The History of Mathematical Proof in Ancient Traditions

Demonstration in Chinese and Vietnamese mathematics 515

duration of their study as specifi ed in the Xin Tang shu (Th e New History of
the Tang [dynasty]) are listed in Table 15.1.
Th e order of the books in Table 15.1 is that adopted in the Xin Tang shu ;
it remains unclear why the list begins with the treatises Sun zi and Wu
cao , certainly less important than the treatises under numbers 3, 7 and 9,
as suggested by an inspection of their extant versions listed in Table 15.2

Table 15.1. Th e mathematical curriculum of the Tang State University

Number Title Duration of study Programme^ a^

1 Sun zi (Master Sun) One year for two
treatises together

Regular

2 Wu cao (Five departments) Regular
3 Jiu zhang (Nine categories) Th ree years for two
treatises together

Regular

4 Hai dao (Sea island) Regular
5 Zhang Qiujian ( [Master]
Zhang Qiujian)

One year Regular

6 Xiahou Yang ([Master]
Xiahou Yang)

One year Regular

7 Zhou bi (Th e gnomon of
the Zhou [dynasty])

One year for two

treatises together

Regular

8 Wu jing suan
(Computations in the fi ve
classical books)

Regular

9 Zhui shu (Mending
procedures) b

Four years Advanced

1 0 Qi gu (Continuation [of
traditions] of ancient
[mathematicians])

Th ree years Advanced

1 1 Ji yi (Records of [things]
left behind for posterity)

Not specifi ed Supplementary

1 2 San deng shu (Numbers
of three ranks)

Not specifi ed Supplementary

Notes:
a^ Th e terms ‘regular’ and ‘advanced’ are not found in the original descriptions; they
are added for the convenience of the reader. For the explanation of these terms, see
below.
b^ Th e meaning of the title remains unclear; see Yan 2000 : 125–32.

Tang [dynasty]), compiled in 1060, see XTS 44: 2a. Th e lists of the books and the duration of

their study specifi ed in these two sources are identical. For a translation of the description

found in the Xin Tang shu , see des Rotours 1932 : 139–42, 154–5; see also Siu 1995 : 226; Siu and

Volkov 1999.