A History of Chinese Mathematics

Since the end of the 19th century, a number of specialised journals, albeit with a large audience, have regularly included articles on the history of Chinese mathematics, while a number of books on the history of mathematics include a chapter on the subject. Thus, the progressive increase in our knowledge of the content of Chinese mathematics has been accompanied by the realisation that, as far as results are concerned, there are numerous similarities between Chinese mathematics and other ancient and medieval mathematics. For example, Pythagoras' theorem, the double-false-position rules, Hero's formulae, and Ruffini-Harner's method are found almost everywhere. As far as the reasoning used to obtain these results is concerned, the fact that it is difficult to find rational justifications in the original texts has led to the reconstitution of proofs using appropriate tools of present-day elementary algebra. Consequently, the conclusion that Chinese mathematics is of a fundamentally algebraic nature has been ventured. However, in recent decades, new studies, particularly in China and Japan, have adopted a different approach to the original texts, in that they have considered the Chinese modes of reasoning, as these can be deduced from the rare texts which contain justifications. By studying the results and the methods explicitly mentioned in these texts hand in hand, this Chinese and Japanese research has attempted to reconstruct the conceptions of ancient authors within a given culture and period, without necessarily involving the convenient, but often distorting, social and conceptual framework of present-day mathematics.