5 Ancient Chinese Mathematics
Documented civilization Dates from c. 3000 BC. Until around
AD 200, China refers roughly to the area in the map: north
of the Yangtze and around the Yellow river. A more de-
tailed timeline map can be found here.
Earliest mathematics Oracle Bone enumeration dates from the
Shang dynasty (c. 1600–1046 BC), commensurate with the
earliest known Chinese character script. Most information
on the Shang comes from later commentaries, though orig-
inal oracle bones have been excavated, particularly from
the ancient capital Anyang. Astronomy, the calendar and
trade were dominant drivers of mathematics.
Zhou dynasty (1046–256 BC) and the Warring States period (475–221 BC) Many mathematical texts
were written, though most have been lost; content must be inferred from later commentaries.
Rapid change created pressure for new systems of thought and technology. Feudal lords em-
ployed philosophers, of whom the most famous was Confucius (c. 500 BC).
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Technological
developments included the compass (for navigation) and the use of iron in warfare.
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Later history and expansion After the victory of the Qin Emperor Shi Huang Di
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in 221 BC, China
was ruled by a succession of dynasties. In 1912, the Qing dynasty was overthrown and the
monarchy abolished, by which time Chinese territory had expanded to roughly its modern
borders. A Civil War (1927–1949) resulted in victory for the communists under Mao Zedong
and the foundation of the modern Chinese state. While this simple description might suggest
a long calm in which culture and technology could develop in comfort, in reality the empire
experienced many rebellions, schisms and flux, often exacerbated by the changing whims of
emperors and later leaders.
Transmission of knowledge East Asia (modern China, Korea, Japan, etc.) is geographically sepa-
rated from other areas of early civilization by tundra, desert, mountains and jungle. During
the Han dynasty (c. 200 BC–AD 220) a network of trading routes known as the silk road was es-
tablished, connecting China, India, Persia and Eastern Europe; the Great Wall was in part con-
structed to protect these trade routes. Geographical separation meant that trade was limited,
and there is little evidence of mathematical and philosophical ideas making the journey until
many centuries later. For instance, there is no evidence of sexagesimal notation being used in
China, suggesting that Babylonian and Greek astronomy did not travel eastwards beyond In-
dia. Similarly, there are eastern mathematical ideas (e.g., matrix-style calculations) which saw
no analogue in the west until many centuries later. There are, however, indications that early
decimal calculations in India may have been inspired by the Chinese counting board method.
On balance, it seems reasonable to conclude that Chinese and Mediterranean mathematics de-
veloped essentially independently.
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An adviser to Lu, a vassal state of the Zhou. Confucianism emphasises stability and unity as a counter to turmoil.
Taoism, the competing contemporary philosophical system, is more comfortable with change and adaptation.
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Sun Tzu’s military classic The Art of War dates from this time.
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Famous for book-burning, rebuilding the great walls, and for the Terracotta Army of Xi’an.
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