On Elegance (Unsourced)

"A proof tells us where to concentrate our doubts. […] An elegantly executed proof is a poem in all but the form in which it is written." (Morris Kline)

"Complex numbers are really not as complex as you might expect from their name, particularly if we think of them in terms of the underlying two dimensional geometry which they describe. Perhaps it would have been better to call them 'nature's numbers'. Behind complex numbers is a wonderful synthesis between two dimensional geometry and an elegant arithmetic in which every polynomial equation has a solution."

"Engineering is not merely knowing and being knowledgeable, like a walking encyclopedia; engineering is not merely analysis; engineering is not merely the possession of the capacity to get elegant solutions to non-existent engineering problems; engineering is practicing the art of the organizing forces of technological change. [...] Engineers operate at the interface between science and society." (Gordon S Brown)

"I was struck by the art with which mathematicians remove, reject, and little by little eliminate everything that is not necessary for expressing the absolute with the least possible number of terms, while preserving in the arrangement of these terms a discrimination, a parallelism, a symmetry which seems to be the visible elegance and beauty of an eternal idea." (Edgar Quinet)   

"In the Theory of Numbers it happens rather frequently that, by some unexpected luck, the most elegant new truths spring up by induction." (Carl F Gauss)

"Mathematics is much more than a language for dealing with the physical world. It is a source of models and abstractions which will enable us to obtain amazing new insights into the way in which nature operates. Indeed, the beauty and elegance of the physical laws themselves are only apparent when expressed in the appropriate mathematical framework." (Melvin Schwartz)

"One would be hard put to find a set of whole numbers with a more fascinating history and more elegant properties surrounded by greater depths of mystery - and more totally useless - than the perfect numbers." (Martin Gardner)

"Pure mathematics can be practically useful and applied mathematics can be artistically elegant." (Paul R Halmos)

"The equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle." (Edward Witten )

"[…] the feeling of mathematical beauty, of the harmony of numbers and of forms, of geometric elegance. It is a genuinely esthetic feeling, which all mathematicians know. And this is sensitivity." (Henri Poincaré)

"The mathematician is perfect only in so far as he is a perfect being, in so far as he perceives the beauty of truth; only then will his work be thorough, transparent, comprehensive, pure, clear, attractive, and even elegant." (Johann Wolfgang von Goethe)

"There is no getting out of it. Through and through the world is infected with quantity. To talk sense is to talk in quantities. […] You cannot evade quantity. You may fly to poetry and to music, and quantity and number will face you in your rhythms and your octaves. Elegant intellects which despise the theory of quantity are but half developed. They are more to be pitied than blamed." (Alfred N Whitehead)

"There was a moment when I knew how nature worked. It had elegance and beauty. The goddamn thing was gleaming." (Richard Feynman)

"Today we can say that the abstract beauty of the theory is flanked by the plastic beauty of the curve, a beauty that is astounding. Thus, within this mathematics that is a hundred years old, very elegant from a formal point of view, very beautiful for specialists, there is also a physical beauty that is accessible to everyone. [...] By letting the eye and the hand intervene in the mathematics, not only have we found again the ancient beauty, which remains intact, but we have also discovered a new beauty, hidden and extraordinary. [...] Those who are only concerned with practical applications may perhaps tend not to insist too much on the artistic aspect, because they prefer to entrench themselves in the technicalities that appertain to practical applications. But why should the rigorous mathematician be afraid of beauty?" (Benoît B Mandelbrot)

"What is especially striking and remarkable is that in fundamental physics, a beautiful or elegant theory is more likely to be right than a theory that is inelegant. A theory appears to be beautiful or elegant (or simple, if you prefer) when it can be expressed concisely in terms of mathematics we already have." (Murray Gell-Mann)