The history of architecture presents many examples of architects autonomously discovering and using mathematical structures and patterns. Historically this kind of quasi architectural-mathematical discovery was the product of the architect’s intuition and inspiration, and was not subject to rigorous mathematical treatment. However, in some sense the application of mathematical patterns is perfectly deliberate. Although this kind of geometry was probably not even known to mathematicians when these works were conceived, its presence could nonetheless be easily observed in nature. How and in what sense does nature instantiate these geometries? One could say, albeit naively, that mathematics provides us with abstract and general models, whereas nature utilises them with a certain degree of freedom, insofar as it is constrained by external factors such as the quality of the soil, the amount of sunlight available, the presence of plants, etc.1 The metaphor of nature’s interpreting geometry also helps us discard as a misunderstanding any reductive interpretation of the architect’s work as being exclusively based on an out of hand and uncritical use of geometrical patterns. The process of using patterns has to be conceived of as an intellectual exchange between the ideal elements of geometry and architecture’s pragmatism. One of the major goals of this paper is to demonstrate, by using historical and contemporary evidence, patterns’ aptness to suit the high demands of contemporary architectural work. I argue that this is not specifically related to today’s architectural scenario. On the contrary, a substantial part of the article is devoted to the examination of how architects have taken advantage of the opportunities offered by mathematics and their respective contributions to the advancement of mathematics. In particular, I will be looking at three case study examples of this connection between architecture and mathematics, which will help bring to light the following:

- how mathematics can be reduced to visual patterns, which offer a wide range of formal and diagrammatic interpretation within architectural work;
- how the use of mathematical patterns does not restrain the designer’s creativity (on the contrary, its abstract characteristics can produce novelties);
- whether – consciously or unconsciously – mathematical patterns are formal tools which allow coherence;
- how mathematical patterns can help the systemic development of a project;
- how geometry can induce formal control, but cannot ensure the project’s success alone. The paper is essentially an expository survey, and includes detailed analysis within the later sections. I will begin by defining mathematical patterns.