- CHINA 33
devoted to the mathematical proof in the proper sense of the term." Du Zhigeng
also attempted to synthesize the traditional Chinese classics, such as the Jiu Zhang
Suanshu and the Suan Fa Tong Zong, with works imported from Europe, such
as Archimedes' treatise on the measurement of the circle. Thus in China, West-
ern mathematics supplemented, but did not replace, the mathematics that already
existed.
The first Manchu Emperor Kang Xi (1654-1722) was fascinated by science and
insisted on being taught by two French Jesuits, Jean-Frangois Gerbillon (1654-
1707) and Joachim Bouvet (1656-1730), who were in China in the late 1680s. This
was the time of the Sun King, Louis XIV, who was vying with Spain and Portugal
for influence in the Orient. The two Jesuits were required to be at the palace from
before dawn until long after sunset and to give lessons to the Emperor for four
hours in the middle of each day (Li and Du, 1987, pp. 217-218).
The encounter with the West came at a time when mathematics was undergo-
ing an amazing efflorescence in Europe. The first books on the use of Hindu-Arabic
numerals for computation had appeared some centuries before, and now trigonome-
try, logarithms, analytic geometry, and calculus were all being developed at a rapid
pace. These new developments took a firmer hold in China than the ancient Greek
mathematics of Euclid and Archimedes. Jami (1988) reports on an eighteenth-
century work by Ming Antu (d. 1765) deriving power-series expansions for certain
trigonometric functions. She notes that even though the proofs of these expansions
would not be regarded as conclusive today, the greatest of the eighteenth-century
Chinese mathematicians, Wang Lai (1768-1813), professed himself satisfied with
them.^9 Thus, she concludes, there was a difference between the reception of Eu-
clid in China and the reception of the more computational modern mathematics.
The Chinese took Euclid's treatise on its own terms and attempted to fit it into
their own conception of mathematics; but they reinterpreted contemporary math-
ematics completely, since it came to them in small pieces devoid of context (Jami,
1988, p. 327).
Given the increasing contacts between East and West in the nineteenth century,
some merging of ideas was inevitable. During the 1850s the mathematician Li Shan-
Ian (1811-1882), described by Martzloff (1982) as "one of the last representatives
of Chinese traditional mathematics," translated a number of contemporary works
into Chinese, including an 1851 calculus textbook of the American astronomer-
mathematician Elias Loomis (1811-1889) and an algebra text by Augustus de Mor-
gan (1806-1871). Li Shanlan had a power over formulas that reminds one in many
ways of the twentieth-century Indian genius Srinivasa Ramanujan. One of his com-
binatorial formulas, stated without proof in 1867, was finally proved through the
ingenuity of the prominent Hungarian mathematician Paul Turan (1910-1976). By
the early twentieth century Chinese mathematical schools had marked out their own
territory, specializing in standard areas of mathematics such as analytic function
theory. Despite the difficulties of war, revolution, and a period of isolation during
the 1960s, transmission of mathematical literature between China and the West
continued and greatly expanded through exchanges of students and faculty from
the 1980s onward. Kazdan (1986) gives an interesting snapshot of the situation in
China at the beginning of this period of expansion.
(^9) European mathematicians of the time also used methods that would not be considered com-
pletely rigorous today, and their arguments have some resemblance to those reported by Jami.