Traditional Chinese Mathematics in the 19 th Century Western World
Vol. 44 No. 1 3/2003
Title 
Traditional Chinese Mathematics in the 19th Century Western World 
Author 
Xiaoqin Wang 
Genre 
Article 
Pages 
7397 
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Language 
Chinese 
Key words 
Traditional Chinese Mathematics, J. F. Davis, E Biot, A Wylie, K.L. Biernazki 
Abstract 
In the 17^{th} and 18^{th} centuries, information on mathematics of ancient china was exclusively drawn from the relevant writings of the Catholic missionaries, who knew nothing but the Gou GU theorem incorporated in ZhouBi, which was erroneously dated back to 1100 B.C. Misunderstandings could be found no less frequently in the Western publications on China. This state continued in the first half of the 19th century. Ignorant of the history of Chinese mathematics, J. F. Davis, authority on Sinology at that time, asserted that the Chinese know nothing about the place value of numbers and they have no algebra. However, the Italian historian of mathematics G. Libri, who fled to France as a political refugee, and got to know the famous French Sinologist S. Julien, discovered the placevalue notations in Cheng Dawei’s Suanfa Tongzong, which had been collected by the Royal Library of France. The French Sinologist E Biot, disciple of S. Julien, made a close study on the same Chinese mathematical work and published ageneral tale of it. Biot also translated the whole of Zhou Bi,but his translation is full of errors. Alexander Wylie, the British missionary and Sinologist who came to China in 1847, was the Western forerunner in the field of the history of Chinese mathematics. In 1852, he fully introduced, for the first time to the West, the Chinese mathematical literature and achievements, including the placevalue, Tayan Rule, Tianyuan Rule, and the method of solving numerical equations of all order, pointing out their world significance, refuting the prevailing erroneous statements on Chinese mathematics in Western publications, exerting farreaching influence on the later Western historians of science. Having been translated into German by K. L. Biernatzki, Wylie’s paper was known to western mathematicians such as M. Cantor, H. Hankel , L. Matthiessen, O. Terquem and J. Bertrand. The last two translated Biernatzki’s translation; the Dayan Rule and Tianyuan Rule were misunderstood by Cantor and Terquem, of whom the former judiciously reappraised the Dayan Rule according to Matthiessen’s corrections. Matthiessen, an acute German mathematician, proved the identity of Chinese Tayan Rule with C. F. Gauss’s rule in his Disquisitiones Arithmeticae, and also offered an explanation of case in which the moduli are not relatively prime in pairs. However, he did not know the Qiuyi Rule, by means of which the solution ax ≡1(mod b) is found. Though more about Chinese mathematics was knows to westerners in the 19th century than in the 17^{th} and 18^{th} centuries, their knowledge of this subject was still limited. Some attainment in Chinese mathematics, such as those in The Nine Chapters on the Mathematical Art, one of the most important mathematical classics in China, Liuhui’s Cyclotomic Rule, Zu Chongzhi’s famous fractional value of π, Zugeng’s derivation of the volume of a sphere, etc., were unknown to them. Because the original mathematical works and relevant research literatures were extremely scarce, the transmission of traditional Chinese mathematics in the West in the 19^{th} century was not smooth at all. In the first half of 20^{th} century, despite the publication of Y.Mikami’s The Development of Mathematics in China and Japan, the transmission was impeded by suspicion, derogation and prejudice of western historians such as L. Van Hee, G. Loria and G. Vacca. The history of transmission of traditional Chinese mathematics tells us that it could not be properly appreciated and valued through secondhand literatures alone and that both Chinese and western historians of Science should do much more in studying, the translating and promulgating it in order to make it known to more western scholars in the new century. 