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Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.
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Symmetry

 

Hermann Weyl

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Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.

 

David Deutsch

 

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

 

Aristotle

 

Dee goes so far as to assert that, although he called the work hieroglyphic, it is endowed with a clarity and rigour almost mathematical; yet at the same time he leaves it to the reader even to guess that the subject of the elaborate display, which he is asked to view in such dim light, is the hermetic quest. The semblance of clarity is achieved by discussing the dark subject under the guise of a symbolic sign invented by Dee, which is his monad. This symbol indeed lends itself easily to digressive secondary interpretations of a numerological, cabbalistic, astrological, cosmological, or mathematical nature, all which, however, are without any doubt given so as to establish significant connexions with the all-embracing central theme, alchemy, which is barely mentioned.

 

John Dee

 

So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentalization is really artificial, and we should take our intellectual pleasures where we find them.

 

Richard Feynman

 

Wherever Mathematics is mixed up with anything, which is outside its field, you will find attempts to demonstrate these merely conventional propositions a priori, and it will be your task to find out the false deduction in each case.

 

Carl Gustav Jacob Jacobi