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Self-Organization of Scientific Specialization and Diversification: A Quantitative Case Study

The dynamics of scientific specialization are investigated in the field of mathematical logic — a major subdiscipline of mathematics, embracing some 15,000 authors from 1874 through 1990. The following dimensions of specialization are described quantitatively, using a comprehensive bibliography: the number of areas of this subdiscipline in relation to the number of contributors; the frequency distribution of the number of areas within logic that those contributors deal with; the analogous frequency distribution of the most prolific logicians; and the degree of division of labour between these prolific logicians. The salient characteristics of these distributions is their skewness, pointing to `Lotka's Law' and other similar distributions, which are discussed as quantitative indicators of scientific self-organization.