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A History of Chinese Mathematics

Jean-Claude Martzloff
Springer Verlag
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The Basic Library List Committee considers this book essential for undergraduate mathematics libraries.

[Reviewed by
Fernando Q. Gouvêa
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A new printing, in paperback, of Martzloff's A History of Chinese Mathematics offers an opportunity to once again call attention to this book. It was originally published in French in 1987, then translated, revised, and updated for the first English edition in 1997. This new printing is described as "corrected", but there is no new preface noting what exactly has been changed.

Already in 1989, a review in China Quarterly described it as "the most informative and the most informed' book on Chinese mathematics "in any language". After the English edition in 1997, it became the standard go-to book for an introduction to the huge subject of the history of Chinese mathematics. Nine years later, Martzloff's book remains the best source for those who want an intellectually serious and historically reliable overview of the history of mathematics in China.

Martzloff, together with Karine Chemla and Catherine Jami, is part of a French research group on the history of Chinese mathematics. Together, they have made substantial contributions to the field. In particular, they have brought to the field a more sophisticated and reflective attitude towards the writing of history. This can be seen clearly in the attention Martzloff gives to what he calls "the historiographical context", namely, past works on the history of Chinese mathematics and the (sometimes reasonable, sometimes plain wrong) attitudes they brought to the subject. Also of note are the discussions of modes of reasoning, transmission of knowledge (both within the Chinese mathematical community and between China and other societies), and the cultural context.

There is substantial research interest on the history of mathematics in China, and new publications constantly appear (for example, MAA Reviews recently discussed Fleeting Footsteps, by Lam Lay Yong and Ang Tian Se). Translations of the main texts also continue to appear. (This is cause for great joy among those of us who cannot read Chinese, of course!) Nevertheless, Martzloff remains the best introduction to the subject and his "Bibliographical Orientation" at the end should open up a huge world of texts and historical studies for anyone who wants to go further.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME. He is the author, with William Berlinghoff, of Math through the Ages: A Gentle History for Teachers and Others.

 Part I: The Historiographical Context, The Historical Context, The Notion of Chinese Mathematics, Applications of Chinese Mathematics, The Structure of Mathematical Works, Mathematical Terminology, Modes of Reasoning, Chinese Mathematicians, The Transmission of Knowledge, Influences and Transmission, Main Works and Main Autors (from Origins to 1600) Part II: Numbers and Numeration, Calculating Instruments, Techniques for Numerical Computation, Geometry, Indeterminate Problems, Approximation Formulae, Li Shanlan's Summation Formulae, Infinite Series, Magic Squares and Other Magic Figures Appendix I: Adaptations of European Mathematical Works Appendix II: Adaptations of European Mathematical Works (17th-19th Centuries).