Abstract:
The presentation will begin with a short description of the Chinese mathematical treatises published prior to the 16th century; the speaker will briefly introduce their contents and the most interesting methods and results obtained by their authors, as well as the history of the development and decline of this tradition. A special attention will be paid to the particular features of these treatises, in particular, to their structure: the texts were organized as series of problems accompanied by the answers and by the algorithms used for their solutions; these algorithms were supposed to be performed with the so-called “counting rods” and, in a later time period, with the beads abacus. It will be shown that the treatises did not contain formal proofs of correctness of these methods, yet justifications of some methods can be found in the commentaries that accompanied some treatises. The speaker will also briefly describe the system of state mathematics education created in China in the second half of the first millennium CE; some time later similar systems were established in Korea and Japan.
After that the speaker will provide an overview of the works on the history of Chinese mathematics published in Mainland China, Taiwan, Hong Kong, Japan, in Russia, in Western Europe, and in North America. Among the publications in Chinese language a special attention will be paid to the works of Ruan Yuan 阮元, Li Yan 李儼, Qian Baozong (Baocong) 錢寳琮, Yan Dunjie 嚴敦杰, Du Shiran 杜石然, Guo Shuchun 郭書春, Bai Shangshu 白尚書, Horng Wann-Sheng 洪萬生, and others; the Japanese publications will be represented by the works of Mikami Yoshio 三上義夫 and Kawahara Hideki 川原秀城. The speaker will also focus on the works of Soviet/Russian researchers A.P. Yushkevich, E.I. Berezkina, S.V. Zinin and V.K. Zharov, as well as on the publications of Western historians of Chinese mathematics D.E. Smith, J.-C. Martzloff, K. Chemla, C. Jami, and J. Dauben.
In the concluding part, the speaker will discuss the texts that still remain untranslated and/or insufficiently well studied, and briefly discuss the directions of future studies.
Keywords: mathematics in ancient and medieval China; history of mathematics and mathematics education in ancient and medieval East Asia
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