Demonstration in Chinese and Vietnamese mathematics 511
a ‘model examination paper’ found in a nineteenth-century Vietnamese
mathematical treatise that turned out to be instrumental in reconstructing
the role played by the commentaries on mathematical texts in the context
of institutionalised mathematical instruction in traditional China and
Vietnam.
Mathematics education in traditional China
In Western historiography the part played by Chinese mathematics educa-
tion arguably remains underestimated, probably due to a particular stand
adopted by the nineteenth-century European authors and perpetuated in
the publications of infl uential historians of the twentieth century. A highly
negative (as much as inaccurate) evaluation of mathematics education
in traditional China was off ered by the French sinologist Édouard Biot
(1803–50) who presented mathematics education in the Mathematical
College ( Suan xue ) as follows: 4 ‘... to call it a “mathematics school”
would mean to praise too high the studies in this elementary [educational]
institution’. 5 In this chapter I will not investigate reasons for this surpris-
ingly low evaluation of the mathematical education in China – to do so, one
probably would need to study the history of the image of China in Europe,
in particular in France, created by various individuals and institutions
beginning with the Jesuits. 6 Certainly, at the time when Biot was writing his
lines, not much was known about the history of Chinese mathematics; Biot
himself never systematically worked on Chinese mathematics and had only
a partial access to the original texts. 7 It is interesting to note that Biot (mis-
takenly) believed that the Jiu zhang suan shu (Computational
(^4) In this chapter I use both the characters suan and suan even though in modern editions
of historical materials the former is oft en changed to the latter, since their original meaning, as
the dictionary Shuo wen jie zi by Xu Shen (55?–149? ce ) specifi es, was not the
same: the character suan meant the counting rods, and suan , the operations performed
with the instrument. In this chapter I use suan if it occurred in a title of a book or in a name
of an institution at least once in an edition of the quoted source.
(^5) ‘... le nom d’école des mathématiques donnerait une trop haute idée des études de cet
établissement élémentaire.. .’ (Biot 1847 : 257, n. 1 ). In this chapter the translations from
French and Chinese are mine, unless stated otherwise.
(^6) Biot 1847 : v–ix.
(^7) Biot was familiar with three of the twelve books used for mathematics instruction in
seventh-century China, namely, with the mathematical treatises Qi gu suan jing
(Computational treatise on the continuation of [traditions of ] ancient [mathematicians]) and
Sun zi suan jing (Computational treatise of Master Sun), as well as the astronomical
treatise Zhou bi suan jing (Computational treatise on the gnomon of Zhou
[dynasty]). He was unable to identify correctly the titles of the other treatises (p. 261), and the