514 alexei volkov
Chinese mathematical instruction of the fi rst millennium ce
It remains unclear when and where mathematical subjects were introduced
into the curriculum of Chinese state educational institutions. Sun claims
that the Mathematical College ( Suan xue ) was established during
the Northern Zhou dynasty (557–81) in the capital of this state, Chang’an
(modern Xi’an); 18 the students of the College were called suan fa sheng
, literally, ‘students of computational methods’. Lee reports that he was
unable to fi nd any evidence confi rming that the Mathematical College was
indeed established under the Northern Wei dynasty (386–534), as Sun sug-
gested.^19 However, Lee agrees that the subject had been taught offi cially in
the North for a long time even before the Northern Wei, in particular by
offi cial historians, who excelled in calendar calculation. Th e system of state
mathematics education established by the early seventh century in China
united under the rule of the Sui (581–618) and Tang (618–907) dynasties
comprised two elements: (1) the state mathematics examinations held on a
regular basis, and (2) the Mathematical College operating under the control
of the governmental agency called ‘Supervisorate of National Youth’ ( Guo zi
jian );^20 the latter was metaphorically referred to by some modern
authors as the ‘State University’. In Song dynasty China the Mathematical
College returned under the authority of the Supervisorate of National Youth
for a relatively short period of time, 1104–1131; 21 the College functioned
before and aft er this period of time under the auspices of other governmen-
tal agencies. 22 Th is explains why ten out of twelve mathematical treatises
used as textbooks during the Tang dynasty (618–907) were re-edited and
reprinted with educational purposes in 1084 and 1200–1213. Mathematical
courses also constituted a part of the curricula of the future astronomers and
calendar experts instructed at the courts of the non-Chinese Jin dynasty
(1115–1234), and, later, Yuan (1271–1368). 23
Th ere exist several descriptions of the instruction in the Mathematical
College ( Suan xue ) during the Tang dynasty; the descriptions specify
the number of students, a list of the textbooks, the periods of time allotted
to the study of each book, as well as other details. 24 Th e textbooks and the
18 Sun 2000 : 138.
19 Lee 2000 : 515, n. 230.
20 Rendered ‘Directorate of Education’ by Hucker 1985 : 299 and ‘Directorate of National Youth’
by Lee 2000.
21 Li 1977 : 271–9; Lee 2000 : 519–20.
22 Hucker 1985 : 461.
23 Lee 2000 : 520–3.
24 Th e descriptions are found in the Tang liu dian (Th e six codes of the Tang [dynasty]),
compiled in 738, see TLD 21: 10b and in the Xin Tang shu (Th e New History of the