The paper presents an interpretation of the development of theories that led to the formation of the science management model reflected in the Strategy of Scientific and Technological Development of Russia. The author discovers in the Strategy model the principles, which were proclaimed by W. Bush in his report 75 years ago: giving universities the role of drivers of the country innovative development, team organization and a new social contract. Moreover, the Strategy’s practice embodies the same idea of centralizing support for academic research within a single federal agency. In Russia, the Russian Science Foundation has become such an agency. At the same time, further development of management concepts is influenced by foreign trends, including the desire for convergence of sciences in the US research enterprise, the formation of the 3rd generation of innovation policy in Europe, the transition to humanistic terminology in the «Great Reset» project, etc. These trends stimulate Russia's desire to gain a foothold on the «Science Frontier» and offer an adequate response to the Great Challenges. However, to solve these problems, it is necessary to overcome the looseness of the science management structure, implement a hybrid system of public and private support for science, and ensure coordinated efforts within the framework of «bottom-up» innovation processes, with the participation of all stakeholders and with a thorough diagnosis of the strengths and problems of specific regions.