Mathematics and entrepreneurship research

While economics, psychology, political science and some areas of sociology make extensive use of mathematics, organizational and management research rarely does so. This is unfortunate because mathematics can be utilized to describe phenomena, build new theories, and refine existing ones. In this chapter, we discuss why and how mathematics can provide important contributions to the study of entrepreneurship. Indeed, we argue that research in entrepreneurship offers a compelling case for the use of mathematics. Building theory in entrepreneurship is difficult because it often involves a multi-level analysis, where the analysis needs to move between the individual, group, firm or population level (Davidson and Wiklund, 2001; Busenitz et al., 2003; West, 1997). Unlike other methods, mathematics enables researchers to structure relationships between various levels of analysis, and can therefore encourage more theory development in entrepreneurship. The number and type of research questions in the area of entrepreneurship that can be described mathematically is virtually endless. These include (but are not limited to) identifying thresholds of accumulated knowledge on which the attractiveness of an opportunity is assessed; characterizing how varying environmental conditions affect market entry or entrepreneurial behavior; identifying the relationship between entrepreneurship and economic growth; analyzing the emergence of alternative levels and concentration of entrepreneurial activity in a region; and studying the characteristics of entrepreneurial behavior in families and groups. The number of mathematical methods that can be used to tackle these questions is also considerable.