Although mathematicians often use it, mathematical beauty is a philosophically challenging concept. How can abstract objects be evaluated as beautiful? Is this related to the way we visualise them? Using a case study from graph theory (the highly symmetric Petersen graph), this paper tries to analyse aesthetic preferences in mathematical practice and to distinguish genuine aesthetic from epistemic or practical judgements. It 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.

中文翻译：

---

数学中的审美偏好：案例研究†

尽管数学家经常使用它，但数学美是一个哲学上具有挑战性的概念。抽象的物体如何被评价为美的？这与我们想象它们的方式有关吗？使用图论（高度对称的彼得森图）的案例研究，本文试图分析数学实践中的审美偏好，并将真正的审美与认知或实践判断区分开来。它认为，在进行审美判断时，数学家可能对视觉表征的感知特性和抽象结构的数学特性的组合做出反应；后者似乎具有更大的重量。因此，数学美主要涉及数学家对抽象美学的敏感性。