论文标题
人类寻求在艺术中发现数学美的追求
The human quest for discovering mathematical beauty in the arts
论文作者
论文摘要
用20世纪的英国数学家G. H. Hardy的话说，“人类的功能是'发现或观察“数学”（1）。几个世纪以来，从古希腊人开始，人类一直追求艺术和自然界的美和秩序。这种对数学美的追求导致发现了经常性的数学结构，例如黄金比率，斐波那契和卢卡斯数字，它们无处不在的存在一直在诱使艺术家和科学家的思想。此任务的迷人带有高风险。实际上，艺术是人类创造力的确定表达，其数学理解将为我们提供解码人类文化及其进化的关键（2）。但是，直到最近，人类对数学美追求的范围和规模才通过三个独立的创新的同时汇合而从根本上扩大。大型艺术档案馆的质量数字化，计算能力的激增以及稳健的统计方法的开发以捕获大量数据的隐藏模式，这使得揭示了人类眼睛的 - 否则对大型艺术语料库隐藏的数学不明显。从伯克霍夫（3）的基础工作开始，从成立开始，计算美学领域的进步就达到了一个量表，这是十年前无法想象的。最近的扩展不仅限于视觉艺术（2），但包括音乐（4），故事（5），语言语言（6），笑话中的幽默（7），甚至方程式（8）；有关全面审查，请参见参考。 9。
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.
