536 alexei volkov
in the structure’ of the procedure. Each of the terms employed here most
probably had a precise technical meaning diffi cult or even impossible to
restore, yet one can safely conjecture that in the latter case the examinee
was supposed to provide a sequence of correct operations leading to the
solution without their detailed justifi cation.
If the phrase about the ‘lack of the commentaries’ referred to the compi-
lations of the examinees, one can suggest that they were supposed to write
their explanations in the format similar to that of the offi cially established
commentaries and, most probably, used these commentaries as the best
available models. If the second interpretation of the phrase is correct, the
description of the examination procedure suggests an even larger role of
the commentaries found in the treatises used for instruction. Whichever
interpretation of the phrase ‘as for those without commentaries’ is adopted,
the role of the commentaries is apparent: they were not only providing
explanations or justifi cations of the algorithms found in the treatises, but
also became the models for the examination papers.Conclusions
Until recently the historians of Chinese mathematics tacitly assumed that the
commentaries on mathematical texts, especially those authored by Liu Hui
and Zhao Shuang, were ‘purely mathematical works’ written by professional
mathematicians for unidentifi ed target groups, presumably small commu-
nities of experts and disciples. Th is assumption is most probably correct;
my hypothesis is that the embedding of Liu Hui’s and Zhao Shuang’s com-
mentaries into the context of state education radically changed the way in
which they were interpreted and used. Aft er having been edited by the team
of Li Chunfeng, the commentaries on the treatises constituting the curricu-
lum set the guidelines for the instructors and students of the Mathematical
College. More specifi cally, in order to demonstrate their correct under-
standing of an algorithm found in a mathematical treatise, the students and
examinees had to perform the operations the algorithm prescribed with the
correctly inserted numerical values. Th is reconstruction is corroborated by
at least three documents: (1) the commentaries of Li Chunfeng’s team on
the Hai dao suan jing written in the seventh century ce with the purpose
of being used as didactical material in the Mathematical College and
conspicuously featuring computations performed according to the algo-
rithms devised by Liu Hui; (2) the aforementioned description of Tang
examinations, and (3) the Vietnamese model examination paper. Th e