The Han dynasty was founded by Liu Bang, who emerged victorious in the civil war that followed the collapse of the unified but short-lived Qin dynasty. A golden age in Chinese history, the Han dynasty’s long period of stability and prosperity consolidated the foundation of China as a unified state under a central imperial bureaucracy, which was to last intermittently for most of the next two millennia. During the Han dynasty, territory of China was extended to most of the China proper and to areas far west. Confucianism was officially elevated to orthodox status and was to shape the subsequent Chinese civilization. Art, culture and science all advanced to unprecedented heights. With the profound and lasting impacts of this period of Chinese history, the dynasty name “Han” had been taken as the name of the Chinese people, now the dominant ethnic group in modern China, and had been commonly used to refer to Chinese language and written characters. The Han Dynasty also saw many mathematical innovations being invented such as the method of Gaussian elimination which appeared in the Chinese mathematical text Chapter Eight Rectangular Arrays of The Nine Chapters on the Mathematical Art. Its use is illustrated in eighteen problems, with two to five equations. The first reference to the book by this title is dated to 179 AD, but parts of it were written as early as approximately 150 BC, more than 1500 years before the Europeans came up with the method in the 18th century.

After the initial Laissez-faire policies of Emperors Wen and Jing, the ambitious Emperor Wu brought the empire to its zenith. To consolidate his power, Confucianism, which emphasizes stability and order in a well-structured society, was given exclusive patronage to be the guiding philosophical thoughts and moral principles of the empire. Imperial Universities were established to support its study and further development, while other schools of thought were discouraged.

Major military campaigns were launched to weaken the nomadic Xiongnu Empire, limiting their influence north of the Great Wall. Along with the diplomatic efforts led by Zhang Qian, the sphere of influence of the Han Empire extended to the states in the Tarim Basin, opened up the Silk Road that connected China to the west, stimulating bilateral trade and cultural exchange. To the south, various small kingdoms far beyond the Yangtze River Valley were formally incorporated into the empire.

Emperor Wu also dispatched a series of military campaigns against the Baiyue tribes. The Han annexed Minyue in 135 BC and 111 BC, Nanyue in 111 BC, and Dian in 109 BC. Migration and military expeditions led to the cultural assimilation of the south. It also brought the Han into contact with kingdoms in Southeast Asia, introducing diplomacy and trade.

After Emperor Wu, the empire slipped into gradual stagnation and decline. Economically, the state treasury was strained by excessive campaigns and projects, while land acquisitions by elite families gradually drained the tax base. Various consort clans exerted increasing control over strings of incompetent emperors and eventually the dynasty was briefly interrupted by the usurpation of Wang Mang.

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