The Nine Chapters by Liu Hui(劉徽) in the three kingdoms(220∼265 AD) is the fundamental source of the traditional Chinese Mathematics and has not only remained the lighthouse of the traditional Chinese Mathematics over the last 2000 years, but also has exerted a profound influence on the development of mathematics in the neigh-bouring countries and regions. At last it also translated into English. In this paper, some differences between the Orignal and the New Translated Nine Chapters will be introduced and a problem of Mathematical Treatise in Nine Sections (Shushu Jiuzhang, 수서구장, 1247) of Qin Jiushao(진구소, 1202∼1261 AD) in the Song (송, 960∼1261 AD) Dynasty It looks like an insect in the amber but not error.

Since algebra before the 19th century was the study of equations and equations are not differentiated from polynomials because of lack of the equality sign, the algebraic symbolism of polynomials plays very important role for tile history of algebra. We deal with the evolution of literal notations of polynomials in western and eastern worlds, and then compare their history.

This article shows Hilbert's Paris address within the context of his career and the mathematics of his day. And the text of Hilbert's speech will be considered in some detail, particularly those parts of it that reflects his vision of mathematics most clearly. At the end it is attempted to show the limitations of the standard view of Hilbert as an advocate of a formalist approach to mathematics.

It is said that mathematics is neutral and free from any thought. But the history of mathematics refuses it. This paper aims to investigate modernism and postmodernism in mathematics and to scrutinize them. For this, first modernism is characterized by concentrating on Descartes' philosophy, and next postmodern view which criticizes modernism is discussed. Finally it is claimed that mathematical realism and postmodernism can be comparable in different dimensions.

The aim of this paper is to outline a nature of pure mathematics up to the point at which its main theses can be clearly grasped and compared with other philosophical positions. Also, We analyze the contents and discuss the nature of questions which lie in pure mathematics.

Mathematics and arts are reflection of the spirit of the ages, since they have human inner parallel vision. Therefore, in ancient Greek ages, the artists' cannon was actually geometric ratio, golden section. However, in middle ages, the Euclidean Geometry was disappeared according to the Monastic Mathematics, then the art was divided two categories, one was holy Christian arts and the other was secular arts. In this research, we take notice of Renaissance Painting and Perspective Geometry, since Perspective Geometry was influenced by Renaissance notorious painter, Massccio, Leonardo and Raphael, etc. They drew and painted works by mathematical principles, at last, reformed the paradigm of arts. If we can say Euclidean Geometry is tactile geometry, the Perspective Geometry can be called by visual geometry.

In this paper, we examine human perception and mentality on the shape, and study the correlation of golden section with nature and human being.

This paper aims to consider the genesis of irrational numbers and to suggest a method for teaching the concept of irrational numbers. It is the notion of “incommensurability” in geometrical sense that makes Pythagoreans discover irrational numbers. According to the historica-genetic principle, the teaching method suggested in this paper is based on the very concept, incommensurability which the school mathematics lacks. The basic ideas are induced from Clairaut's and Arcavi's.

We seek the possibility of application of ICT(Information ＆ Communication Technology) to the experience learning in mathematics. Especially we focused on regular polyhedron in the middle school mathematics and on geodesic dome. We investigate related historical tales about the subjects which seem quite helpful of motivating to understand them. Then by using them and by ICT we develop an experience learning program for geodesic dome as an application of regular polyhedron. Through the program we expect that students show positive attitude in mathematical tendency and curiosity about mathematics and that the application of ICT to the experience learning in mathematics is very effective to improve their learning skill in mathematics.

The nonlinear fourth order elliptic equations with jumping nonlinearity was modeled by McKenna. We investigate the trends for the researches of the existence of solutions of a fourth order semilinear elliptic boundary value problem with Dirichlet boundary Condition, ${\Delta}^2u{＋}c{\Delta}u=b_1[(u＋1)^{-}1]{＋}b_2u^+$ in ${\Omega}$, where ${\Omega}$ is a bounded open set in $R^N$ with smooth boundary ${\partial}{\Omega}$.