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I admit that this is an idle question, but I wondered why it is that mathematics appears "beautiful cold and austere" to those who are particularly gifted at it. The full quite from wikipedia on this is, from Russell:

Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.

I can relate to ideas, from wikipedia, of "elegance", and "depth", which may be why I like chat about philosophy. And, applied mathematics can be pleasing, I agree.

But it's those terms "austere" and "cold" which I cannot relate to. Is that Betrand's philosophy, or does it apply to some aspect of maths -- that is only available to some few?

  • a bit "what is a star" but yea – user25714 Apr 7 '17 at 3:11
  • oh come on what's wrong with this question -- please? – user25714 Apr 7 '17 at 3:45
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    Someone who took several hundred pages to prove that 1 + 1 = 2 might possibly be drawn to the cold and austere. Russell's view says more about Russell than about math. At least that's a point of view that might be argued. What is different about math versus music is that you can only appreciate math to the degree that you've spent years learning to understand it; whereas music and art can be appreciated by anyone. But that doesn't make math's beauty cold and austere; only difficult to access. Once one accesses it, it can be warm and fuzzy. Fuzzy sets for example :-) – user4894 Apr 7 '17 at 4:01
  • @user4894 appreciate the comment, thanks – user25714 Apr 7 '17 at 4:29
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    Maybe relevant: The Phenomenology of Mathematical Beauty, in Gian-Carlo Rota & Fabrizio Palombi, Indiscrete thoughts, Birkhäuser (1997) – Mauro ALLEGRANZA Apr 7 '17 at 12:26
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Belated and subjective, but I had an answer that didn't appear in the comments so I thought I'd mention it:

The beauty of mathematics is cold and austere because of how dreadfully, terrifyingly simple it is. It certainly doesn't look like it from the outside, I'm sure -- but having studied, you quickly realize that unlike any other field mathematics contains absolutely nothing but what is absolutely necessary -- indeed, it could be defined as "that which follows from a minimal set of assumptions."

Where beauty in other forms is, to paraphrase Millay, 'clothed' in trappings of culture or appeal or simply a richer narrative of many interweaving parts, the beauty of mathematics is 'bare'. There is something sublime in a proof -- most especially, those that start from incredibly obvious assumptions and yet prove that something not at all obvious must hold in incredibly generality -- and yet by its very nature there is nothing else, nothing but that sublime-ness.

Thus is the beauty of mathematics 'sublimely pure,' 'cold and austere.'

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