The Unreasonable Attractiveness of Mathematics to Artists and Scientists

Mathematics, not least in popular writings on the topic, is often credited with a special affinity to beauty. For example, mathematical theorems are sometimes described as ‘beautiful’, or a particular proof may be deemed more ‘elegant’ than another. But it is far from clear how mathematical objects such as theorems or proofs could function as bearers of aesthetic value. Thus, an air of mystery surrounds these invocations of ‘mathematical beauty’, its source and cognitive function. The sense of mystery is compounded by the fact that such aesthetic judgments are not exclusively the preserve of mathematical experts, but have also proved attractive to non-experts, including artists. This ‘unreasonable attractiveness’ of mathematics suggests that, perhaps, there is more to the appreciation of the aesthetic dimension of mathematics than initially meets the eye. The present chapter argues that there are at least three ways in which mathematics, over the past century, has attracted the attention of artists: as tool, as subject matter, and as ideal. It is the latter—mathematics as intellectual ideal and practice—which, it is argued, explains why interest in the relation between mathematics and art reached considerable levels towards the middle of the twentieth century. At the same time, sparked by a growing interest in the role of mathematical models, philosophers of science increasingly turned their attention to mathematics and its cognitive function. Following a review of extant notions of beauty and elegance in mathematics, it is argued that the ‘beauty’ of an elegant mathematical proof may not reflect any intrinsic feature of a proof, but rather its performative success in establishing the truth of its conclusion. In what has sometimes been called ‘aesthetic induction’, the very signs of epistemic success (e.g. the mathematical features of empirically successful scientific theories) are being re-interpreted as signs of ‘beauty’. Artists, too, have valued mathematics not for its subject matter per se, but for its perceived rigour as an intellectual practice; this is illustrated using examples from a range of artists across the ages. The final three sections of the chapter aim to establish a link between Wigner’s puzzle—concerning ‘the unreasonable effectiveness of mathematics in the natural sciences’—and the recent philosophical debate about mathematical models. The chapter concludes by reflecting on a convergence (of sorts) between art and science, as both have moved away from a simplistic understanding of the goal of representation and have instead looked to mathematics as an anchor of artistic and scientific practice.