Mathematics of ancient and medieval algorithms according to selected treatises of Chinese scientists

The talk is devoted to the mathematics of medieval and ancient China as a model of constructive thinking. Computing technology in ancient China of the 3rd century AD. – XIV centuries was reflected in several dozen treatises, which allow us to fix traditional Chinese mathematics as an established concept. The technology is based on a Chinese computing tool, suan-pan. Based on the texts of the Decateuch ("The Ten Books") treatises and later works it is possible to analyze the computing traditions of China. Suan-pan has always been used in traditional computing practice. All problems in the literature were divided ac-cording to the methods for solving them or according to their use in real human activity, so we can identify the main characteristics of the problems and the corresponding algorithms. According to A.N. Kolmogorov many problems solved in traditional Chinese mathematics can be attributed to the intuitionistic calculus of problems or interpreted as the calculus of decidable problems [1]. We will illustrate our story with copies from the treatises in question for clarity of the computational process and the main characteristics of the problems. We will present to the listener a minimal vocabulary of ancient and medieval Chi-nese mathematics, thanks to which algorithms can be systematized: they use the same alphabet, represented by a table of operators and a constructive mod-el that implements the problem using a set of algorithms. In other words, the study of the texts of the treatises of Zhu Shijie, Qin Jiushao, and Li Ye made it possible to propose an alphabet (operators) for the computational process in Xuan Pan and, in a sense, to formalize the texts of solutions to problems. For more than one and a half thousand years, a library of algorithms has emerged that is quite correctly written in the specified alphabet. Thus, the thinking style of a particular culture is modeled by a system of ethno-pedagogical mathematical knowledge.
1. Kolmogorov A.N. O principe tetrium non datur// Matematicheskij sbornik. 1925. T. 32. №4. P. 646–667.
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