ChineseMathematics 93
Fig. 6Illustration from theShushu jiuzhang, p. 167.We have, as often in the early history of mathematics, an impressive part of a structure which has
survived almost by chance while the rest is missing. Failing dramatic discoveries of the texts from
the earlier period, we must be content with what remains, and try to understand the aim of this
‘school’ which was not a school. While our evidence for a ‘culture of mathematicians’ during the
Song is sparse, the books do seem to aim at a specialist audience, whether it existed or not. Libbrecht
emphasizes both the practicality of theShushu jiuzhang:
In a splendid work on architecture, theYing-tao fa-shih, there is a full description of materials and constructions, but
what is lacking is plans for carrying out the work: the calculation of the building materials, the number of workmen,
the provisions and wages. All this we find in Ch’in Chiu-shao’s work. (Libbrecht 1973, p. 8)
at the same time as its ‘advanced’ nature:
In Ch’in’s work all the basic operations (even the square root extraction) are taken for granted. For a beginner’s
textbook its problems are much too complex; it would be useful only for advanced students...It is possible that
they [the Song texts] were unsuccessful substitutes for older books written in a less advanced phase of mathematical
knowledge. But as mentioned earlier, none of the writers was a mathematics teacher; even Li Yeh [Li Zhi]’s work,
which was printed in the thirteenth century, was never used as a textbook. (Libbrecht, 1973, pp. 8–9)
What can be said at the moment is that the work of the Song mathematicians, for the student who
is prepared to overcome some formidable initial obstacles, is a really promising field of research.
While much progress has been made in understanding them, there are still controversial points
and open questions. The mixture of practical setting with the pursuit of difficulty apparently for its
own sake, while not unique to the Chinese, could lead us to think again about what mathematics
is ‘for’.