The eminent Russian and Soviet scientist Sergey Kapitsa devoted at least a dozen books to the topic of demographic problems of the world's population. He developed a mathematical model of human development from the epoch of paleontology to the present day, and showed a quadratic growth of the population during this time. He proved that we are living in an age of demographic transition and explosion, when rapid population growth ends and there is a sharp decline worldwide. The democratic explosion occurs around the 1950s and 2050s. The general aging of the world's population begins. It is interesting that the conclusions of S. P. Kapitsa very accurately correspond to the UN studies and projections for the same periods of time. Then there are two alternatives for human development - either stagnation and decline of modern civilization, or growth of the quality of life. There is a very serious picture of demography in modern Russia. The author attempts to outline ways to overcome this grave situation. It is a matter of "little" - we need an understanding of the problem and the political will to preserve and survive the people in our country.