On 4 November 2016, the historic Paris Climate Agreement of the United Nations entered into force, requiring signatory countries to maintain global warming at the level of 1.5−2 °C. According to the calculations of the Intergovernmental Panel on Climate Change (IPCC), to achieve this goal, a 2/3 reduction in greenhouse gas energy emissions into the atmosphere compared with gaseous energy-related emissions in 2019 (33.3 Gt) by about 2050 (1.5 °C) or by 2070 (2 °C) is required. According to the International Renewable Energy Agency (IRENA), this is only possible with the implementation of a great energy transition from the use of currently dominant fossil hydrocarbon fuels—coal, oil, and natural gas—to the predominant use of renewable energy sources (RES) by 2040−2050, when the share of renewable energy in the total energy balance will reach 40% and above. In this work, mathematical description of an upcoming energy transition has been carried out, including long-term scenario writing of the world’s demographic dynamics and global energy demand, calculation of the dynamics of industrial CO2 emissions and CO2 accumulation in the Earth’s atmosphere, as well as the corresponding changes in the average global temperature of the Earth’s surface in the 21st century. A mathematical description of the impact of energy consumption on climate change was carried out taking into account long-term trends in the dynamics of energy consumption. Using the performed mathematically-oriented scenario writing, it is suggested that a great energy transition with the achievement of the goals of the Paris Agreement is possible only by 2060. Renewable energy could sufficiently displace and replace hydrocarbon fuels to achieve climate safety without compromising economic development. As a result, humanity will receive an environmentally friendly decentralized distributed energy system, connected by «smart» grids, controlled by intelligent digital technologies.