What is going on with Russell's "beauty cold and austere" of mathematics?

Philosophy Asked by user25714 on August 21, 2020

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?

2 Answers

I hate that quote. Mathematics is a human creation, warm and kind, flawed and repairable, just like art (which was perfectly clear to the Eastern philosophers and poets, see Lu Chi' s Wen Fu in the 3rd century). To turn mathematics into an untouchable statue means to put a weapon in the hands of tyrants to intimidate and deceive their subjects. A child who experiences an AHA moment during an experiment in math or geometry is much more of a follower of Archimedes than an academic flying on his Laputa carpet enveloped in a cloud of arrogance and stupidity.

Answered by István Lénárt on August 21, 2020

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 incredible 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.'

Answered by linkhyrule5 on August 21, 2020

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