4. Chinese mathematics
1. Introduction
Fu Xi created the eight trigrams in remote antiquity to communicate the virtues of the gods and parallel the trend of
events in earthly matters, [and he] invented the nine-nines algorithm to coordinate the variations in the hexagrams.
(Liu Hui, cited Shen et al. 1999, p. 52)
Mathematics is an important subject in the six arts. Through the ages all scholars who have participated in discussions
on astronomy and calendars have to master it. However, you may consider it as a minor occupation, not as a major
one. (Yen Chih-tui (sixth centuryce), cited Libbrecht 1973, p. 4)The usual warnings to avoid thinking of ancient mathematics in modern terms seem quite
unnecessary in the Chinese case. Certainly the Chinese, like the Greeks, recognized a particular
study called mathematics (suanshu). As a component of education, they seem often to have given
it a rather subordinate role, as the second quote above shows. And yet, it was (as usual) essen-
tial for the standard preoccupations of irrigation, public works, and taxation. More particular to
the Chinese, if still widespread, was the idea that the harmony of the universe is mathematically
ordered, as the first quote expresses; guidance for future conduct can be gained from the 64 signs
of theYijing, or ‘Book of Changes’.^1 Between abstract philosophy and low-level ditch-digging
stood the essential practice of the calendar-makers and astrologers, who ensured—with variable
success—that a complicated year ran smoothly enough and unlucky events in the heavens were
accounted for. The earliest textbook, theZhoubi suanjing(Cullen 1996), is an attempt to deal with
these questions, and the problem of harmonizing the competing periods of days, months, and
years is at least partly reponsible for the sophisticated number theory required for the ‘Chinese
remainder theorem’.
The relation of the various parts was a complex one, and yet Chinese mathematics is still often
characterized as simply ‘practical’. It is true that the bare classical texts often confront the reader as
if that were their aim; but we have already seen in the Babylonian case that more may lie beneath
the surface. Here, as an illustration, are two problems from the founding text, theNine Chapters.
Now given a person carrying cereal through three passes. At the outer pass, one-third is takenaway astax. At the
middle pass, one-fifth is takenaway. At theinner pass, one-seventh is takenaway.Assume the remaining cereal is
5 dou. Tell: how much cereal is carried originally?
Answer: 10dou 938 sheng. (Shen et al. 1999, problem 6.27, p. 345)
Now chickens are purchased jointly; everyone contributes 9, the excess is 11; everyone contributes 6, the deficit is 16.
Tell: the number of people, the chicken price, what is each?
Answer: 9 people, chicken price 70. (Shen et al. 1999, problem 7.2, pp. 358–9)
- Although popular in the 1960s and often used in the West as an alternative to Tarot cards for fortune-telling, theYijing
(‘I Ching’) is a serious philosophical document, among other things.