Japanese Mathematics in the Edo Period 1600-1868 : A Study of the Works of Seki Takakazu? ?-1708 and Takebe Katahiro 1664-1739

More than ?fteen years have passed since this book was published in French. Ideally this work, which originated from a doctoral thesis defended in 1990 at the University of Paris Diderot, should have been partially rewritten for the English edition, thereby incorporating the latest research results in its argumentation. But this was not the choice taken, since it would have delayed making this work, which brings together useful information for all those who are interested in wasan and eager to delve more deeply into its tradition, available to the English reader. Indeed, the special feature of this study is to present a high-level mathematical production while at the same time placing it in its historical context. This context here is Tokugawa Japan and, more speci?cally, the milieu of the scholars of samurai (warrior) origin. While explaining the indispensable social, economical and poli- cal background, we have not neglected mathematical analysis, since wasan reached its most beautiful results with the two mathematicians Seki Takakazu and Takebe Katahiro. Their works abound in lessons, not only for all those who are interested in the history of algebra and of analysis, but also in epistemological questions.

Japanese mathematics, known also under the name of wasan, experienced a remarkable development between the seventeenth and nineteenth centuries. Wasan took its roots from the Chinese tradition of mathematics and shared its language and its categories of problems, but gave it a new impetus, transforming the Chinese algebraic method of the "heavenly element" into a powerful tool with a much wider scope. All domains of mathematical research were revisited in the light of this new algebra.

This book focuses on the first period of the development of wasan. It offers a survey of the earliest manuals for learning the use of the abacus published in the seventeenth century, notably the famous Jinkoki, which counted among the bestsellers of the Tokugawa period. The works of the two greatest mathematicians of this period, Seki Takakazu and Takebe Katahiro, and the way they transformed the face of mathematics, are examined in detail, with particular emphasis on the historical context, the relations between these two mathematicians and the political leaders of the epoch, and the role that mathematics played in this rapidly rising society.