Mathematical Approaches in Contemporary Architectural Practices: The Case of Baku

Mathematics has long served as a fundamental tool in architecture, enabling the transformation of abstract concepts into spatial realities. This study explores the relationship between mathematics and contemporary architecture through a qualitative case analysis of three iconic structures in Baku: the Mirvari Restaurant, Baku Crystal Hall, and Crescent Mall. Despite differing in function and construction period, these buildings were selected for their shared formal characteristics such as shell structures, curvilinear geometries, and parametric design logic and their common placement along the Caspian Sea waterfront, exposing them to similar environmental dynamics. The research investigates how mathematical principles such as parametric geometry, structural optimization, and environmental simulation contribute to the form and performance of these structures. Conducted through literature review, formal-spatial analysis, and contextual interpretation, the study is structured around four key themes: design generation, material efficiency, climatic responsiveness, and cultural symbolism. The findings reveal that mathematics not only ensures technical precision but also enhances aesthetic expression and cultural meaning. This analysis underscores the productive and integrative role of mathematics in shaping functional, sustainable, and evocative architecture in the digital age.