It is difficult to give an idea of the vast extent of modern mathematics. The word 'extent' is not the right one: I mean extent crowded with beautiful detail—not an extent of mere uniformity such as an objectless plain, but of a tract of beautiful country seen at first in the distance, but which will bear to be rambled through and studied in every detail of hillside and valley, stream, rock, wood, and flower. But, as for every thing else, so for mathematical theory—beauty can be perceived but not explained.
The Collected Mathematical Papers of Arthur Cayley
Presidential Address to the British Association September 1883 (p. 449)
This "shuddering before the beautiful", this incredible fact that a discovery motivated by a search after the beautiful in mathematics should find its exact replica in Nature, persuades me to say that beauty is that to which the human mind responds at its deepest and most profound.
Truth and Beauty: Aesthetics and Motivations in Science Shakespeare, Newton, and Beethoven, or Patterns of Creativity (p. 54)
Admiration of those beauties of the inanimate world, which modern poetry so largely and so eloquently describes, is not, even in the best of us, one of the original instincts of our nature. As children, we none of us possess it. No uninstructed man or woman possesses it. Those whose lives are exclusively passed amidst the ever changing wonders of sea and land are also those who are most universally insensible to every aspect of Nature not directly associated with the human interest of their calling. Our capacity of appreciating the beauties of the earth we live on is, in truth, one of the civilized accomplishments which we all learn, as an art;
and, more, that very capacity is rarely practised by any of us except when our minds are most indolent and most unoccupied.
The Woman in White The First Epoch The Story Begun by Walter Hartright Chapter VIII (pp. 41-2)
Among the many and varied literary and artistic studies upon which the natural talents of man are nourished, I think that those above all should be embraced and pursued with the most loving care which have to do with things that are very beautiful and very worthy of knowledge.
On the Revolutions of the Heavenly Spheres Book One (p. 510)
It is quite clear that beauty does depend on one's culture and upbringing for certain kinds of beauty, pictures, literature, poetry and so on...But mathematical beauty is of a rather different kind. I should say perhaps it is of a completely different kind and transcends these personal factors. It is the same in all countries and at all periods of time.
In Helge Kragh Dirac: A Scientific Biography Chapter 14 (p. 288)
We may try to make progress by following in Hamilton's footsteps, taking mathematical beauty as our guiding beacon, and setting up theories which are of interest, in the first place, only because of the beauty of their mathematics. We may then hope that such equations will ultimately prove their value in physics, basing this hope on the belief that Nature demands mathematical beauty in her laws.
Proceedings of the Royal Irish Academy Hamiltonian Methods and Quantum Mechanics (p. 59) Volume 63, Section A, Number 3, January 1964
It is impossible to follow the march of one of the greatest theories of physics, to see it unroll majestically its regular deductions starting from initial hypotheses, to see its consequences represent a multitude of experimental laws down to the smallest detail, without being charmed by the beauty of such a construction, without feeling keenly that such a creation of the human mind is truly a work of art.
The Aim and Structure ofPhysical Theory Chapter II (p. 24)
Emerson, Ralph Waldo
I do not wonder at a snow-flake, a shell, a summer landscape, or the glory of the stars; but at the necessity of beauty under which the universe lies.
Essays and Lectures The Conduct of Life Fate (p. 967)
For the world is not painted, or adorned, but is from the beginning beautiful; and God has not made some beautiful things, but Beauty is the creator of the Universe.
Essays and Lectures Essays Second Series The Poet (p. 449)
Our Science, which we loved above everything, had brought us together. It appeared to us as a flowering garden. In this garden there were well-worn paths where one might look around at leisure and enjoy oneself without effort, especially at the side of a congenial companion. But we also liked to seek out hidden trails and discovered many an unexpected view which was pleasing to our eyes; and when the one pointed it out to the other, and we admired it together, our joy was complete.
In S. Chandrasekhar Truth and Beauty: Aesthetics and Motivation in Science Chapter 3, Section VI (p. 52)
Leibniz, Gottfried Wilhelm
The beauty of nature is so great and its contemplation so sweet. ..whoever tastes it, can't help but view all other amusements as inferior.
In Ernst Peter Fischer Beauty and the Beast Chapter 2 (p. 47)
Misner, Charles W. Thorne, Kip S. Wheeler, John
Some day a door will surely open and expose the glittering central mechanism of the world in all its beauty and simplicity.
Gravitation Chapter 44 (p. 1197)
...what are the mathematical entities to which we attribute this character of beauty and elegance, and which are capable of developing in us a kind of aesthetic emotion? They are those whose elements are harmoniously disposed so that the mind without effort can embrace their totality while realizing the details. This harmony is at once a satisfaction of our aesthetic needs and an aid to the mind, sustaining and guiding.
The Foundations of Science Science and Method Chapter III (p. 391)
Beautiful are the things we see
More beautiful those we understand
Much the most beautiful those we do not comprehend.
Introductory Lecture Copenhagen Anatomical Theater 1673 Source unknown
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