Berikut ini ada beberapa ungkapan dari matematikawan tentang kecantikan ilmu matematika, tapi dalam bahasa inggris, saya tidak begitu berani untuk menterjemahkannya karena bahasanya begitu berat dan ada beberapa yang membuat saya tidak mengerti, alhasil malah tidak membuat matematika kelihatan cantik tapi malah sebaliknya.
Dan ungkapan-ungkapan tersebut adalah sebagai berikut:
It seems to me now that mathematics is capable of an artistic excellence as great as that of any music, perhaps greater; not because the pleasure it gives (although very pure) is comparable, either in intensity or in the number of people who feel it, to that of music, but because it gives in absolute perfection that combination, characteristic of great art, of godlike freedom, with the sense of inevitable destiny; because, in fact, it constructs an ideal world where everything is perfect but true.
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.
Beauty depends on size as well as symmetry.
The mathematician does not study pure mathematics because it is useful; he studies it because he delights in it and he delights in it because it is beautiful.
Mathematics in this sense is a form of poetry, which has the same relation to the prose of practical mathematics as poetry has to prose in any other language. The element of poetry, the delight of exploring the medium for its own sake, is an essential ingredient in the creative process.
Mathematics, as much as music or any other art, is one of the means by which we rise to a complete self-consciousness. The significance of Mathematics resides precisely in the fact that it is an art; by informing us of the nature of our own minds it informs us of much that depends on our minds.
The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way. Beauty is the first test: there is no permanent place in this world for ugly mathematics.
Born of man’s primitive urge to seek order in his world, mathematics is an ever-evolving language for the study of structure and pattern. Grounded in and renewed by physical reality, mathematics rises through sheer intellectual curiosity to levels of abstraction and generality where unexpected, beautiful, and often extremely useful connections and patterns emerge. Mathematics is the natural home of both abstract thought and the laws of nature. It is at once pure logic and creative art.
Mathematics, D. J. Struik, ed, Princeton University Press, 1990
I can hardly tell with what pleasure I have read the letters of those very distinguished men Leibniz and Tschirnhaus. Leibniz’s method for obtaining convergent series is certainly very elegant…
Gauss: You have no idea how much poetry there is in the calculation of a table of logarithms!
Characteristic of Weyl was an aesthetic sense which dominated his thinking on all subjects. He once said to me, half-joking, “My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful.” (Herman Weyl (1885-1955))
To Goethe again we owe the profound saying: “the mathematician is only complete in so far as he feels within himself the beauty of the true.”
“A mathematician,” said old Weierstrass, “who is not at the same time a bit of a poet will never be a full mathematician.”
Last time, I asked: “What does mathematics mean to you?” And some people answered: “The manipulation of numbers, the manipulation of structures.” And if I had asked what music means to you, would you have answered: “The manipulation of notes?”