The “Pythagorean theorem„ and Chinese Mathematics Liu Hui’s Commentary on the 勾股 (Gou-Gu) Theorem in Chapter Nine of the Jiu Zhang Suan Shu

The following is a preliminary and relatively brief, exploratory discussion of the nature of early Chinese mathematics, especially geometry, considered largely in terms of one specific example: the Pythagorean Theorem, known in its Chinese version as the Gou-Gu theorem. In addition to drawing some fundamental comparisons with western traditions, especially with Greek mathematics, some general observations are also made concerning the character and development of early Chinese mathematics. Above all, why did Chinese mathematics develop as it did, as far as it did, but never in the abstract, axiomatic way that it did in Greece? Many scholars have suggested that answers to these kinds of questions are to be found in social and cultural factors in China. Some favor the sociological approach, emphasizing for example that the Chinese were by nature primarily concerned with practical problems and their solutions, and therefore had no interest in developing a highly theoretical mathematics. Others have stressed philosophical factors, taking another widely-held view that Confucianism placed no value on theoretical knowledge, which in turn worked against the development of abstract mathematics of the Greek sort. While both of these views contain elements of truth, and certainly play a role in understanding why the Chinese did not develop a more abstract, deductive sort of mathematics along Greek lines, a different approach is offered here. To the extent that knowledge is transmitted and recorded in language, oral and written, logical and linguistic factors cannot help but have played a part in accounting for the development of Chinese mathematics.