Takebe Katahiro's Epistemology of Mathematics
XU Zelin(Department of Mathematics,Tianjin Normal University,Tianjin 300074; Institute of Mathematics,Academy of Mathematics and System Science,CAS ,Beijing 100080,China)
xiang xing,man gan and shu are three categories discussed in Daisei Sankei,written by the Japanese mathematician Takebe Katahiro of the Edo era. They are also disciplines in Daisei Sankei,and are called sanyao(three main points).Stemming from shushu in traditional Chinese culture,these categories are hard to understand, and are ignored in the history of Japanese mathematics all the time. This paper, which proceeds from the cultural tradition of Chinese mathematics, interprets these words again, and puts forward some completely new viewpoints. The paper considers that among the mathematicians of Using Chinese Characters, Takebe Katahiro was the first to state systematically the essence of mathematics science,discussed an object of mathematics and its existence,involved the discussion to mathematics variable, and categorized the real number system under the cultural sphere of Chinese xiangshu xue.His mathematical standpoint of sanyao is a reflection of epistemology of mathematics of Using Chinese Characters, and has mathematics philosophy significance.
【CateGory Index】：
O113.13


Chinese Journal Fulltext Database 
3 Hits



1 
ZHOU Chang(Department of Applied Mathematics and Applied Physics,Xi'an Institute of Post and Telecommunications,Xi'an 710121,China);The Trailblazer of Analysis in Wasan:Takebe Katahiro[J];Journal of Inner Mongolia Normal University(Natural Science Edition);200801 
2 
XU Zelin(School of Mathematical Science,Tianjin Normal University,Tianjin 300074,China);Nationalism and East Asian Mathematical Historiography[J];Studies in the History of Natural Sciences;200701 
3 
ZHOU Chang,ZHANG Jianke(Department of Applied Mathematics and Applied Physics,Xi'an Institute of Post and Telecommunications,Xi'an 710121,China);Takebe's Mathematical Thought and Methodology[J];Studies in the History of Natural Sciences;200802 



Chinese Journal Fulltext Database 
10 Hits



1 
Sheng Banghe;The Asianism of Japan in the Transitional Period from the 19~(th) to the 20~(th) Century[J];HISTORICAL RECEARCH;200003 
2 
Tegus, LUO Jianjin(Department of History of Science and Management of Science and Technology,Inner Mongolia Normal University,Huhhot 010022,China);A COMPARATIVE STUDY  EASTERN AND WESTERN SERIES IN QINGTIMES[J];Journal of Inner Mongolia Normal University(Natural Science Edition);200301 
3 
Sheng Banghe and He Aiguo;The Three Schools of Contemporary Historical Thinking in China and their Social Origins[J];Historiography Quarterly;200304 
4 
GUO Huaguang,CHANG Chunyan,WANG Xiaoyan(College of Mathematics and Information Science,Guangzhou University,Guangdong Guangzhou 510405,China);On the Cultural Characteristic of Mathematics[J];Journal of Mathematics Education;200503 
5 
Xu Zelin (Department of Mathematics, Northwest University, 710069, Xi′an);An Inquiry Into the Comparison Between the Tetsujutsu of China and Japan[J];;199704 
6 
ZOU Da hai (Institute for the History of Science, CAS, Beijing 100010, China);Li Yan and the π in the History of Ancient Chinese Mathematics[J];China Historical Materials of Science and Technology;200102 
7 
Li Wenlin;The Tendencies of Algorithm and Deduction for Demarcation of Periods in the History of Mathematics[J];Journal of Dialectics of Nature;198602 
8 
Xu Zelin;Kyokusujutsu in Wasan and Bud of ExtremumConcept in Traditional Mathematics of China[J];Journal of Dialectis of Nature;200201 
9 
ZHA Youliang(Institute of Science of Science,Sichuan Academy of Social Sciences,Chengdu 610072,China);On Qin Jiushao's Thinking Method of Mathematics[J];Studies In Dialectics of Nature;200301 
10 
Xu Zelin(Tianjin Normal University, Tianjin 300073);A COMPARISON OF THE THEORY OF EQUATIONS BETWEEN CHINA AND JAPAN[J];STUDIES IN THE HISTORY OF NATURAL SCIENCES;199903 
