For most of history of mankind, its population grew with blow-up. However, the growth slows down in last decades and tends to stabilization. We introduce the concept of life-saving technologies, which development is treated as the engine of history, and formulate the principle of the technological imperative, which directly binds the number of living people to the level of technological development. On this basis, we build a mathematical model of global population growth and identify its limits. As far as mankind approaches them the demographic transition occurs, for which we propose a phenomenological model in good agreement with the data.

theoretical demography, global demography, hyperbolic law, blow-up growth, demographical imperative, technological imperative, life-saving technologies, demographical transition, limits of growth, age pyramid

Mathematical modelling in actual problems of science and technics