The Unreasonable Aesthetic of Mathematics in the Sciences

Abstract

Eugene Wigner was a Nobel prize winning physicist, recognized for his work related to fundamental symmetry principles. In his 1960 speech-turned-publication, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” he claimed that some applications of math are miraculous. He was amazed that mathematical concepts appear unexpectedly in the natural science of physics, and when they do appear, they are often inspired by intuitions of beauty. Still, applied mathematics shows accurate measurements with unparalleled regularity and precision. In his discussion, Wigner defines mathematics and physics before delving into the role and success of mathematics in the natural sciences. Yet estranged from the rest of the text, the example he opens with discusses the social sciences. Though Wigner can be read as providing an account of why math is justified, at least within physics, the application of math within social sciences, like economics, is left for the reader to ponder. The following is an extension of Wigner’s curiosity applied to the social sciences, with particular attention to the role of beauty in applied mathematics. The central research question is the following: do the same aesthetic principles that define the miraculous application of mathematics in physics, apply in economics? After examining Wigner’s (1960) original paper, I draw upon the work of Areezo Islami (2016), Mark Wilson (2000), Nancy Cartwright (1999), Jennifer Jhun (2016), and Philip Mirowski (2012) to develop aesthetic categories that serve three purposes: (1) they provide clear vocabulary for explaining why certain theories and applied mathematics are found convincing, by identifying the aesthetic principles that underwrite belief in them; (2) they enable the retrospective abstraction of successful theories, allowing us to abstract and articulate the aesthetic criteria of successful theories and then attempt to reverse engineer their success using those same aesthetic principles; and (3) they establish a standpoint for evaluating new ideas, either by assessing their conformity to existing aesthetic standards or by identifying the emergence of new ones.