ChineseMathematics 91
Fig. 4Li Zhi’s ‘round town’ form theCeyuan haijing.- Qin Jiushao(c.1202–61), who worked in the south, and during a boisterous life (details on
various websites, or in Libbrecht) wrote the long and semi-practicalShushu Jiuzhang(Compu-
tational Techniques in Nine Chapters). As well as material which can be found elsewhere, this
provides the most advanced source for the ‘Chinese Remainder Theorem’: how to find a num-
bernwhich leaves remaindersa,b,c,...when divided byp,q,r,....^11 TheShushu jiuzhangis a
complex work, organized around practical problems but often dealing with them in far-fetched
ways. Among other things it illustrates the disturbed politics of the period by some of its ques-
tions: how to arrange soldiers in formation, how to find the distance of an enemy camp. At the
same time, the mathematics introduced into the solution of the problems seems sometimes to
pursue difficulty for its own sake. - Zhu Shijie(dates unknown, end of thirteenth century), another northerner, wrote two books
which were printed but never seem to have been used for teaching. Like the other ‘difficult’ Song
writings, they were probably soon forgotten. The very long (over 1000 pages)Siyuan yujian
(approximately: ‘Mirror trustworthy as jade relative to the four unknowns’, see Martzloff 1995,
p. 153) is, of course, again a collection of problems. However, it is very much more, since the
problems lead to sums of series, high degree equations (again!), in fact a highly organized
algebra whose ideas are similar to those of Li Zhi.
Since it is partly by chance that our key texts from the Song survived there may have been others.
Many of the methods, and even the problems seem to have been common, and one wonders why.
- There is no space to deal with this problem here, or the questions raised by Qin’s treatment of it. His results were not
rediscovered until the time of Gauss (1800)—and are in some respects more general than Gauss’s work.