Art and Math, Forever

It is even less widely known that mathematics has determined the direction and content of much philosophic thoughts, has destroyed and rebuilt religious doctrines, has supplied substance to economic and political theories, has fashioned major painting, musical, architectural, and literary styles, has fathered our logic, and has furnished the best answers we have to fundamental questions about the nature of man and the universe [1].

These words are by Morris Kline in his fundamental volume Mathematics in Western Culture, first published in 1953.

There have been intellectual periods in history in which the relationships between mathematics and the arts have been more evident and clear: the geometry and arts of ancient Greece, both founded on the idea of proportion; the rediscovery of Greek science during the Renaissance, a period in which it was in many cases very difficult to distinguish between an artist and a scientist, as many were both; projective geometry, non-Euclidean geometries, geometries of multiple dimensions, abstract spaces, dynamical systems, chaos theory. Each of these great ideas has changed our way of looking at the external world and consequently the way of "making art."

In 1953, when Kline wrote his book, Benoit Mandelbrot had not yet invented (or discovered) fractal geometry and its properties, including the importance of scaling and self-similarity and the Hausdorff dimension. It would become possible to describe the shape and the evolution of clouds, of mountains, of the geometries of the infinitely large and infinitely small. From the beginning of his discovery Mandelbrot tried to apply his new geometric ideas to the world of the arts, as many artists and scientists did before him and many others are trying to do and will continue doing as new ideas are discovered. The story of the relationships between art and mathematics had a more or less precise starting point but it is a never-ending one.