History of Science and Engineering Annotation << Back The History of the Formation of Mathematical Logic, Set Theory, and their Significance for the Development of Science Dibirova Z.G., Gadzhieva A.M. This article focuses on the historical development of mathematical logic and set theory, highlighting their key milestones and significant discoveries. It explores the main ideas and achievements from ancient times to the present, as well as the contributions of prominent scholars such as Aristotle, Cantor, Godel, and others. The article emphasizes the importance of formal systems, the resolution of paradoxes, and the establishment of the foundations of modern mathematics. The study highlights the significance of logic and set theory in shaping scientific thinking and their impact on contemporary mathematical practices and philosophy. Keywords: Arithmetic, logic, mathematical logic, set theory, logical calculi, formalization, axiomatization, mathematical theory, set, cardinal numbers, ordinal numbers, logical systems, set theory, model theory, problem formulation. DOI: 10.25791/intstg.2.2026.1601 Pp. 34-38.