One studies Chinese mathematics primarily as an approach to the remarkably integrated mind of a civilization in which intellectual concepts, social organization, and aesthetic expression were thoroughly interconnected. The extent to which thirteenth-century Chinese mathematics anticipated modern or Western results is of comparatively minor relevance. As Nathan Sivin states in his Foreword, “Ideas which... were perceived merely as the outdated and misguided backdrop of 'modern' anticipations must now be evaluated as seriously as the latter, for they played no less important a role in defining the ancient scientist's conception of the natural world—and thus the direction and style of his investigation.”
That said, a modern Westerner can hardly overlook the two most important ways in which Ch'in Chiu-shao advanced the mathematics of his time and place: he stated the solution for the “Chinese remainder problem” for indeterminate equations of the first degree, which is more general than Gauss's rule of 1801; and he developed an algorithm for solving equations of higher degree (including the tenth degree), which is identical with Horner's (1819). Ch'in's account of his method for solving indeterminate problems stretched the limits of the art, for it is the first generally stated formulation in Chinese mathematical literature.
One further comparative historical note may be pertinent. Libbrecht writes that “Chinese mathematics forms part of medieval mathematics, of the algorithmic phase we find in all civilized countries at that time. In reading Ch'in's text, I tried to place it within this algorithmic mathematical conception, which was the preamble to modern algebraic logistic.” Using this approach through internal analysis, the author compares the treatment of indeterminate equations during this period in India, Islam, and Europe and finds that Ch'in's techniques were unprecedented. This alone should demonstrate the importance of this study to universal mathematical history.
The essence of the book remains its insight into Chinese thought and life, as revealed by the general concepts and methods that fall into place alongside each other and by the practical mathematical problems posed by Ch'in that tie into the everyday realities of his time. It is through study of this last aspect that the book will be useful to China scholars generally.
This is the first volume in a new series, The MIT East Asian Science Series, of Which Nathan Sivin is general editor.