80 A History ofMathematics
2. Sources
The reader iscomparativelywell served by recent publications on Chinese mathematics. By this
I mean that they are comprehensive and good, although the local library may have to be persuaded
to invest in a copy. First among them is the classic work of Joseph Needham (1959). It has been
claimed that the mathematical part of Needham’s enormous work is the weakest, ‘superficial and
largely dependent on obsolete Western-language sources’ being a recent judgment (Sivin 2004);
but all subsequent scholars owe him an immense debt, and his emphasis on the social context
is particularly valuable. Much more recent and very full is Martzloff (1995). This is thought-
fully structured, the first part on context and the second on content. Martzloff is scholarly, and
anxious to give Chinese mathematics due credit; but he is equally cautious (some might say too
cautious) about claims which rest on evidence which is scanty or late, or on conjectures about
how things must have been. One could hardly wish for a fuller introduction, and it is highly
recommended.
Of equal value—since the classic books are at the heart of Chinese mathematics—is the fact
that several of these have been translated in the past 30 years, usually with a large amount of
discussion and background material. This is most useful since there are no selections in Fauvel and
Gray which deal with the subject. Certainly the most important is Shen et al.’s (1999) translation,
with a very full commentary, of the fundamentalNine Chapters on the Mathematical Art, which fills
the major gap; but also valuable are the translations of Cullen (1996), Lam (1977), Lam and Ang
(1992), Swetz (1992), and the commentary of Libbrecht (1973).^4 The reader who can lay hands
on some or all of these will be in an excellent position to form informed judgements. On the later,
less studied period after 1600, Martzloff (1981) and Jami (1990) are both in French, but, if you
can locate and read them, they provide a good opening on current research.
For a general history of China, an introduction—with much of interest concerning the history
of science—is contained in Needham’s volume I (1954). A more recent ‘classic’ is Fairbank (1992).
Nathan Sivin has a good selected bibliography on Chinese science, including mathematics, online
(Sivin 2004), and the new Chinese section of the St Andrew’s website provides more detail on
particular topics, for example, theNine Chaptersor individual mathematicians. Finally, there is a
great deal of research activity, both in the standard publications (Historia Mathematica,Arch. Hist.
Exact Sci.) and in specialist journals addressing Chinese science. Reference to some of these will be
made where relevant.
3. An instant history of early China
The succession of dynasties, sometimes orderly and sometimes confused, which structures Chinese
history is not ‘general culture’ as the European succession of states and empires is thought to be.
What we need is a quick summary which is angled towards the main periods of mathematical
interest, so far as we know them. Because the most important discussions concern the early
period—up to about 600ce—I shall cover that here, with brief inserts on the other key periods as
we come to them.
- There is still no translation of the key work on which this is based, Qin Jiushao’s thirteenth-centuryShushu jiushang
(Computational Techniques in Nine Chapters); but perhaps one is on the way.