traditions and myths in the historiography of Egyptian mathematics......Page 790 9.2 Reading ancient Greek mathematics......Page 810 9.3 Number, shape, and the nature of space: thinking through Islamic art......Page 836 9.4 The historiography and history of mathematics in the Third Reich......Page 862 About the contributors......Page 890 A......Page 900 B......Page 902 C......Page 904 D......Page 906 E......Page 907 F......Page 908 G......Page 909 H......Page 911 I......Page 912 K......Page 914 L......Page 915 M......Page 916 N......Page 918 O......Page 919 P......Page 920 R......Page 921 S......Page 923 T......Page 924 U......Page 925 W......Page 926 Z......Page 927 Table of Contents 6 Introduction 10 GEOGRAPHIES AND CULTURES 14 1. Global 14 1.1 What was mathematics in the ancient world? Greek and Chinese perspectives 16 1.2 Mathematics and authority: a case study in Old and New World accounting 36 1.3 Heavenly learning, statecraft, and scholarship: the Jesuits and their mathematics in China 66 1.4 The internationalization of mathematics in a world of nations, 1800–1960 94 2. Regional 114 2.1 The two cultures of mathematics in ancient Greece 116 2.2 Tracing mathematical networks in seventeenth-century England 142 2.3 Mathematics and mathematics education in traditional Vietnam 162 2.4 A Balkan trilogy: mathematics in the Balkans before World War I 186 3. Local 206 3.1 Mathematics education in an Old Babylonian scribal school 208 3.2 The archaeology of mathematics in an ancient Greek city 238 3.3 Engineering the Neapolitan state 262 3.4 Observatory mathematics in the nineteenth century 282 PEOPLE AND PRACTICES 308 4. Lives 308 4.1 Patronage of the mathematical sciences in Islamic societies 310 4.2 John Aubrey and the 'Lives of our English mathematical writers' 338 4.3 Introducing mathematics, building an empire: Russia under Peter I 362 4.4 Human computers in eighteenth- and nineteenth-century Britain 384 5. Practices 414 5.1 Mixing, building, and feeding: mathematics and technology in ancient Egypt 416 5.2 Siyaq: numerical notation and numeracy in the Persianate world 438 5.3 Learning arithmetic: textbooks and their users in England 1500–1900 457 5.4 Algorithms and automation: the production of mathematics and textiles 477 6. Presentation 502 6.1 The cognitive and cultural foundations of numbers 504 6.2 Sanskrit mathematical verse 528 6.3 Antiquity, nobility, and utility: picturing the Early Modern mathematical sciences 546 6.4 Writing the ultimate mathematical textbook: Nicolas Bourbaki's 574 INTERACTIONS AND INTERPRETATIONS 598 7. Intellectual 598 7.1 People and numbers in early imperial China 600 7.2 Mathematics in fourteenth-century theology 628 7.3 Mathematics, music, and experiment in late seventeenth-century England 648 7.4 Modernism in mathematics 672 8. Mathematical 694 8.1 The transmission of the Elements to the Latin West: three case studies 696 8.2 'Gigantic implements of war': images of Newton as a mathematician 716 8.3 From cascades to calculus: Rolle's theorem 746 8.4 Abstraction and application: new contexts, new interpretations in twentieth-century mathematics 764 9. Historical 788 9.1 Traditions and myths in the historiography of Egyptian mathematics 790 9.2 Reading ancient Greek mathematics 810 9.3 Number, shape, and the nature of space: thinking through Islamic art 836 9.4 The historiography and history of mathematics in the Third Reich 862 About the contributors 890 Index 900 A 900 B 902 C 904 D 906 E 907 F 908 G 909 H 911 I 912 J 914 K 914 L 915 M 916 N 918 O 919 P 920 Q 921 R 921 S 923 T 924 U 925 V 926 W 926 X 927 Y 927 Z 927 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.