28 2. MATHEMATICAL CULTURES I
is nothing positive that serves as an evidence of any actual Indian influence upon
the Chinese mathematics."
The Tang Dynasty (seventh and eighth centuries). The Tang Dynasty was a period
of high scholarship, in which, for example, block printing was invented.
The Song Dynasty (960-1279). The period of disorder after the fall of the Tang Dy-
nasty ended with the accession of the first Song emperor. Confucianism underwent
a resurgence in this period, supplementing its moral teaching with metaphysical
speculation. As a result, a large number of scientific treatises on chemistry, zool-
ogy, and botany were written, and the Chinese made great advances in algebra.
The Mongol conquest and the closing of China. The Song Dynasty was ended in the
thirteenth century by the Mongol conquest under the descendants of Genghis Khan,
whose grandson Kublai Khan was the first emperor of the dynasty known to the Chi-
nese as the Yuan. As the Mongols were Muslims, this conquest brought China into
contact with the intellectual achievements of the Muslim world. Knowledge flowed
both ways, of course, and the sophisticated Chinese methods of root extraction seem
to be reflected in the works of later Muslim scholars, such as the fifteenth-century
mathematician al-Kashi. The vast Mongol Empire facilitated East-West contacts,
and it was during this period that Marco Polo (1254-1324) made his famous voyage
to the Orient.
The Ming Dynasty (fourteenth to seventeenth centuries). While the Mongol con-
quest of Russia lasted 240 years, the Mongols were driven out of China in less than
a century by the first Ming emperor. During the Ming Dynasty, Chinese trade and
scholarship recovered rapidly. The effect of the conquest, however, was to encourage
Chinese isolationism, which became the official policy of the later Ming emperors
during the period of European expansion. The first significant European contact
came in the year 1582, when the Jesuit priest Matteo Ricci (1552-1610) arrived
in China. The Jesuits were particularly interested in bringing Western science to
China to aid in converting the Chinese to Christianity. They persisted in these
efforts despite the opposition of the emperor. The Ming Dynasty ended in the
mid-seventeenth century with conquest by the Manchus.
The Ching (Manchu) Dynasty (1644-1911). After two centuries of relative pros-
perity the Ching Dynasty suffered from the depredations of foreign powers eager
to control its trade. Perhaps the worst example was the Opium War of 1839-1842,
fought by the British in order to gain control of the opium trade. From that time on
Manchu rule declined. In 1900 the Boxer Rebellion against the Western occupation
was crushed and the Chinese were forced to pay heavy reparations. In 1911 the
government disintegrated entirely, and a republic was declared.
The twentieth century. The establishment of a republic in China did not quell the
social unrest, and there were serious uprisings for several decades. China suffered
badly from World War II, which began with a Japanese invasion in the 1930s. Al-
though China was declared one of the major powers when the United Nations was
formed in 1946, the Communist revolution of 1949 drove the ruler Chiang Kai-
Shek to the island of Taiwan. The United States recognized only the government
in Taiwan until the early 1970s. Then, bowing to the inevitable, it recognized the
Communist government and did not use its veto power when that government re-
placed the Taiwanese government on the Security Council of the United Nations.
At present, the United States recognizes two Chinese governments, one in Beijing
and one on Taiwan. This view is contradicted by the government in Beijing, which