A History of Mathematics From Mesopotamia to Modernity

ChineseMathematics 81

Dynasties

From earlier than 1000bceuntil the revolution of 1912 which both ended the monarchy and

brought a new approach to ‘Westernization’, China (although initially smaller) was at least theor-

etically ruled by a king, later styled ‘emperor’, whose role in ensuring the harmony of the world

and the social system was essential. As is usual, emperors succeeded one another in an orderly way

on the whole, as a ‘dynasty’ (compare the dynasties of ancient Egypt, or the Tudors and Stuarts

in England); but from time to time the succession was broken, one dynasty overthrew another or

competing dynasties divided China between them. A not entirely rigid boundary, symbolized by the

Great Wall, separated China and ‘civilization’ from the successive groups of threatening barbarians

(Huns, Tatars, Mongols) outside; sometimes a successful barbarian conquest was followed by the

adaptation of the conquerors to Chinese culture.

History, including the history of writing, calendar computations, highly skilled work in bronze,

and some written texts containing basic mathematics, starts in theZhang dynasty (‘Shang’), before

1000 bce. The dates are not certain, but the historical existence of the Zhang is not in doubt.

Zhou dynasty (‘Chou’),c.1000 to 221bce

The form of Chinese writing, including the writing of numbers, was fixed. There must have
been considerable development of mathematics during this period, particularly its later part, but
virtually no documents survive—this is traditionally blamed on the famous ‘Burning of the Books’
by the first emperor of Qin. From about 500bce, under a system which Needham describes as
similar to European feudalism, the country was divided into provinces (‘Warring States’) ruled by
great lords and the emperor’s authority was minimal. From this time date the main philosophical
currents, Confucianism and Daoism (‘Taoism’). These (together with Buddhism at a later date) had
varying influences on scientific outlook. In Needham’s view, Confucianism was socially orthodox
and uninterested in science, and Daoism was the reverse. Interestingly, the founding work of
Daoism, Lao-Zi’sDao De Jing(?third centurybce—estimates vary) provides one of the earliest
references to the practice of mathematics:
Good mathematicians do not use counting rods. (Lao Zi,The Dao De Jing, cited in Lam and Ang 1992, p. 22)
Lao Zi’s view of the most inventive tool of Chinese mathematics would turn out to be mistaken, as
we shall see; one could compare the dogmatism of his near-contemporary Plato. In any case, he
tells us that already in his time there were good mathematicians and more ordinary ones.

Qin dynasty (‘Ch’in’), 221–207bce

A strong unifying and repressive government was instituted for the first time. This, although

shortlived, has always been seen as a landmark in the central organization of the country. ‘Feud-

alism’ was ruthlessly eliminated. Nonetheless, society remained rigidly stratified into ‘estates’ with

merchants, according to Confucian principles, at the bottom in prestige if not in power.

Han dynasty, 202bce–220ce

The overthrow of the Qin was accompanied by a relative liberalization. The main features of
subsequent Chinese society took shape, in particular rule by a bureaucracy recruited from the