Theory of Social Relays’ Applications: Mathematics and Public Administration

The theory of social relays studies social activity as an evolving phenomenon. It has a significant applied potential, allows explaining the realities of scientific cognition and social practice, answering the questions why cognition and social practice occur in this way and not in another way, presenting the subjects of sci­ences, as well as proposing promising research tasks that encourage new investi­gations. The article offers examples of how social relay theory addresses prob­lems relevant to the field of the history and philosophy of mathematical cognition, as well as to the theoretical foundations of public governance. In mathematics, the problem of the spread of formal proofs in areas of mathe­matics outside its foundations is considered, and it is shown that this spread is caused by the reproduction of the social relay of proofs using formal logical-mathematical systems, existing in parallel with the social relay of substantive (non-formal) proofs. In the same way, the parallelism of geometric and algebraic proofs of theorems on properties of geometric objects in the 19th century is ex­plained by the existence of two simultaneously existing social relay races. The contribution of the theory of social relays to the formation of ideas about the subject and practice of public governance is considered in the second part of the article. This contribution, as shown, consists in realizing the relay nature of administrative activity as reflexive and codified (procedural) and presenting the main theoretical concepts of public administration as different types of ad­ministrative activity: vertically integrated, agency-shaped, activity based on civil society involvement, as well as administrative activity based on data collection, its analytics and the use of this analytics in decision-making.