A thesis on two phases of genesis of science, the line of demarcation being the emergence of philosophy, is advanced. The first phase of science genesis under the civilization of the Ancient East is observed. The failure of the process of science genesis in reaching the crowning stage is explained by specific character of social and economic development of the Ancient East. The idea on religion being the first institutional form of the rising science whose genesis reached its crowning phase under the socio-economic, ideologicalpolitical and cultural conditions in Ancient Greece is grounded.