In this work is an attempt to mathematically prove the existence of the demographic transition taking into account one of its features, such as extension of human life dependent on the growth of the human population. Determined the functional form of this dependence, and the relationship between the probability of death, life expectancy, and social involving in the states of T (the influence of "traditional" values of concepts) and R (in the range of rules and possibilities of modern civilization). One of the consequences of change in live style of human population and social groups from the "traditional" to "rational" (modern) type of existence was called as a demographic transition [1]. Demographic transition is characterized by the almost simultaneous, but not a parallel decrease in mortality and fertility, and intensive population growth. In his monograph [1] prof. Okolski, demographic transition theory sees as the most progressive achievements and specific paradigm of modern demography. At the same time he points out that some demographers wouldn't agree with global (universal character) of demographic transition. If the demographic transition has a global character than the mathematical way of describing it's processes (in the present work is considered one of them-the life expectancy of people) should demonstrate a clear and explicit (functional) dependence on the size of the entire humanity.
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