Demonstration in Chinese and Vietnamese mathematics 523
needed for the solution of the problems. 41 In other words, the candidates
were asked to design algorithms that were not mere replicas of the algo-
rithms found in the textbooks (otherwise the examination would have been
reduced to a simple test of the students’ memory) but their generic versions
designed according to the modifi ed parameters. Th is hypothesis, however
appealing it might have seemed, could not be provided by Siu and Volkov
with any supporting evidence since the examination papers written by the
candidates during the mathematics examinations of the Tang and the Song
dynasties do not now exist. However, rather unexpectedly, a supporting
piece of evidence was found in a Vietnamese mathematical treatise.
Mathematics examinations in traditional Vietnam:
the case of a model examination paper
Th e available information concerning the traditional Vietnamese math-
ematics and the relevant references to the earlier works can be found else-
where;^42 it can be very briefl y summarized as follows. Th e number of extant
mathematical treatises amounts to twenty-two; the earliest extant treatise is
conventionally credited to an author of the fi ft eenth century while the other
treatises were compiled in the eighteenth to early twentieth centuries. Th eir
style and contents are very close to those of Chinese mathematical treatises
compiled prior to the introduction of Western mathematics into China. 43
Th e Vietnamese system of state education and civil examinations similar
to the Chinese one dates back to the eleventh century ce , yet Chinese educa-
tion and examinations were present in Vietnam well before that time, since
the country technically remained a province of China until the mid tenth
century. 44 Th ere is no information about institutions specifi cally focused on
mathematics education, yet historical records mention the examinations in
‘counting/computations’ (Viet. toán ) that took place in 1077, 1179, 1261,
1363, 1404, 1437, 1472, 1505, 1698, 1711, 1725, 1732, 1747, 1762, 1767, and
41 Th is statement was made in Siu and Volkov 1999 and amply illustrated in Siu 1999 and Siu
2004 : 174–7.
42 Volkov 2002 ; 2008 ; 2009.
43 Th e reader can fi nd more details on the extant treatises in Volkov 2009 : 156–9; the
descriptions in Volkov 2002 and Volkov 2008 do not take into account the most recent
fi ndings.
44 Th e reader can fi nd descriptions of the traditional Vietnamese education in Richomme 1905 :
9–28; Tran 1942 ; Vu 1959 : 28–57; Nguyen 1961 : 10–40; Woodside 1988 : 169–233. Th e short
description of Ennis 1936 : 162–4 draws upon the early yet still useful works of Luro ( 1878 ) and
Schreiner ( 1900 ).