Mathematical Beauty, Understanding, and Discovery

Cellucci, Carlo

doi:10.1007/s10699-014-9378-7

Cited by 28 publications

(24 citation statements)

References 21 publications

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“…Although some scientists claim that the concept of beauty cannot be analysed, many give an insight into the way they understand the concept, by reducing it to certain aesthetic properties like simplicity, symmetry, harmony, or unity (the concept of beauty is systematically analysed in Engler (), McAllister (), Breitenbach (), De Regt ((), Gaut and Lopes (), Cellucci ()). One question that arises is whether these aesthetic values can be regarded as universally accepted.…”

Section: Beauty and Aesthetic Valuesmentioning

confidence: 99%

“…Although when discussing the concept of truth or utility, it is standard to focus on the aesthetic properties of scientific theories, it is important to note that scientists praise many objects as aesthetically valuable, for example, mathematical proofs, scientific discoveries, scientific experiments, observations, and models. The concept of mathematical beauty, and the question of how mathematics applies to physics, has received systematic attention in the literature (Cellucci, ; Engler, ; McAllister, ; Montano, ). Systematic analysis has also been given to the aesthetic value of experiments in physics and biology and their epistemic role (Holmes, , ; Parsons & Reuger, ; Reuger, ).…”

Section: Beauty and Aesthetic Valuesmentioning

confidence: 99%

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Aesthetic values in science

Ivanova

2017

Philosophy Compass

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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.

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Section: Beauty and Aesthetic Valuesmentioning

confidence: 99%

Section: Beauty and Aesthetic Valuesmentioning

confidence: 99%

Aesthetic values in science

Ivanova

2017

Philosophy Compass

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“…From a theoretical standpoint, the case of interest is situated at the crossroad of two general perspectives for conceptualizing mathematical beauty, objectivism and subjectivism, the latter also referred to as projectivism [6,36]. From the perspective of objectivism, mathematical beauty is an intrinsic property of a problem, theorem, or proof, and is consequently independent of the observer and the socio-historical context surrounding it [6].…”

Section: Conceptualization Of Mathematical Beautymentioning

confidence: 99%

“…From the perspective of objectivism, mathematical beauty is an intrinsic property of a problem, theorem, or proof, and is consequently independent of the observer and the socio-historical context surrounding it [6]. Dreyfus and Eisenberg [11] list the characteristics that contribute to the aesthetics of a solution or proof as: clarity, simplicity, brevity, conciseness, structure, power, cleverness, and surprise.…”

Section: Conceptualization Of Mathematical Beautymentioning

confidence: 99%

Surprise and the Aesthetic Experience of University Students: A Design Experiment

Marmur¹,

Koichu²

2016

jhummath

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Little is known about instructional means by which the aesthetic experience of mathematics can be enhanced for undergraduate learners. This paper presents and discusses an iterative lesson design process towards creating an opportunity for students to appreciate the beauty of an unexpected solution to a challenging calculus problem. The lesson design draws on insights from both mathematics education research on aesthetics and research on aesthetic appreciation in music. The data were collected over the course of five lessons with different groups of calculus students in which the intended problem was presented in two different ways. In addition, stimulated-recall interviews were conducted with nine students who took part in the later lessons and exhibited strong emotions regarding the problem. The data suggest that the students' aesthetic response to the problem was essentially conditioned by the extent of their surprise as a result of revealing a clever solution to the problem after being exposed to repeated failed attempts. Implications for practice are drawn.

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“…Thus, a number of authors in aesthetics and the philosophy of mathematics have tried to shed light on mathematical beauty by highlighting its relation to such factors as order, harmony, unity, symmetry and simplicity (see Osborne 1984, Engler 1990 and, more recently, Inglis and Aberdein 2014 whose careful analysis sheds doubt on the connection between beauty and simplicity). Others have argued that judgments about the beauty of mathematics are related to the understanding or enlightenment that the mathematics affords (see Rota 1997 andCellucci 2015;cf. also Hardy's 1940 classic 'mathematician's apology').…”

mentioning

confidence: 99%

Introduction to Special Issue: Aesthetics in Mathematics†

Breitenbach

Rizza

2017

Philosophia Mathematica

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Mathematicians often appreciate the beauty and elegance of particular theorems, proofs, and definitions, attaching importance not only to the truth but also to the aesthetic merit of their work. As Henri Poincaré (1930: 59) put it, mathematical beauty is a 'real aesthetic feeling that all true mathematicians recognise'. Others went further, regarding mathematical beauty as a key motivation driving the formulation of mathematical proofs and even as a criterion for choosing one proof over another. As Hermann Weyl famously and provocatively declared, 'My work always tried to unite the true with the beautiful, but when I had to choose one or the other, I usually chose the beautiful' (cited in Chandrasekhar 1987: 52). Talk of the beauty of mathematical theorems, proofs, and definitions may thus be commonplace. And yet the tendency among mathematicians to judge mathematical work according to aesthetic standards raises a number of difficult questions: (1) What is mathematical beauty? What, if anything, distinguishes it from other kinds of beauty? Is it a feature of abstract objects or grounded in sensible properties? Is it a genuine aesthetic category or can it be reduced to non-aesthetic, possibly epistemic, criteria? (2) What is the status of aesthetic judgments in mathematics? Are they objective judgments grounded, for instance, in the mathematician's cognition of such properties as symmetry or simplicity? Do they rely on subjective responses

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Mathematical Beauty, Understanding, and Discovery

Cited by 28 publications

References 21 publications

Aesthetic values in science

Aesthetic values in science

Surprise and the Aesthetic Experience of University Students: A Design Experiment

Introduction to Special Issue: Aesthetics in Mathematics†

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