Word
Gems
What is a
man but the sum of his thoughts?
Beauty:
Math
& Science
- Hermann
Weyl: "My
work has always tried to unite the true with the beautiful and when I had to choose one or
the other, I usually chose the beautiful."
- Buckminster Fuller: "When I am working on a problem, I
never think about beauty. I
only think of how to solve the problem. But, when I have finished, if the solution is not
beautiful, I know it is wrong."
- Werner Heisenberg, writing to Albert
Einstein: "You may object that by speaking of simplicity and beauty I am
introducing aesthetic criteria of truth, and I frankly admit that I am strongly attracted
by the simplicity and beauty of the mathematical schemes which nature presents us. You
must have felt this too: the almost frightening simplicity and wholeness of the
relationship, which nature suddenly spreads out before us."
- Albert Einstein: "The
pursuit of truth and beauty is a sphere of activity in which we are permitted to remain
children all our lives."
- Jules Henri Poincare: "The scientist does not study nature
because it is useful; he studies it because he delights in it, and he delights in it
because it is beautiful. If nature were not beautiful, it would not be worth knowing, and
if nature were not worth knowing, life would not be worth living. Of course, I do not here
speak of that beauty which strikes the senses, the beauty of qualities and appearances;
not that I undervalue such beauty, far from it, but it has nothing to do with science; I
mean that profounder beauty which comes from the harmonious order of the parts and which a
pure intelligence can grasp. This it is which gives body, a structure so to speak, to the
iridescent appearances which flatter our senses, and without this support the beauty of
these fugitive dreams would be only imperfect, because it would be vague and always
fleeting."
- H. E. Huntley, The Divine Proportion: "If a poet
sees beauty in a rainbow ... so does the physicist in the laws governing its
manifestation. The surface beauty of the rainbow ... is appreciated by all men: it is
given. But the buried beauty, uncovered by the industrious researches of the physicist, is
understood only by the scientifically literate. It is acquired: education is
essential."
- J. B. Shaw: "The mathematician is fascinated with the
marvelous beauty of the forms he constructs, and in their beauty he finds everlasting
truth."
- J. W. A. Young: "Mathematics has beauties of its own -- a
symmetry and proportion in its results, a lack of superfluity, an exact adaptation of
means to ends, which is exceedingly remarkable and to be found only in the works of the
greatest beauty. When this subject is properly ... presented, the mental emotion should be
that of enjoyment of beauty..."
- J.J. Sylvester Presidential Address to British Association, 1869:
"The world of ideas which it [mathematics] discloses or illuminates, the
contemplation of divine beauty and order which it induces, the harmonious connexion of its
parts, the infinite hierarchy and absolute evidence of the truths with which it is
concerned, these, and such like, are the surest grounds of the title of mathematics to
human regard, and would remain unimpeached and unimpaired were the plan of the universe
unrolled like a map at our feet, and the mind of man qualified to take in the whole scheme
of creation at a glance."
- Bertrand Russell: "Mathematics, rightly viewed, posses not
only truth, but supreme beauty -- a beauty cold and austere, like that of sculpture."
- Eric Temple Bell (1883-1960): "Guided only by their feeling
for symmetry, simplicity, and generality, and an indefinable sense of the fitness of
things, creative mathematicians now, as in the past, are inspired by the art of
mathematics rather than by any prospect of ultimate usefulness."
- Godfrey H. Hardy (1877 - 1947), A Mathematician's Apology:
"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."
- Albert Einstein: "Everything should be made as simple as
possible, but not simpler."
- Albert Einstein: "... in nature is actualized the idea of
mathematical simplicity."
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