We often hear people speak of something as being beautiful. For example, many believe that mathematics is a beautiful subject. What they mean by being beautiful varies by context, and is often regarded as a sort of subjective sentiments. That is, by a common belief, if someone does not "feel it", then it is impossible to explain "it" to them.

But is it really? For example, many abhor mathematics and do not believe that it is beautiful. Is it truly impossible for me to communicate my appreciation of the subject's aesthetic qualities? I'd like to believe it is not the case given that as human beings we share more or less equivalent mental faculties. If I were to advocate beauty of mathematics, what would be appropriate way of doing it so that the communication is philosophically sound? To provide a non-example, some mathematicians argue that mathematics is beautiful because it describes order and symmetry. But why is description of order and symmetry necessarily beautiful? So I don't think such arguments are philosophically sound or of much value as far as to convince a "non-believer" is concerned.

  • You can make arguments only to those who share some minimal basis for receiving them. That human beings share mental faculties is not enough for aesthetic judgments, as opposed to intellectual ones. If the basis for them is emotion (as many suspect) it is not surprising that some people are not receptive. You may still succeed not through argument but through evocation, presenting a side of mathematics that appeals to their emotions. Symmetry, surprising connections, mystique of shapes and numbers have a potential for that. Only then can one build some arguments around it. – Conifold Sep 19 '19 at 19:27
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    Some resources might be: Kant’s third critique; Heidegger’s On the Origin of the Work of Art; possibly Derrida’s The Truth in Painting – Joseph Weissman Sep 19 '19 at 21:39
  • This question could be improved by simplifying it to one primary question (and maybe explicitly asking for philosophical resources and references if that’s the core thing you want to achieve.) – Joseph Weissman Sep 28 '19 at 14:11
  • My favorite examples to evoke layman's interest in the mystic "beauty" of math is Zeno's Paradox and the unintuitive categorical difference of rationals vs irrationals. Zeno's paradox can invoke intellectual interest of infinitesimals. Showing the alternating topology of rationals and irrationals while the cardinality of irrationals are still bigger than rationals can evoke interest in Baire category theorem which may show why mundane experience is not enough to understand seemingly simple yet unexplainable phenomena. In effect, u're trying to change empiricism-like mind towards rationalism... – Double Knot Mar 18 at 18:43

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