The Effects of Funding Changes upon the Rate of Knowledge Growth in Algebraic and Differential Topology,1955-75

This paper reports the initial results of a study of the effects of funding variations upon the rate of knowledge growth in algebraic and differential topology. It is part of an exploratory effort to determine an appropriate methodology for the study of funding changes. The study is based on a marginal productivity model of funding of effects. The rate of scientific knowledge growth is defined as the rate at which important problems are located and solved. It is measured as the rate of production of important papers, as judged by a panel of scientists. The model indicates that under certain conditions funding variations should have little or no effect upon the rate of knowledge growth. The results of the study are consistent with the predictions in the model, although all conditions could not be tested and methodological uncertainties remain.