The human quest for discovering mathematical beauty in the arts

Abstract

In the words of the twentieth-century British mathematician G. H. Hardy, "the human function is to 'discover or observe' mathematics" (1). For centuries, starting from the ancient Greeks, mankind has hunted for beauty and order in arts and in nature. This quest for mathematical beauty has led to the discovery of recurrent mathematical structures, such as the golden ratio, Fibonacci, and Lucas numbers, whose ubiquitous presences have been tantalizing the minds of artists and scientists alike. The captivation for this quest comes with high stakes. In fact, art is the definitive expression of human creativity, and its mathematical understanding would deliver us the keys for decoding human culture and its evolution (2). However, it was not until fairly recently that the scope and the scale of the human quest for mathematical beauty was radically expanded by the simultaneous confluence of three separate innovations. The mass digitization of large art archives, the surge in computational power, and the development of robust statistical methods to capture hidden patterns in vast amounts of data have made it possible to reveal the---otherwise unnoticeable to the human eye---mathematics concealed in large artistic corpora. Starting from its inception, marked by the foundational work by Birkhoff (3), progress in the 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 the visual arts (2) but includes music (4), stories (5), language phonology (6), humor in jokes (7), and even equations (8); for a comprehensive review, see ref. 9.