Abstract: The subject of the study is discrete mathematical chemistry as a new field of knowledge in theoretical chemistry. Particular attention is paid to such aspects of research as: the characteristics of the stages of its development in connection with scientific and social problems, their connection with the formation of the subject and the features of methodology, the difference between discrete mathematical chemistry from mathematical chemistry, chemoinformatics and digital chemistry, the connection with these sciences is traced. The object of research is mathematical discrete chemistry in the context of its history. The methodology of the research includes the principle of the relationship between historical and logical, which made it possible to identify turning points in the history of discrete mathematical chemistry associated with its theorization, and a systematic approach, in which the hierarchy of mathematical models in modern mathematical chemical sciences is considered, revealing the peculiarity of the subject of discrete mathematical chemistry. It is concluded that discrete mathematical chemistry is an independent field of knowledge that arose as a result of the integration of methods of non-numerical mathematics and various fields of chemical knowledge. It has gradually emerged from various fields of chemical sciences, has its own specifics, which distinguishes it from mathematical chemistry, chemoinformatics and digital chemistry according to the following criteria: 1) the method of introducing discrete mathematics into chemistry without the participation of an intermediary in this process – physics, 2) a special style of mathematical thinking in chemistry, 3) the degree of idealization in mathematical modeling. Its mathematical apparatus is a mathematical modeling, which is used to formalize many chemical sciences. It is a research tool and the language of modern chemistry.
The novelty of the research lies in the fact that the specificity of discrete mathematical chemistry is revealed, its identity and independence are established, and its methodological boundaries are determined in accordance with the hierarchy of mathematical chemical sciences. The research results contribute to the methodology of chemistry and the philosophy of science.

Abstract: The subject of this research is the method of interpretation in theoretical chemistry as a combination of cognitive procedures and approaches on the example of interaction of the classical theory of structure and quantum chemistry within the framework of their history and logic of development. It is demonstrated that the process of interpretation encompasses several historical stages of the development of quantum chemistry, marking the transition from meaningful symbolic concepts of the theory of structure towards formal-logical quantum-chemical terms, and the reverse interaction of these theories – the implementation of the latter into the theory of structure. The interpretational method in quantum chemistry contributes to the construction of more complex mathematical schemes underlying the natural scientific content. Such schemes include various approximations and assumptions, as well as the elements of arbitrariness in selection of the mathematical schemes by the theoretician, which reduces the accuracy of explanations and predictions of quantum chemistry. The object of this research is the methodology of theoretical chemistry, in terms of which takes place the interaction between quantum chemistry and classical theory of structure, their cognitive abilities, structure and dynamics of theoretical knowledge. The novelty lies in the fact that the interpretation in natural sciences is yet to be fully research; the study of interpretation in the context of constructivist approach in the philosophy of science allows revealing the logical-methodological and gnoseological aspects of interpretation. The acquired results contribute to the methodology of chemistry, epistemology, and philosophy of science. It is concluded that the process of interpretation is the construction of more complex mathematical schemes, which leads to the gap between mathematical and natural scientific content of the concepts; between mathematical description, natural-scientific theoretical representations, and experiment. The gap is accompanied by origination of the new concepts of quantum chemistry as a result of integration of the various fields of knowledge and extinction of concepts of the classical theory of structure, as well as determination of the limits of mathematical method in chemistry.