"CHINESE mathematics", defined by the Chinese themselves in ancient times as the art of calculation" (suan chu), covers a vast range of practices and currents of thought that grew up in China between the first millennium BC and the fall of the Manchu dynasty in 191 1. After that date Chinese mathematics became westernized and the traditional practices were virtually impenetrable to those without specialized training.
Divination, astronomy and mathematics
Although writing already played an important role in China at the time of the composition of the earliest canonical writings (the classics" which were always so essential in the training of intellectual elites), mathematics was not then considered to be a body of knowledge that it was necessary to record in specialized texts.
It seems, however, that mathematics was instrumental in the emergence of what the sinologist L. Vandermeersch has judiciously called "divinatory rationality". Beginning with oracles in the form of tortoise shells, animal bones or the leaves of the Chinese yarrow, the prognostics made using this form of divination were based on the interpretation of all manner of natural signs, especially meteorological and astronomical phenomena such as rainbows, halos, winds, meteors, positions and conjunctions of stars, eclipses and sunspots. This magical worldview did not however exclude recourse to purely rational investigations. The diviners attempted with some success to fit all their observations into numerical and arithmetical schemes devised for the recording of memorable past phenomena and the prediction of certain recurrent events. Some predictions of periodically recurring celestial phenomena began to be confirmed by observation, led to the birth of the calendar and mathematical astronomy.
Each successive dynasty in China made its mark by introducing a new system for computing the calendar so that the historical events recorded by annalists could be reassessed and future events predicted. The ruling class therefore needed qualified personnel who specialized in calendrical and astronomical calculations. A body of imperial chronologers thus gradually came into being, serving both as historian-annalists and astronomer-calendrists.
The continuing requirements of Chinese dynasties in the ages explain why the search for appropriate methods of predicting the most visible celestial phenomena conjunctions of stars, occultations, eclipses) was foremost in the minds of mathematicians.
However, as the astronomer-calendrists of imperial China usually had a lowly social status, and as their knowledge was handed down from father to son, their activities were often denigrated and looked upon simply as a static way of upholding tradition.
The overwhelmingly dominant factor in the history of Chinese mathematical astronomy is the extraordinary durability of conflicts between rival schools. From the beginning of our era to the sixteenth century, the Chinese calendar underwent no less than fifty reforms. However, these conflicts turned out to be more constructive than destructive in that they were almost always settled by the concordance between observed reality and the predictions.
Unfortunately, very few works devoted exclusively to mathematical astronomy have survived. Monographs written by non-specialists, abridged versions of which were included in the annals of successive dynasties, are practically all that remain.
The social background of Chinese mathematics
During the Han dynasty (206 BC to 220 AD), another branch of mathematics appeared, this time recorded in specialized manuals. Collections of problems and their solutions were organized in chapters according to their practical applications. The descriptions in these texts are often so detailed and realistic that it is almost possible to reconstruct from them entire chapters of Chinese social and economic life at a given period. …