Demonstration in Chinese and Vietnamese mathematics 513
deductions performed in an axiomatic system. 11 Th e statement of Biot as
well as his reasons to claim the inferiority of Chinese textbooks certainly
deserve a further investigation which, unfortunately, would lead us far
beyond the scope of the present chapter.
A detailed description of mathematics instruction (once again, in the
framework of a general outline of the state education in China of the Tang
dynasty) was off ered almost a century later by Robert des Rotours (1891–
1980) who, unlike Biot, avoided any critical remarks concerning the con-
tents and the level of the mathematical instruction in China. 12 Th e critique
of Chinese mathematics education was back in 1959 when Needham ener-
getically accused Ming Confucian scholarship of ‘confi n[ing] mathematics
to the back rooms of provincial yamens ’ and the ‘deadening infl uence’ of the
examination system. 13 Yet his accusations missed the target, since the Song
dynasty (960–1279) algebra he praised in the same paragraph had vanished
some sixty years prior to the beginning of the Ming dynasty (1368–1644)
and thus certainly well before the introduction of the examination system
featuring the formalized way of writing examination papers known as
‘eight-legged essays’ he referred to. 14 Chinese mathematics education was
once again judged unsatisfactory by U. Libbrecht and J.-C. Martzloff. 15 I n
turn, M.-K. Siu and A. Volkov briefl y addressed the critique of the latter
authors, yet a full analysis of the role of the state mathematics education
in traditional China remains a challenging task. 16 In this chapter I will
not discuss general issues such as whether the state examinations system
impeded or boosted the development of mathematics in China, 17 b u t s h a l l
focus instead on the changes in the interpretation and understanding of
mathematical treatises which might have happened as the result of their
embedding into the curriculum of the state educational institutions in the
seventh century ce.
12 Des Rotours 1932.
13 Needham 1959 : 153–4; esp. see fn. f on p. 153.
14 Lee 2000 : 143–4.
15 Libbrecht 1973 : 5; Martzloff 1997 : 79–82.
16 Siu and Volkov 1999.
17 See, among others, interesting observations of Wong 2004 on the role of the ‘Confucian’
context in modern mathematics education.
11 See, for instance, P.-N. Collin , Manuel d’arithmétique démontrée... , Paris , 1828 (7th edn),
which, as its very title suggests, was supposed to provide ‘demonstrations’. Th e format of this
textbook is similar to that of a large number of contemporaneous French textbooks, such as
the anonymous Abrégé d’arithmétique, à l’usage des écoles chrétiennes (Rouen, 1810), Abrégé
d’arithmétique à l’usage des écoles primaires (Paris, 1850), Abrégé d’arithmétique décimale...
(Perpignan, 1855, actual printing 1856), among many others.