History of mathematics in China: A factor in world history and a source for new questions (Q1126881)

This article, whose bibliography (2 pages) contains almost exlusively previous articles by the sole author during the last 11 years, and no mention of the numerous Chinese books on the subject released during this period, deals with the Jiuzhang suanshu (JZSS), the famous Nine Chapters of the Han dynasty and its posterity, Chinese and non-Chinese (the title of the article is not explicit). First, the author gives succinct but interesting precisions on the socio-economic context of the JZSS. Second, she proceeds at length to explain Chinese algorithms and their proofs in a non-historical and mainly mathematical and formal way, contrasting with the beginning of the article. On the whole, there is a tendency to present and explain Chinese results in an unhistorical, formal and above all overgeneralized way, for example when the Chinese ``Gaussian elimination method'' for system of linear equations is said to cover ``all possible cases'' of such equations. All this is strongly reminiscent of the content of hundredth of Chinese articles and even books on the JZSS, published unceasingly during more than 20 years, from 1980. Third, in its own idiosyncratic way, the author repeats well-known conclusions, or rather theories, more or less similar to those propounded by \textit{Joseph Needham} at the end of the volume 3 of his \textit{Science and Civilisation in China} (Cambridge, 1959; Zbl 0099.24101): the famous historian of Chinese science and technology tends to view Chinese mathematics not as an isolated body of knowledge but as a mathematical corpus situated at the origin of other medieval mathematics and inserted in an active way in the wider current of world mathematics. This is approximately true in a general and imprecise way but problems arise when questions of mutual influence are precisely discussed: the same theme -- root extraction, Horner's methods, decimals, etc. -- recur again and again everywhere, as it is well known but nobody has still explained in a satisfactory way how these methods really developed. And here, once more, all is explained mainly by means of formal analogies between algorithms and problems found in China, Islamic countries and India. We also note in passing that the author presents here a one-sided -- and false by omission -- view of the problem of the Jesuit reaction at the occasion of the first encounter between European and Chinese mathematics at the beginning of the seventeenth century: after having expounded, in the first part of her paper, the superiority of Chinese mathematics (especially in the case of the rules of false double position), the author notes, with indignation, that the Jesuits had ``concluded that Western mathematics was superior [to Chinese mathematics]!'' To be sure, the Jesuit reaction was such but it should also be noted that the Chinese reaction -- shared by the most influential of them at the time -- was essentially the same as that of the Jesuits (but, of course for different reasons): from a Chinese point of view, Chinese logistic was inferior to Western mathematical techniques such as written computation (opposed to abacus arithmetic) trigonometry, logarithms and the like. And that is precisely why Western mathematics and astronomy (or rather Western algorithmic methods) were extensively adopted by the Chinese elite from the seventeenth century onwards. Finally, the author devotes one page and a half to ``new questions'', questions of a general kind, mostly about algorithms and ``mathematical objects'', offered to the sagacity of the reader.