Reviving Ancient Chinese Mathematics


Book Description

Twentieth-century China has been caught between a desire to increase its wealth and power in line with other advanced nations, which, by implication, means copying their institutions, practices and values, whilst simultaneously seeking to preserve China’s independence and historically formed identity. Over time, Chinese philosophers, writers, artists and politicians have all sought to reconcile these goals and this book shows how this search for a Chinese way penetrated even the most central, least contested area of modernity: science. Reviving Ancient Chinese Mathematics is a study of the life of one of modern China’s most admired scientific figures, the mathematician Wu Wen-Tsun. Negotiating the conflict between progress and tradition, he found a path that not only ensured his political and personal survival, but which also brought him renown as a mathematician of international status who claimed that he stood outside the dominant western tradition of mathematics. Wu Wen-Tsun’s story highlights crucial developments and contradictions in twentieth -century China, the significance of which extends far beyond the field of mathematics. On one hand lies the appeal of radical scientific modernity, "mechanisation" in all its forms, and competitiveness within the international scientific community. On the other is an anxiety to preserve national traditions and make them part of the modernisation project. Moreover, Wu’s intellectual development also reflects the complex relationship between science and Maoist ideology, because his turn to history was powered by his internalisation of certain aspects of Maoist ideology, including its utilitarian philosophy of science. This book traces how Wu managed to combine political success and international scientific eminence, a story that has wider implications for a new century of increasing Chinese activity in the sciences. As such, it will be of great interest to students and scholars of Chinese history, the history of science and the history and philosophy of mathematics.




Reviving Ancient Chinese Mathematics


Book Description

Twentieth-century China has been caught between a desire to increase its wealth and power in line with other advanced nations, which, by implication, means copying their institutions, practices and values, whilst simultaneously seeking to preserve China's independence and historically formed identity. Over time, Chinese philosophers, writers, artists and politicians have all sought to reconcile these goals and this book shows how this search for a Chinese way penetrated even the most central, least contested area of modernity: science. Reviving Ancient Chinese Mathematics is a study of the life of one of modern China's most admired scientific figures, the mathematician Wu Wen-Tsun. Negotiating the conflict between progress and tradition, he found a path that not only ensured his political and personal survival, but which also brought him renown as a mathematician of international status who claimed that he stood outside the dominant western tradition of mathematics. Wu Wen-Tsun's story highlights crucial developments and contradictions in twentieth -century China, the significance of which extends far beyond the field of mathematics. On one hand lies the appeal of radical scientific modernity, "mechanisation" in all its forms, and competitiveness within the international scientific community. On the other is an anxiety to preserve national traditions and make them part of the modernisation project. Moreover, Wu's intellectual development also reflects the complex relationship between science and Maoist ideology, because his turn to history was powered by his internalisation of certain aspects of Maoist ideology, including its utilitarian philosophy of science. This book traces how Wu managed to combine political success and international scientific eminence, a story that has wider implications for a new century of increasing Chinese activity in the sciences. As such, it will be of great interest to students and scholars of Chinese history, the history of science and the history and philosophy of mathematics.




A History of Chinese Mathematics


Book Description

This book is made up of two parts, the first devoted to general, historical and cultural background, and the second to the development of each subdiscipline that together comprise Chinese mathematics. The book is uniquely accessible, both as a topical reference work, and also as an overview that can be read and reread at many levels of sophistication by both sinologists and mathematicians alike.




Fleeting Footsteps


Book Description

The Hindu-Arabic numeral system (1, 2, 3, ...) is one of mankind's greatest achievements and one of its most commonly used inventions. How did it originate? Those who have written about the numeral system have hypothesized that it originated in India; however, there is little evidence to support this claim. This book provides considerable evidence to show that the Hindu-Arabic numeral system, despite its commonly accepted name, has its origins in the Chinese rod numeral system. This system was widely used in China from antiquity till the 16th century. It was used by officials, astronomers, traders and others to perform addition, subtraction, multiplication, division and other arithmetic operations, and also used by mathematicians to develop arithmetic and algebra. Based on this system, numerous mathematical treatises were written. Sun Zi suanjing (The Mathematical Classic of Sun Zi), written around 400 A.D., is the earliest existing work to have a description of the rod numerals and their operations. With this treatise as a central reference, the first part of the book discusses the development of arithmetic and the beginnings of algebra in ancient China and, on the basis of this knowledge, advances the thesis that the Hindu-Arabic numeral system has its origins in the rod numeral system. Part Two gives a complete translation of Sun Zi suanjing. In this revised edition, Lam Lay Yong has included an edited text of her plenary lecture entitled "Ancient Chinese Mathematics and Its Influence on World Mathematics", which was delivered at the International Congress of Mathematicians, Beijing 2002, after she received the prestigious Kenneth O. May Medal conferred by the International Commission on the History of Mathematics. This should serve as a useful and easy-to-comprehend introduction to the book.




The Sea Island Mathematical Manual: Surveying and Mathematics in Ancient China


Book Description

An annotated translation and analysis of the Haidao Suanjing, a Chinese mathematical classic composed by Liu Hui in A.D. 263. All ancient societies practiced the art of land surveying. In fact, tradition tells us that geometry--land measure--had its origins in such surveying. However, an examination of early Western literature reveals few records concerning the practical uses of geometry and mathematics in the tasks of surveying. Recent research into the content and origins of early Chinese mathematics is beginning to reveal the existence of strong traditions and interest in the methodologies and applications of land survey. It is from these Chinese sources that a clearer picture of how people adapted mathematics and geometry to the needs of surveying emerges. The Haidao Suanjing, or Sea Island Mathematical Manual, is one of the "Ten Classics" of traditional Chinese mathematics, and its contents demonstrate the high standards of theoretical and mathematical sophistication present in early Chinese surveying theory. The Haidao established the mathematical procedures for much of East Asian surveying activity for the next one thousand years. The contents of the Haidao also testify to the ability of the Chinese to systematize mathematics and hint at the use of proof in Chinese mathematics, a concept usually associated with Greek mathematical thought. Frank Swetz provides an analysis of the Haidao's surveying problems. In particular, he details surveying techniques and undertakes a mathematical exposition of the Chinese chong cha solution procedures. The Haidao is a testimony to the ingenuity and skill of China's early surveyors and its author, Liu Hui. This study complements and extends the findings of Swetz's previous book, Was Pythagoras Chinese? An Examination of Right Triangle Theory in Ancient China




Anachronisms in the History of Mathematics


Book Description

The controversial matters surrounding the notion of anachronism are difficult ones: they have been broached by literary and art critics, by philosophers, as well as by historians of science. This book adopts a bottom-up approach to the many problems concerning anachronism in the history of mathematics. Some of the leading scholars in the field of history of mathematics reflect on the applicability of present-day mathematical language, concepts, standards, disciplinary boundaries, indeed notions of mathematics itself, to well-chosen historical case studies belonging to the mathematics of the past, in European and non-European cultures. A detailed introduction describes the key themes and binds the various chapters together. The interdisciplinary and transcultural approach adopted allows this volume to cover topics important for history of mathematics, history of the physical sciences, history of science, philosophy of mathematics, history of philosophy, methodology of history, non-European science, and the transmission of mathematical knowledge across cultures.




Was Pythagoras Chinese?


Book Description




Chinese Mathematics


Book Description

This volume presents a record of mathematical developments in China over a period of more than 2000 years. It goes into greater detail than ever previously available in English. Because the emphasis in Chinese mathematics is on algorithms rather than proofs, readers will find results such as Bezout's theorem and Horner's method appearing in a very different context from the familiar tradition of Euclidean deductive geometry. The Chinese always preferred algebraic methods, and by the 13th century A.D. they were the best algebraists in the world. The original Chinese point of view is retained by the translators. They have supplemented the text with short explanatory comments and references to all relevant reference sources available in the West. An extensive bibliography is included, creating a work which will appeal to general readers interested in Chinese history as well as historians of mathematics.




Empty And The Full, The: Li Ye And The Way Of Mathematics - Geometrical Procedures By Section Of Areas


Book Description

During Song (960 to 1279) and Yuan (1279 to 1368) dynasties, China experienced a peak in high-level algebraic investigation through the works of famous mathematicians such as Qin Jiushao, Zhu Shijie, Yang Hui and Li Ye. Among these is Li Ye's short treatise on a curious ancient geometrical procedure: The Development of Pieces of Areas According to the Collection Augmenting the Ancient Knowledge (Yigu yanduan). The aim of this monography is to contradict traditional scholarship which has long discredited the importance of Li Ye's treatise, considering it a mere popular handbook. The author aims to show that Li Ye's work actually epitomizes a completely new aspect of ancient Chinese mathematics: a crossroad between algebra, geometry, and combinatorics containing elements reminiscent of the Book of Changes (Yi Jing). As well as Li Ye used field measurement as pretext for investigations on quadratic equations and Changes, the present study uses Li Ye's small treatise as pretext for philosophical investigations on link between mathematics and their history. The real topic of the study is the exploration of another expression of proof and generality in Chinese mathematics. This book not only completes the edition of Li Ye's works and presents new features of Chinese mathematics, but also fills a gap in the translation of Chinese mathematics treatises.It is the first book entirely dedicated to the diagrammatic practice of algebra in the history of Chinese mathematics. This practice is more important than expected. While being a monograph, the book is short and detailed enough to be used by students in class. It can also be used as an entry door to the research field of history of Chinese mathematics.




Chinese Mathematics History


Book Description

The book provides highlights on the key concepts and trends of evolution in Chinese Mathematics History, as one of the series of books of “China Classified Histories”.