Many of the methods commonly used to research mathematical practice, such as analyses of historical episodes or individual cases, are particularly well-suited to generating causal hypotheses, but less well-suited to testing causal hypotheses. In this paper we reflect on the contribution that the so-called hypothetico-deductive method, with a particular focus on experimental studies, can make to our understanding of mathematical practice. By way of illustration, we report an experiment that investigated how mathematicians attribute aesthetic properties to mathematical proofs. We demonstrate (...) that perceptions of the aesthetic properties of mathematical proofs are, in some cases at least, subject to social influence. Specifically, we show that mathematicians’ aesthetic judgements tend to conform to the judgements made by others. Pedagogical implications are discussed. (shrink)

Philosophers of science discuss whether theory selection depends on aesthetic judgments or criteria, and whether these putatively aesthetic features are genuinely extra-epistemic. As examples, judgments involving criteria such as simplicity and symmetry are often cited. However, other theory selection criteria, such as fecundity, coherence, internal consistency, and fertility, more closely match those criteria used in art contexts and by scholars working in aesthetics. Paying closer attention to the way these criteria are used in art contexts allows us to understand some (...) evaluative and developmental practices in scientific theory selection as genuinely aesthetic, enlarging the scope of the goals of science. (shrink)

Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to their visualisations? Using an example from graph theory, this paper argues that, in making aesthetic judgements, mathematicians may be responding to a combination of perceptual properties of visual representations and mathematical properties of abstract structures; the latter seem to carry greater weight. Mathematical beauty thus primarily involves mathematicians’ sensitivity to aesthetics of the abstract.

Scientists often use aesthetic values in the evaluation and choice of theories. Aesthetic values are not only regarded as leading to practically more useful theories but are often taken to stand in a special epistemic relation to the truth of a theory such that the aesthetic merit of a theory is evidence of its truth. This paper explores what aesthetic considerations influence scientists' reasoning, how such aesthetic values relate to the utility of a scientific theory, and how one can justify (...) the epistemic role for such values. The paper examines ways in which the link between beauty and truth can be defended, the challenges facing such accounts, and explores alternative epistemic roles for aesthetic values in scientific practice. (shrink)

ABSTRACT This paper explores the role of aesthetic judgements in mathematics by focussing on the relationship between the epistemic and aesthetic criteria employed in such judgements, and on the nature of the psychological experiences underpinning them. I claim that aesthetic judgements in mathematics are plausibly understood as expressions of what I will call ‘aesthetic-epistemic feelings’ that serve a genuine cognitive and epistemic function. I will then propose a naturalistic account of these feelings in terms of sub-personal processes of representing and (...) assessing the relation between cognitive processes and certain properties of the stimuli at which they are directed. (shrink)

What do mathematicians mean when they use terms such as ‘deep’, ‘elegant’, and ‘beautiful’? By applying empirical methods developed by social psychologists, we demonstrate that mathematicians' appraisals of proofs vary on four dimensions: aesthetics, intricacy, utility, and precision. We pay particular attention to mathematical beauty and show that, contrary to the classical view, beauty and simplicity are almost entirely unrelated in mathematics.

I discuss the role of beauty in physics. Physicists are sometimes described as platonists for their conviction that the fundamental laws are elegant and aesthetic arguments represent an important epistemic tool. After a review of the ideas of Plato and some of the leading figures of modern physics, which suggest that this is indeed the case, I present a list of current aesthetic criteria. I focus on symmetry and unity and demonstrate their increasing relevance in an array of experimentally verified (...) theories. I also deal with an open issue of naturalness as the third criterion. The laws of nature appear increasingly beautiful as we uncover them, and it is important to see if the trend continues in the future. (shrink)

The main aim of this paper is to examine the practice of describing intellectual pursuits in aesthetic terms, and to investigate whether this practice can be accounted for in the framework of a standard conception of aesthetic experience. Following a discussion of some historical approaches, the paper proposes a way of conceiving of aesthetic experience as both epistemically motivating and epistemically inventive. It is argued that the aesthetics of intellectual pursuits should be considered as central rather than marginal to our (...) philosophical accounts of aesthetic experience, and that our views about the relation between the aesthetic and cognitive domains should be reconfigured accordingly. (shrink)

This article starts an engagement on the aesthetics of experiments and offers an account for analysing how aesthetics features in the design, evaluation and reception of experiments. I identify two dimensions of aesthetic evaluation of experiments: design and significance. When it comes to design, a number of qualities, such as simplicity, economy and aptness, are analysed and illustrated with the famous Meselson-Stahl experiment. Beautiful experiments are also regarded to make significant discoveries, but I argue against a narrow construal of experimental (...) aims. By drawing on the plurality of goals experimenters have and diversity of aesthetic responses, I argue that experiments are aesthetically appreciated both when they discover and when they produce disruptive results. (shrink)

This article explores the aesthetic dimensions of scientific experimentation, addressing specifically how aesthetic features enter the construction, evaluation and reception of an experiment. I highlight the relationship between experiments and artistic acts in the early years of the Royal Society where experiments do not serve only epistemic aims but also aim to generate feelings of awe and pleasure. I turn to analysing which aspects of experiments are appreciated aesthetically, identifying several contenders, from the ability of an experiment to uncover nature’s (...) beauty, to encapsulating original designs and human creativity. Following this analysis, I focus on the notion of beauty: what makes an experiment beautiful? Several common qualities are explored, from the simplicity and economy of the experiment, to the significance of the experimental results. (shrink)

ABSTRACT Mathematicians frequently use aesthetic vocabulary and sometimes even describe themselves as engaged in producing art. Yet aestheticians, in so far as they have discussed this at all, have often downplayed the ascriptions of aesthetic properties as metaphorical. In this paper I argue firstly that the aesthetic talk should be taken literally, and secondly that it is at least reasonable to classify some mathematics as art.

Philosophical aesthetics has recently been expanding its purview—with exciting work on everyday aesthetics, somaesthetics, gustatory aesthetics, and the aesthetics of imperceptibilia like mathematics and human character—reclaiming territory that was lost during the nineteenth and twentieth centuries, when the discipline begun concentrating almost exclusively on the philosophy of art and restricted the aesthetic realm to the distally perceptible. Yet there remains considerable reluctance towards acknowledging the aesthetic character of many of these objects. This raises an important question—partly made salient again by (...) the ongoing expansion of the aesthetic domain, and partly by the fact that many still seem resistant to this aesthetic diversification—which aestheticians seem to avoid: what, if anything, constrains the scope of beauty or the aesthetic? I argue that form, construed as comprising a degree, however minimal, of experienceable complexity, is necessary and sufficient for an object's candidature for the possession of aesthetic properties. Such a condition serves to discriminate between attempts to expand the scope of the aesthetic that are legitimate and those that are not. If correct, my view suggests that the aesthetic realm, though not limitless, is very broad indeed—but this, I think, is as it should be. (shrink)

Aesthetics in philosophy of mathematics is too narrowly construed. Beauty is not the only feature in mathematics that is arguably aesthetic. While not the highest aesthetic value, being interesting is a sine qua non for publishability. Of the many ways to be interesting, being explanatory has recently been discussed. The motivational power of what is interesting is important for both directing research and stimulating education. The scientific satisfaction of curiosity and the artistic desire for beautiful results are complementary but both (...) aesthetic. (shrink)

Mathematicians often conduct aesthetic judgements to evaluate mathematical objects such as equations or proofs. But is there a consensus about which mathematical objects are beautiful? We used a comparative judgement technique to measure aesthetic intuitions among British mathematicians, Chinese mathematicians, and British mathematics undergraduates, with the aim of assessing whether judgements of mathematical beauty are influenced by cultural differences or levels of expertise. We found aesthetic agreement both within and across these demographic groups. We conclude that judgements of mathematical beauty (...) are not strongly influenced by cultural difference, levels of expertise, and types of mathematical objects. Our findings contrast with recent studies that found mathematicians often disagree with each other about mathematical beauty. (shrink)

In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to (...) consider and which to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic factors in mathematical research. (shrink)

Scientists regularly invoke broadly aesthetic properties like elegance and simplicity when evaluating theories, but why should we expect aesthetic pleasure to signal an epistemic good? I argue that aesthetic judgements in science are best understood as a special case of affective cognition, and that the feelings on which these judgements are based are the upshots of metacognitive monitoring of the quality of our engagement with theory and evidence. Finding a theory beautiful fallibly signals that it fits well with our background (...) knowledge and that it’s neither artificially adjusted to accommodate otherwise disconfirming evidence nor fitted to noise in the data, which makes aesthetic pleasure a good heuristic for theory evaluation. (shrink)

Thought experiments (TEs) are important tools in science, used to both undermine and support theories, and communicate and explain complex phenomena. Their interest within philosophy of science has been dominated by a narrow question: How do TEs increase knowledge? My aim is to push beyond this to consider their broader value in scientific practice. I do this through an investigation into the scientific imagination. Part one explores questions regarding TEs as “experiments in the imagination” via a debate concerning the epistemic (...) status of computer simulations in science. I outline how, against Hacking, TEs also have “a life of their own” and I argue against accounts that privilege experiments over simulations (and by extension TEs) in light of their capacity to surprise in a productive way. Part two develops a pluralist account of the nature of the imagination in science. At its core, my view is that when we attend to a number of examples of TEs and consider the context in which they are used, we see that TEs engage a variety of our imaginative capacities. Existing monistic views fail to recognise the richness of the imagination and its potential in science. Part three looks to the “beauty” of TEs which is currently overlooked in the aesthetics of science literature. I put forward a new account that demonstrates the epistemic value of aesthetic features in science by showing how an appropriate fit between form and content enhances the usability of a TE, and its effectiveness as a prompt for our imagination. This also enables a more nuanced take on the proposed similarities between TEs and literary fictions. In the concluding chapter, I outline ways in which the core features of my account can be extended beyond TEs to illuminate the significance of the imagination and aesthetic values in other areas of science. (shrink)

This paper offers a systematic analysis of Poincaré’s understanding of beauty in science. In particular, the paper examines the epistemic significance Poincaré attributes to aesthetic judgement by reconstructing and analysing his arguments on simplicity and unity in science. I offer a consistent reconstruction of Poincaré’s account and show that for Poincaré simplicity and unity are regulative principles, linked to the aim of science—that of achieving understanding of how phenomena relate. I show how Poincaré’s account of beauty in science can be (...) incorporated within his wider philosophy of science. (shrink)

Can aesthetic judgements legitimately be linked to the success of scientific theories? I suggest that a satisfactory answer to this question should account for the persistent attraction that aesthetic considerations seem to have for scientists, while also explaining the apparent instability of the link between the beauty of a theory and its truth. I argue that two widespread tendencies in the literature, Pythagorean and subjectivist approaches, have difficulties meeting this twofold challenge. I propose a Kantian conception of aesthetic judgements as (...) second‐order considerations, related to our own intellectual capacities for making sense of the world, and argue that it fares better. (shrink)

Recent attempts at defining mathematical beauty fall roughly into two schools of thought. One takes its starting point in the subjective experience of the mathematician and characterises mathematical beauty in cognitive terms. The other seeks to reduce beauty to objective notions such as truth, symmetry, or simplicity. This second approach is popular among analytic philosophers, who are committed to seeing mathematics and science as prototypically rational enterprises. I criticise this stance on the grounds that this commitment makes its supporters approach (...) beauty in mathematics not with a genuine desire to sympathetically understand it, but with the preconceived goal of explaining it away and playing it down. (shrink)