The numbers of beauty: can maths foster creativity?

It is pretty obvious that disciplines such as Architecture and Design need Mathematics as a technical tool. What is less obvious is that Mathematics can be a very useful creative tool for architects and designers. Let us consider, for instance, the works of the catalan architect Antoni Gaudí, whose peculiar architecture, pervaded by curved shapes, is the result of a clever use of the theory of the so called ruled surfaces. The use that Gaudí makes of geometry may well be defined a "creative" one: mathematics for him is not only a bare technical tool, but it is also a useful creative support, capable to supply him with inspiration and new ideas. This view is actually shared by many other architects that, overcoming Gaudí's fairly classical geometry, completely disengage from traditional paradigms, to be inspired by a new geometric world, whose principles are those of the non-Euclidean geometries, topology, fractal geometry or high dimensional geometry. This gives birth to the topological architecture of UNStudio, Toyo Ito, Santiago Calatrava, Foster + Partners and many others, in a list which could go on at will, including even more original works, whose realization was absolutely unthinkable a few years ago, due to the innovative materials and technologies it requires. The creative use of mathematics goes beyond architecture, to infiltrate other disciplines, which are apparently even more distant. All done in the spirit of Salvador Dalí, one of the most visionary artists of his time, who in his book Fifty Secrets of Magic Craftmanship (1948) recommends to the young artist: «You have to use geometry as a guide to the symmetry in the composition of your works. I know that the romantic painters argue that these mathematical frameworks kill the artist's inspiration, giving him too much to think about. Do not hesitate a moment to reply that, on the contrary, it is exactly not to have to think and reflect on certain things, that you use them».