Topology from Art and Math to contemporary cities

Mathematics is not a mere tool of kitchen recipes, but has contributed to, if not determined, our way of conceiving space on Earth and even in the Universe. A lack of awareness of mathematics as an essential tool of our culture has led to a major delay in the use of instruments that mathematicians have used for decades. A case in point is topology, the science of transformations, the science of invariants. Its relatively recent discovery by architects has led to a remarkable transformation of the art of conceiving and building space. A notorious cultural leap has led to construction using techniques and material that allow realizing transformation, rendering it almost continuous, a sort of contradiction between the finished construction and its deformation. The so called fluid topological architecture is the final result of a set of new ideas of space. New topological ideas are used in art, and has been materialized in recent buildings in towns all around the world, such as the Guggenheim Museum in Bilbao, the National Library in Astana, the Moebius Bridge in Bristol, the MAXXI museum in Rome, the Max Reinhardt Haus of Eisemann, the Moebius House of Van Berkel. I will illustrate this story using various examples from the topological gold jewels in pre-Colombian culture in South America to the new development in modern cities. I conclude with a reflection on the ethical and artistic aspects of this new topological public architecture