Nine Chapters On Mathematical Modernity

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).

A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as the advent of the computer, chaos theory, topology, mathematical physics, and the solution of Fermat's Last Theorem. Containing more than 100 illustrations and figures, this text, aimed at advanced undergraduates and postgraduates, addresses the methods and challenges associated with studying the history of mathematics. The reader is introduced to the leading figures in the history of mathematics (including Archimedes, Ptolemy, Qin Jiushao, al-Kashi, al-Khwarizmi, Galileo, Newton, Leibniz, Helmholtz, Hilbert, Alan Turing, and Andrew Wiles) and their fields. An extensive bibliography with cross-references to key texts will provide invaluable resource to students and exercises (with solutions) will stretch the more advanced reader.

The figure of Dai Zhen (1724–1777) looms large in modern Chinese intellectual history. Dai was a mathematical astronomer and influential polymath who, along with like-minded scholars, sought to balance understandings of science, technology, and history within the framework of classical Chinese writings. Exploring ideas in fields as broad-ranging as astronomy, geography, governance, phonology, and etymology, Dai grappled with Western ideas and philosophies, including Jesuit conceptions of cosmology, which were so important to the Qing dynasty (1644–1911) court’s need for calendrical precision. Minghui Hu tells the story of China’s transition into modernity from the perspective of 18th-century Chinese scholars dedicated to examining the present and past with the tools of evidential analysis. Using Dai as the centering point, Hu shows how the tongru (“broadly learned scholars”) of this era navigated Confucian, Jesuit, and other worldviews during a dynamic period, connecting ancient theories to new knowledge in the process. Scholars and students of early modern Chinese history, and those examining science, religious, and intellectual history more broadly, will find China’s Transition to Modernity inspiring and helpful for their research and teaching.

The international New Math developments between about 1950 through 1980, are regarded by many mathematics educators and education historians as the most historically important development in curricula of the twentieth century. It attracted the attention of local and international politicians, of teachers, and of parents, and influenced the teaching and learning of mathematics at all levels—kindergarten to college graduate—in many nations. After garnering much initial support it began to attract criticism. But, as Bill Jacob and the late Jerry Becker show in Chapter 17, some of the effects became entrenched. This volume, edited by Professor Dirk De Bock, of Belgium, provides an outstanding overview of the New Math/modern mathematics movement. Chapter authors provide exceptionally high-quality analyses of the rise of the movement, and of subsequent developments, within a range of nations. The first few chapters show how the initial leadership came from mathematicians in European nations and in the United States of America. The background leaders in Europe were Caleb Gattegno and members of a mysterious group of mainly French pure mathematicians, who since the 1930s had published under the name of (a fictitious) “Nicolas Bourbaki.” In the United States, there emerged, during the 1950s various attempts to improve U.S. mathematics curricula and teaching, especially in secondary schools and colleges. This side of the story climaxed in 1957 when the Soviet Union succeeded in launching “Sputnik,” the first satellite. Undoubtedly, this is a landmark publication in education. The foreword was written by Professor Bob Moon, one of a few other scholars to have written on the New Math from an international perspective. The final “epilogue” chapter, by Professor Geert Vanpaemel, a historian, draws together the overall thrust of the volume, and makes links with the general history of curriculum development, especially in science education, including recent globalization trends.

This book is a biography of a remarkable Scottish missionary worker, Alexander Wylie, a classical nineteenth century artisan and autodidact with a gift and passion for languages and mathematics. He made significant contributions to knowledge transfer, both to and from China: in missionary work as a printer, playing an important role in the production and distribution of a new Chinese translation of the Bible; as a teacher, translating into Chinese key western texts in science and mathematics including Newton and Euclid and publishing the first Chinese textbooks on modern symbolic algebra, calculus and astronomy; and as a writer in English and an internationally recognised major sinologist, bringing to the West much knowledge of China and contributing extensively to the development of British sinology. The book concludes with an overall evaluation of Wylie’s contribution to knowledge transfer to and from China, noting the imbalance between the significant corpus of scholarly work specifically on Wylie by Chinese scholars in Chinese and the lack of academic studies by western scholars in English.

Now available in a one-volume paperback, this book traces the development of the most important mathematical concepts, giving special attention to the lives and thoughts of such mathematical innovators as Pythagoras, Newton, Poincare, and Godel. Beginning with a Sumerian short story--ultimately linked to modern digital computers--the author clearly introduces concepts of binary operations; point-set topology; the nature of post-relativity geometries; optimization and decision processes; ergodic theorems; epsilon-delta arithmetization; integral equations; the beautiful "ideals" of Dedekind and Emmy Noether; and the importance of "purifying" mathematics. Organizing her material in a conceptual rather than a chronological manner, she integrates the traditional with the modern, enlivening her discussions with historical and biographical detail.

Through ten case studies by international specialists, this book investigates the circulation and production of scientific knowledge between 1750 and 1945 in the fields of agriculture, astronomy, botany, cartography, medicine, statistics, and zoology. In this period, most of the world was under some form of imperial control, while science emerged as a discrete field of activity. What was the relationship between empire and science? Was science just an instrument for imperial domination? While such guiding questions place the book in the tradition of science and empire studies, it offers a fresh perspective in dialogue with global history and circulatory approaches. The book demonstrates, not by theoretical discourse but through detailed historical case studies, that the adoption of a global scale of analysis or an emphasis on circulatory processes does not entail analytical vagueness, diffusionism in disguise, or complacency with imperialism. The chapters show scientific knowledge emerging from the actions of little-known individuals moving across several Empires—European, Asian, and South American alike—in unanticipated places and institutions, and through complex processes of exchange, competition, collaboration, and circulation of knowledge. The book will interest scholars and undergraduate and graduate students concerned with the connections between the history of science, imperial history, and global history.

The focus of this volume is the history of imperial science between 1600 and 1960, although some essays reach back prior to 1600 and the section about decolonization includes post-1960 material. Each contributed chapter, written by an expert in the field, provides an analytical review essay of the field, while also providing an overview of the topic. There is now a rich literature developed by historians of science as well as scholars of empire demonstrating the numerous ways science and empire grew together, especially between 1600 and 1960.