Mathematics is the foundation of architecture. The relationship between math and architecture dates back to the earliest examples of man's building of functional structures. In ancient Byzantine, Egyptian, Greek, Islamic and Roman societies, mathematicians were architects, and architects were mathematicians. Mathematicians were called upon when great structures like pyramids, stadia, temples, ziggurats and irrigation projects were to be designed and built.
Without mathematics in any historical epoch, structures would lack integrity. For a building to have strength and stability, it must have precise angles, wall lengths and roof measurements.
Architectural aesthetics or beauty is largely dependent on mathematics. Architects like Louis Sullivan added ornamental designs to buildings to enhance their beauty. Such designs employed symmetry, geometric shapes, fractals and other wallpaper-type patterns that derive from mathematics.
Contemporary architects use computer software engineered specifically for architecture involving partial derivatives, multiple integrals and systems of differential equations. This type of math is also helpful in adding volume to rooms under specific constraints or maximizing the amount of sunlight entering a room. Such mathematical principles and formulas enable architects to make rooms and buildings appear and feel a certain way to their occupants. These principles also provide architecture with utility and enable the architect to ensure that the purpose of the building is evident.