54 karine chemla
main reason for including them in the book is that they reveal historically
interesting modes of continuity with what was analysed above.
Alexei Volkov devotes his chapter to an apparently discrete topic:
mathematical examinations in China and the sphere of Chinese infl uence
in East Asia. However, the link to our questions appears immediately.
Th e issue at hand for him is that of the relation between the practices of
examination in mathematics and mathematical proof as evidenced by the
commentaries on Chinese classics. Th is question leads him to focus on
the extant evidence regarding the teaching of mathematics in this part of
the world.
Among all the channels through which mathematical knowledge was
taught throughout Chinese history, the channel of state institutions is the
least poorly documented. Relying on the extant Chinese administrative
sources, Volkov describes the textbooks used for mathematics in the state
educational system from the seventh century onwards and the way in
which they were used. It is important for us that among these textbooks,
one fi nds precisely Th e Nine Chapters on Mathematical Procedures along
with the commentaries by Liu Hui and Li Chunfeng introduced above. 61
Moreover, Volkov discusses in great detail how the terse description of the
kind of examinations the students had to take by the administrative sources
can be interpreted concretely.
Th e interpretation of the extant administrative sources would have
remained a matter of speculation, had not Volkov discovered a piece
of evidence in nineteenth-century Vietnamese sources. Some elements
of context are needed to understand this point better. As in Japan and
Korea, Vietnamese state institutions had a history closely linked to that of
their parallel institutions in China. In particular, from the Tang dynasty
onwards, Chinese state institutions for teaching were imitated in East
Asia and the textbooks used by these institutions were transmitted in this
process. Moreover, state examinations in mathematics were held in all
other contexts, including in Vietnam, as Volkov shows. Th is explains how
Vietnamese sources clarify practices carried out in China: the margins
oft en keep alive traditions that are modifi ed in the centre.
In Vietnam, an additional factor played a decisive role: at the beginning
of the nineteenth century, Western books had not yet become infl uential
there. Th e extant mathematical writings composed in Vietnam until that
time consequently appear to belong mainly to a tradition on which Chinese
61 Please note that Volkov opts for another interpretation of the title of the Chinese book,
translating it in a diff erent way. Appendix 2 in his chapter presents various transcriptions and
translations for the title of Chinese mathematical texts.