Some Reflections on Main Lines of Mathematical Development

Abstract

There are two major activities of mathematics—theorem-proving and algorithm-creating. While theorem-proving, which originated in ancient Greece, had been being the backbone of the deductive tradition in the history of mathematics, the algorithm-creating, which flourished in ancient and medieval East, formed a strong algorithmic trend in the evolution of mathematics. The main purpose of this paper is to argue the indispensable role in advancing the development of mathematics played by the algorithmic tradition as one of so-called main lines of mathematical development.

Description of the algorithmic characters of the Oriental mathematics constitutes the first part of this paper. Some representative Chinese and Wasan algorithms in ancient and medieval times are observed and their modern implication is discussed. The second part of the paper analyzes the algorithmic tendency in the origin of the modern Western mathematics by taking Descartes’ geometry as a case study. Finally the author proposes some questions about the relation of ancient Oriental mathematics with main lines of mathematical development for further discussion.