CHINESE MATHEMATICS 597 



CHINESE MATHEMATICS 



Br Professor DAVID EUGENE SMITH 



TEACHERS COLLEGE, COLUMBIA UNIVERSITY 



^VyO one who is interested in China and in things Chinese, and no 

 -^^ one to whom the evolution of thought appeals, can fail to ap- 

 preciate the recent articles by Dr. Edmunds, the learned president of 

 the Canton Christian College, upon science among the Chinese.^ His 

 extensive travels in all portions of the country, his own scientific at- 

 tainments, his wide acquaintance with Chinese scholars, his connection 

 with numerous scientific expeditions, and his official position at the 

 head of one of the most progressive colleges in the country, all qualify 

 him to speak as one having authority. 



It is, however, quite natural that one whose tastes are not primarily 

 in the line of mathematics should fail to do justice to the work of 

 Chinese scholars in this field. It is true that this work was not of a 

 high order, and yet it must be said that it ranked with that which was 

 being done in other branches of science, and had not the relatively low 

 standing that would be inferred from Dr. Edmund's statements. These 

 statements are summarized in the following: 



The study of arithmetic has attracted attention among the Chinese from 

 early times, and notices found in historical works indicate some treatises^ extant 

 even in the Han Dynasty (206 b.c.-a.d. 214), followed by a great number of 

 general and particular works down to the Sung Dynasty (1020-1120 a.d.). The 

 Hindu processes in algebra were known to Chinese mathematicians, but though 

 studied even after intercourse between the countries had ceased, these branches 

 made slow progress down to the end of the Ming Dynasty (a.d. 1368-1644).' 



Now as a matter of fact there is a good deal known of the mathe- 

 matics of China in the pre-Christian era, and in certain respects their 

 algebra in the Middle Ages was much in advance of that of their Euro- 

 pean contemporaries. Furthermore, this algebra appears to have been 

 indigenous to China. While Sanskrit was known there very early, and 

 by about 800 a.d. was even taught in Japan (through the writings of 

 the great scholar, K5bo Daishi), there is nothing in the mathematics of 

 either country that shows dependence upon any known works of Hindu 

 scholars. On the contrary, it would seem that Brahmagupta, who 



» The Popular Science Monthly, Vol. LXXTX., p. 521; Vol. LXXX., p. 22. 



* Misprinted ' ' treaties ' ' in the original. 



» Vol. LXXIX., p. 527. Substantially repeated in Vol. LXXX., p. 30. 



