An International Research Comparative Study of the Degree of Cooperation between disciplines within mathematics and mathematical sciences: proposal and application of new indices for identifying the specialized field of researchers

Based on 10 years of data on academic papers from 2005 to 2014 available on the “Web of Science”, we conducted an in-depth review and analysis of collaborative academic research activities and relationships in mathematics/mathematical science and 21 other fields. We focused on the “academic papers co-authored with researchers in other fields” and derived new methods for measuring the degree of research cooperation among disciplines. Our new methods consist of two steps. The first step involves measuring and deriving new indices for identifying the specialized field of each researcher and the degree of concentration of each researcher’s work in his or her field of specialization. The second step, based on the indices, utilizes the Lorenz curve and Gini coefficient to identify the characteristics of each field. We analyzed the temporal trends in the data for 15 major countries from 2007 to 2014, to determine if the degree of cooperation between disciplines is changing. We also analyzed the characteristics of different regions: the European Union, North America, Asia without Japan, and Japan. We confirmed the effectiveness of our new methods and obtained some interesting findings that offer a new perspective on academic research activities.