A model for the growth of mathematical specialties

Abstract

A mathematical model for the growth of two coupled mathematical specialties, differential geometry and topology, is analyzed. The key variable is the number of theorems in use in each specialty. Obsolescences of theorems-in-use due to replacement by more general theorems introduces non-linear terms of the differential equations. The stability of stationary solutions is investigated. The phase portrait shows that the number of theorems in low-dimensional topology relative to those in differential geometry is increasing. The model is qualitatively consistent with the growth of publications in these two specialties, but does not give quantitative predictions, partly because we do not use an explicit solutions as a function of time and partly because only two specialties are used. The methods of analysis and some of the concepts can be extended to the development of more general and realistic models for the growth of specialties.

Can scientific journals be classified in terms of aggregated journal‐journal citation relations using the Journal Citation Reports?

“…Derek de Solla Price (1963) conjectured that specialties would begin to exhibit 'speciation' when the carrying community grows larger than a hundred or so active scientists (Crane, 1972;Kochen, 1983). Furthermore, the proliferation of scientific journals can be expected to correlate with this proliferation of communities because new communities will wish to begin their own journals (Price, 1965).…”

Simulations of opinion changes in scientific communities

“…Nevertheless, it is useful to position our approach in the context of more general studies of science growth. Kochen and Blaivas (1981) continued the approach of Goffman. Using differential equations from epidemiology, they proposed a model for growth of number of theorems in two closely related mathematical disciplines.…”

Scientometrics and information retrieval: weak-links revitalized

“…One factor for such a drift is the ongoing growth of the science system itself, with a hyperbolic growth of scholarly publications (Börner 2010, The Rise of Science and Technology page 4) and an accompanying diversification leading to an increasing number of specialities. The latter have been stated as having an usual size of 120-160 researcher (Kochen and Blaivas 1981), which probably has to do with a maximum size of a network with which one person still can pursuit a regular and indebt exchange of information. Another factor might be the amorphous nature of the overarching discipline of information science to which both areas belong.…”