What mathematical demography tells that we would not know without it

Abstract

The purpose of the mathematics of population is to answer common sense questions, for instance about the effects of changing births on the proportion of old people, or the effect of abortions on the birth rate. Very often the answers it gives are the opposite of those given by common sense, and in such cases we have to adjust our common sense to accord with what the mathematics show to be true. In other instances the direction of an effect is obvious, but we need a technical analysis to estimate its amount.This paper takes up 20 problems, compels each to submit to mathematical analysis, and extracts from the mathematics a result that is of use in its own right. Such results can guide people who are working at some practical issue concerned with population, and they can enable the citizen to have clearer understanding of what is going on in a field that citizens can no longer neglect.