This final chapter reflects on the complex relationships between architectural thinking and properties explored in this book. It commences with a seemingly simple example: a description of the geometric thinking involved in creating a square and assessing its geometric properties. This is the catalyst for discussing the challenges of investigating the relationship between a creative process (design) and a tangible product (a building) when the evidence is incomplete or inconsistent. Three considerations that assist in addressing these challenges are identified. The chapter then reflects on the ways different social and political contexts can trigger the alignment of mathematical thinking and proprieties. In doing so, it suggests why architects from diverse eras and locations might employ similar ideas for radically different purposes. After that, the chapter revisits some of the book’s findings, discussing their implications and future research directions. Finally, the role of the square in the architectural thinking and properties of Palladio, Le Corbusier and Eisenman provides a means of distilling key similarities and differences.