Abstract
This paper is a presidential address by the author who is the president of Japanese Association for Mathematical Sociology. The aim of this article is to describe characteristics of each framework of four main research streams-study of social status, rational choice theory, social network research, and social systems theory-, and to discuss the recent development and critical aporia of each paradigm from empirical-theoretical, positivistic-normative, and micro-macroscopic view, and to advocate that more Sisyphus-like communication based on frontier research among vernacular framework and disciplines is required toward more effective paradigm leading to future development of mathematical sociology.
