The Human Quest for Discovering Mathematical Beauty in the Arts

Abstract

In words of twentieth-century British mathematician G. H. Hardy, the human function is to 'discover or observe' mathematics. For centuries, starting from ancient Greeks, mankind has hunted for beauty and order in arts and in nature. This quest for mathematical beauty has led to discovery of recurrent mathematical structures, such as golden ratio, Fibonacci, and Lucas numbers, whose ubiquitous presences have been tantalizing minds of artists and scientists alike. The captivation for this quest comes with high stakes. In fact, art is definitive expression of human creativity, and its mathematical understanding would deliver us keys for decoding human culture and its evolution. However, it was not until fairly recently that scope and scale of human quest for mathematical beauty was radically expanded by simultaneous confluence of three separate innovations. The mass digitization of large art archives, surge in computational power, and development of robust statistical methods to capture hidden patterns in vast amounts of data have made it possible to reveal the—otherwise unnoticeable to human eye—mathematics concealed in large artistic corpora. Starting from its inception, marked by foundational work by Birkhoff, progress in broad field of computational aesthetics has reached a scale that would have been unimaginable just a decade ago. The recent expansion is not limited to visual arts but includes music, stories, language phonology, humor in jokes, and even equations.