MATHEMATICS TV C/ILVA AND JAPAN. 185 



many mathematicians, in whose hands the Wasan ^n^> or ^'Japanese 

 mathematics," properly so called, was established. It was based, indeed, 

 on the study of Chinese matliematics, imi)orted for a second time, but 

 it began to take a course of its own and arrived at results unknown in 

 China. 



Japanese Mathematics arose in the 17tli century in and near the 

 Emperor's ca})ital, Kyoto. But this city soon yielded precedence to Yedo 

 (now Tokyo), the Shogun's residence, which at the time of Seki Kowa |^ 

 #^P (P-1708) became the centre of mathematical learning in Japan and so 

 remained up to the end of the Wasan in the 19ili century. This state of 

 things widely differs from that which prevailed in the study of medicine for 

 which Kyoto continued to be the centre. Japanese mathematics had a 

 side of practical utility, but it was in essence a sort of game or art, and 

 as such it was cultivated by the Japanese. It owes its nature to the 

 artistic temperament of the Japanese in general and also to the disposition 

 prevalent in Yedo, a large city of consumers, which was controlled by a 

 leisure class. Contemporary with Seki, there were certain noted 

 mathematicians at Kyoto and Osaka, but their works were not so 

 eminent as Seki's nor did there arise such influential Schools in these 

 cities as that of Seki in Yedo. Osaka in fact proved to be a second 

 centre of mathematical learning for a long time, but the scholars of this 

 commercial city were possessed of less propensity than their brethren 

 in Yedo to go down into the depths of unpractical game-like problems, 

 in which Japanese mathematics abounded. This is certainly the reason 

 why the study of pure or abstract mathematics in Osaka was never able 

 to equal the work done at Yedo. On the other hand, the way for the 

 work of the great Ino Tadataka ^^^^^^ (1745-l8lt>j in land surveying 

 had been paved for him by his masters and friends at Osaka. 



Japanese mathematicians used to keep their work or art secret and 

 to reveal it only to a few of their most advanced pupils. It followed, 

 therofore, that even talented men were not able to acquire sufficient 

 knowlegde without entering the school of an intiuential person or persons. 

 Under such circumstances, it was natural that schools were formed, of 

 which that of Seki was the sole one that exercised a vast influence. 

 Aida Ammei's -^Bg^^^ (1747-1817) contention against the illustrious 

 head of the Seki school, Fnjita Teishi ^jgj(^( 1734-1807), was 

 obviously the result of the former's brightness of talent, which he could 

 not bring to subordination under the traditional dignities of an old school. 

 After the controversy between these men, a large number of gifted 



