Topological architecture and fluid architecture are a reality of our times. New digital technologies and new construction techniques, combined with the use of new architectural shapes derived from the latest studies of modern and contemporary mathematics, have profoundly changed the idea of architecture. There always has been an important relationship between mathematics and architecture, from ancient Greece to modern times. The new ideas of space and new geometries have helped to model the idea of space in architecture. It is a long story that continues. It is a strong tradition in the history of architecture. From the point of view of mathematics it is a matter of great interest, although many architects, mostly those linked to history and tradition, think that contemporary topological and fluid architecture is simply not architecture, forgetting that the traditional links between mathematics and architecture change as mathematics and the idea of space change.
