A multidimensional analysis of scientific dynamics .1. Case studies of mathematical logic in the 20th century

Sequences of empirical Lotka-like distributions of the publications of scientific areas are mapped into a multidimensional parameter space. On this basis a new definition of the notion of an epidemic phase of a discipline is introduced. A graphic representation of the parameter space along with results of an exponential regression analysis of the Lotka exponent yield an image of the inner state of a discipline and renders possible a prognosis. Examples, primarily from mathematical logic, are described in detail. The notion of a scientific elite is discussed and the hypotheses of Ortega, Merton, and Price are critically assessed.