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To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in.
--
The Character of Physical Law (1965) Ch. 2

 

Richard Feynman

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Ruskin's special gift was the feeling for beauty, in nature as in art. It was in Beauty that his nature led him to seek reality, and his entirely religious life received from it an entirely aesthetic use. But this Beauty to which he thus happened to dedicate his life was not conceived by him as an object of enjoyment made to charm, but as a reality infinitely more important than life, for which he would have given his own life. From this, as you will see, the whole aesthetic system of Ruskin follows. First, you will understand that the years when he became acquainted with a new school of architecture or of painting were the principal landmarks in the development of his ethics. He would speak of the years when Gothic art presented itself to him with the same gravity, the same emotional nostalgia, the same serenity with which a Christian speaks of the day the truth was revealed to him.

 

John Ruskin

 

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe.

 

Paul Dirac

 

I wanted very much to learn to draw, for a reason that I kept to myself: I wanted to convey an emotion I have about the beauty of the world. It's difficult to describe because it's an emotion. It's analogous to the feeling one has in religion that has to do with a god that controls everything in the whole universe: there's a generality aspect that you feel when you think about how things that appear so different and behave so differently are all run "behind the scenes" by the same organization, the same physical laws. It's an appreciation of the mathematical beauty of nature, of how she works inside; a realization that the phenomena we see result from the complexity of the inner workings between atoms; a feeling of how dramatic and wonderful it is. It's a feeling of awe — of scientific awe — which I felt could be communicated through a drawing to someone who had also had this emotion. It could remind him, for a moment, of this feeling about the glories of the universe.

 

Richard Feynman

 

We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry. There will come with the greater love of science greater love to one another. Living more nearly to Nature is living farther from the world and from its follies, but nearer to the world's people; it is to be of them, with them, and for them, and especially for their improvement. We cannot see how impartially Nature gives of her riches to all, without loving all, and helping all; and if we cannot learn through Nature's laws the certainty of spiritual truths, we can at least learn to promote spiritual growth while we are together, and live in a trusting hope of a greater growth in the future.

 

Maria Mitchell

 

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 highest excellence, is to be found in mathematics as surely as in poetry.

 

Bertrand Russell