A History of Mathematics From Mesopotamia to Modernity

82 A History ofMathematics

‘scholar-gentry’ by examinations. According to Liu Hui (see later), mathematics was one of the six

subjects required (the ‘six gentlemanly arts’), but it did not long remain so.

The Chinese state now occupied its classical area—that is, as far as Guangzhou (Canton) in the

south,^5 and the Great Wall was completed; as Needham suggests,

to check the drift of Chinese groups towards coalescence with nomadic life, or the formation of mixed economies,

at least as much as to keep the nomads out. (Needham 1954, p. 100)

The Han is the first major period for the history of mathematics, since the first works which
were subsequently enshrined as classics were composed during the period. These include most
importantly theNine Chapters on the Mathematical Art, of which more will follow later in
greater detail.
The 400 years which followed the Han dynasty were a time of division, conflict, and occasional
unification. However, contacts with the outside world, in particular India, increased through the
spread of Buddhism which was introduced in the first centuryce. The remaining mathematical
classics date from this period, including Liu Hui’s commentary (third centuryce)ontheNine
Chapters, which transforms it from a collection of questions and answers (as in Section 1) to a
mathematical text. It appears that the occupation of mathematician was respected and relatively
flourishing, even if the work produced was of varying quality.

Sui dynasty, 581–618ce

The Sui dynasty, like the Qin, was a successful unification which ran out of steam after organizing
important canalization projects which helped to unify north and south. It marked a second point at
which mathematics gained a place on the ‘national curriculum’, and the canon of 10 classical texts
which students were required to study was fixed. In fact, a central mathematical school was set up,
but it had few students; and as the official examinations remained exclusively literary/humanistic,
it seems not to have lasted more than a few years.

4.The Nine Chapters

Though it is called theNine Arithmetical Arts, they can reach both the infinitesimal and the infinite. (Liu Hui’s preface

to theNine Chapters, in Shen et al. 1999 p. 53)

Whereas the Greeks of this period were composing logically ordered and systematically expository treatises, the Chinese

were repeating the old custom of the Babylonians and Egyptians of compiling sets of specific problems. (Boyer and

Merzbach 1989, p. 222)

Any consideration of Chinese mathematics has to start with theNine ChaptersorJiuzhang suanshu,

which dominated all subsequent work in much the same way that Euclid’sElementsdominated

Western (including Islamic) mathematics for the next 1500 years. It is not the earliest classic

known—that place is held by the decidedly less mainstreamZhoubi suanjing^6 (Cullen 1996). The

date and ‘authorship’ of this text is as uncertain as that of theNine Chapters; Cullen considers it

to have been a compilation from the early Han dynasty (second to first centurybce). It is a work

5. Sometimes a much wider area was covered, including Korea and northern Vietnam.


6. This title is not explicitly translated by Cullen; Needham translates it as ‘The Arithmetical Classic of the Gnomon and the
   Circular Paths of Heaven’.