This paper tries to show the formation of 'Kyungpook School' that is a nickname given to mathematicians of Kyungpook National University (KNU). In the early period, the role of professor Park Jung-gi was the most important drive to set the research tradition. He made Korea's first english journal in mathematics, Kyungpook Mathematical Journal KMJ which became a cornerstone for students to join the international academic community. Professor Ki U-hang published the most amount of papers in Korea in 1970s and became a role model for young scholars. In this background, KNU's Topology and Geometry Research Center at KNU was chosen as the only Science Research Center in mathematics in 1989, and KNU's mathematicians could get a long-period support for capable mathematics researchers' community.

Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.

Cooperative behavior may seem contrary to the notion of natural selection and adaptation, but is widely observed in nature, from the genetic level to the organism. The origin and persistence of cooperative behavior has long been a mystery to scientists studying evolution and ecology. One of the important research topics in the field of evolutionary ecology and behavioral ecology is to find out why cooperation is maintained over time. In this paper we take a historical overview of mathematical models representing cooperative relationships from the perspective of mathematical biology, which studies population dynamics between interacting biological groups, and analyze the mathematical characteristics and meanings of these cooperative models.