534 alexei volkov
their commentaries on the oldest and presumably highly respected texts in
the collection of the textbooks were edited in the seventh century ce to be
used for instruction. Th e commentaries arguably compiled by Li Chunfeng
and his team for educational purposes thus may have corresponded most
closely to the style of work with ancient texts practised by the instructors of
the Mathematical College. 60 Yet the commentary on the Hai dao suan jing
by Li Chunfeng et al. did not discuss the rationale of the methods; instead,
the commentators explained the terms occurring in the conditions of the
problems and reproduced the procedures provided by Liu Hui with plugged
numerical parameters. Th at is, for Li Chunfeng the relevant interpretation of
a procedure consisted of a correct identifi cation of the parameters involved
and the operations with them. Th e parts of Li Chunfeng’s commentary
devoted to calculations look similar to the ‘computations’ ( cao ) added by
Liu Xiaosun to the Zhang Qiujian suan jing , and both texts resemble closely
the computations in the Vietnamese model examination paper.
Th ese observations suggest the following conjecture. Even though the
format of the Tang dynasty examination papers remains unknown, the
format adopted by the author of the model examination work in the
Vietnamese treatise fi ts surprisingly well into the short description of the
Tang dynasty mathematics examinations quoted above. Th e imaginary
Vietnamese examinee used as his model the solution of a generic problem
found elsewhere in the same treatise and, in particular, provided detailed
calculations close enough to those found in the model problem. Now, what
kind of explanations of the ‘meaning’ of the given problems were the actual
Chinese examinees of the Tang dynasty expected to provide? It is perhaps
not too daring to conjecture that their writings were supposed to resemble
those provided by the commentators of the treatises used as textbooks. In
other words, it appears plausible to suggest that the commentaries of Liu
Hui, Zhao Shuang, Li Chunfeng and others found in the treatises used for
instruction in the Mathematical College were used as the models for the
examination papers; not only did they provide the students with methods
used to investigate the validity of the computational procedures presented
in the treatises, but they also established the particular format to be imi-
tated by the candidates when writing their examination essays.
Th e phrase wu zhu zhe found in the description of the math-
ematics examinations in the ‘advanced programme’ and rendered above60 It appears quite probable that the commentarial activity of Zhen Luan who produced a set
of commented mathematical treatises in the second half of the sixth century ce was directly
related to a system of state mathematics education established, as some authors have suggested,
at the Court of the Northern Zhou dynasty (see above).