Nine Chapters on Mathematical Modernity: Essays on the Global Historical Entanglements of the Science of Numbers in China (Transcultural Research – Heidelberg ... on Asia and Europe in a Global Context)

The book addresses for the first time the dynamics associated with the modernization of mathematics in China from the nineteenth to the mid-twentieth century from a transcultural global historical perspective. Rather than depict the transformations of mathematical knowledge in terms of a process of westernization, the book analyzes the complex interactions between different scientific communities and the ways in which the past, modernity, language, and mathematics were negotiated in a global context. In each chapter, Andrea Bréard provides vivid portraits of a series of go-betweens (such as translators, educators, or state statisticians) based on a vast array of translated primary sources hitherto unavailable to a non-Chinese readership. They not only illustrate how Chinese scholars mediated between new mathematical objects and discursive modes, but also how they instrumentalized their autochthonous scientific roots in specific political and intellectual contexts. While sometimes technical in style, the book addresses all readers who are interested in the global and cultural history of science and the complexities involved in the making of universal mathematics. “While the pursuit of modernity is in the title, entanglement is of as much interest. Using the famous ‘Nine Chapters’ as a framework, Bréard considers a wide range of that entanglement from divination to data management. Bréard’s analysis and thought-provoking insights show once again how much we can learn when two cultures intersect. A fascinating read!” (John Day, Boston University). Andrea Bréard is professor of the history of science at the Université Paris-Sud (France). Trained as a mathematician (TU München) and sinologist (LMU München & Fudan University), she obtained PhDs from the TU Berlin and the Université Paris 7. She has taught in mathematics, history of science, and sinology at the technical universities of Munich and Lille, the École Polytechnique, and the universities of Heidelberg and Frankfurt. She has also held fellowships from the Max-Planck-Institute for the History of Science (Berlin) and the International Research Consortium in the Humanities (Erlangen), and is an associated member of the Cluster of Excellence “Asia and Europe in a Global Context” (University of Heidelberg). Her main research fields are the history of mathematics, modern China, and combinatorial practices in games and divination in early to pre-modern China. Preface 7 Contents 9 List of Figures 11 List of Tables 15 1 Visions of Antiquity 16 Contents 16 1.1 About This Book 20 1.2 Saving the Nation Through Mathematics 22 1.3 Mathematics as History 25 References 31 2 The Ellipse Seen from Nineteenth-Century China 34 Contents 34 2.1 Xia Luanxiang and Conics 38 2.2 The Global Fate of Conics 46 2.3 Using the Past to Solve the New 53 References 60 3 Filling Euclid's Gaps 66 Contents 66 3.1 Beyond the First Six Books of Euclid's Elements 68 3.1.1 Proposition IX.20 71 3.2 Primality in Chinese Sources 77 3.3 Fermat's Little Theorem 84 References 89 4 Negotiating a Linguistic Space In-Between 92 Contents 92 4.1 The Translation Enterprise 93 4.2 A Proto-Grammatical Symbolism 96 4.3 Western and Chinese Algebra 99 4.3.1 A Pragmatic Choice? 112 References 118 5 Discourse Transformed: Changing Modes of Argumentation 121 Contents 121 5.1 The Concept(s) of ``Comparable Categories'' 126 5.2 Li Shanlan's ``Comparable Categories'' 132 5.2.1 A Deductive Structure 134 5.2.2 A Pillar Different from the Nine Chapters (and Euclid) 147 5.3 ``Comparable Categories'' in the West 148 References 154 6 Fate Calculation 算命: The Mathematics of Divination 157 Contents 157 6.1 Mathematical Problems Before the Qing 158 6.2 Hexagrams as Symbolic Algebra 164 6.3 Proving the Scientificity of Correlative Cosmology 169 References 179 7 Data Management and Knowledge Production in Late Qing Institutions 182 Contents 182 7.1 Reform as Context 183 7.1.1 Educational Reform 185 7.1.2 Constitutional Reform 188 7.2 Modernizing Statistical Practices 191 7.2.1 New Modes of Presentation 192 7.2.2 Publicizing `True' Numbers 194 7.2.3 Conceptualizations 198 7.3 What's New in a Number? 202 References 204 8 Applied Versus Pure Mathematics 207 Contents 207 8.1 Mathematics Before it Becomes a Discipline 209 8.2 Mathematical and Other Approaches to Statistics 214 8.3 Surviving the 1949 (Statistical) Revolution 228 References 233 9 Visions of Modernity 237 Contents 237 9.1 The Comeback of ``National Studies'' 238 9.2 The Case of Zhang Yitang 240 9.3 On ``Mathematical Modernity'' 244 References 247 A A Timeline of Mathematics from the Late Ming to the People's Republic of China 249 B Translation of Li Shanlan's Methods for Testing Primality(Kao shugen fa 考數根法), 1872 252 C On Conics (Some Technicalities) 267 Contents 267 C.1 Binomial Expansions 267 C.2 The Circle 269 C.3 The Ellipse 273 C.4 Constructing the Ellipse 276 References 280 Index 283 The book addresses for the first time the dynamics associated with the modernization of mathematics in China from the nineteenth to the mid-twentieth century from a transcultural global historical perspective. Rather than depict the transformations of mathematical knowledge in terms of a process of westernization, the book analyzes the complex interactions between different scientific communities and the ways in which the past, modernity, language, and mathematics were negotiated in a global context. In each chapter, Andrea Bréard provides vivid portraits of a series of go-betweens (such as translators, educators, or state statisticians) based on a vast array of translated primary sources hitherto unavailable to a non-Chinese readership. They not only illustrate how Chinese scholars mediated between new mathematical objects and discursive modes, but also how they instrumentalized their autochthonous scientific roots in specific political and intellectual contexts. While sometimes technical in style, the book addresses all readers who are interested in the global and cultural history of science and the complexities involved in the making of universal mathematics. â#x80;While the pursuit of modernity is in the title, entanglement is of as much interest. Using the famous â#x80;Nine Chaptersâ#x80;#x99; as a framework, Bréard considers a wide range of that entanglement from divination to data management. Bréardâ#x80;#x99;s analysis and thought-provoking insights show once again how much we can learn when two cultures intersect. A fascinating read!â#x80;#x9D; (John Day, Boston University).