In its pure form mathematics is often practiced with inquiry as its motivation and aesthetic discovery as its goal. Defining aesthetic experience is difficult. I consider an aesthetic experience a heightened moment when one finds resonance with the perceived, transcending sensation and emotion, and for some, moving towards the spiritual. An aesthetic moment is not dependent on sensory information. It is cognitive, the mind interacting with perception. Cognition and perception are concerned with ideas, not external objects. Even as basic an experience as color is not dependent on sensory input. Anyone who dreams in color can attest to this. The experience is directly with thoughts, with ideas.

With the advent of technology it is possible to manifest mathematical objects as images, sounds, sculpture and even poetry. Artists in all media have found mathematics (most often described algorithmically) of value in their creative enterprise. Through algorithmic works we discover an inherent beauty and meaning in mathematics, perceived by the senses through objects defined in space or time, for example numbers mapped into color or pitch. Often the source of these works, the mathematical proof, the algorithm, has a beauty (elegance in mathematical parlance) that itself has aesthetic worth. Mathematical ideas can not only be a source for aesthetic construction, but can themselves catalyze aesthetic experience.

Ideas do not need representation in the external, physical world in order to be known. This premise is fundamental to creative activity. Mathematical ideas continue to  contribute greatly to the creative endeavors of our civilization. Masterworks of this mathematic enterprise have survived through millennia not only as tools for science but as resonant ideas of aesthetic substance.

  • BRIAN EVANS, Vanderbilt University U.S.A.