Between 1918 and 1948, Le Corbusier published a series of influential manifestos that drew on mathematical methods, theories, and imagery. From the ‘Purist ManifestoPurist Manifesto’ to Vers Une ArchitectureVers Une Architecture (Towards a New Architecture) and The ModulorThe Modulor, mathematics provided Le Corbusier with a source of authority and a language for architectural form-making that was both rational and poetic. Using proportions, ratios, patterns, symmetry, and Phileban solids—cube, cone, cylinder, sphere—Le Corbusier translated his thinking about geometric experience and perception into architecture. Mathematics provided him with a connection to classicism, to the purity of a Greek temple and the order of a Palladian villa. This chapter investigates the relationship between mathematical thinking and properties in Le Corbusier’s architecture. It commences with an overview of Le Corbusier’s contribution to design and theory before describing the mathematical thinking that shaped his so-called ‘white purist villas’ of the 1920s. Five of these villas, the primary works considered in Part II of this book, are then analysed and illustrated. These are the Maison-Atelier OzenfantMaison-Atelier Ozenfant, Villa CookVilla Cook, Villa PlaneixVilla Planeix, Villa Stein and Villa SavoyeVilla Savoye. The chapter also explores two precursor works, theVilla Jeanneret-Perret Villa Jeanneret-PerretPerret, Auguste and the Villa SchwobVilla Schwob. Through this analysis, the chapter illuminates the strategies Le Corbusier used to control the experience and perception of his geometric constructions. The interpretation of these strategies is supported by observations about the recurrence of inexact geometry, for example, squarish as opposed to square forms. The chapter concludes by summarising applications of mathematics in Le Corbusier’s architectural thinking and identifying a potential dependent relationship between thinking and properties in his white purist villas.