-
Bertrand Russell (1872-1970), Autobiography, George
Allen and Unwin Ltd, 1967, v1, p158
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.
-
Aristotle (384 B.C.-322 B.C.), Poetics
Beauty depends on size as well as symmetry.
-
J.H.Poincare (1854-1912), (cited in H.E.Huntley, The Divine
Proportion, Dover, 1970)
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.
-
J.Bronowski, Science and Human Values, Pelican, 1964.
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.
-
J.W.N.Sullivan (1886-1937), Aspects of Science, 1925.
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.
-
G.H.Hardy (1877 - 1947), A Mathematician's Apology,
Cambridge University Press, 1994.
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.
-
Lawrence University
catalog, Cited in Essays in Humanistic Mathematics, Alvin White, ed, MAA,
1993
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.
-
I.Newton, Letter to H.Oldenburg, the Secretary of the Royal
Society, October 24, 1676, in A Source Book in 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 Leibnitz and Tschirnhaus. Leibnitz's
method for obtaining convergent series is certainly very elegant...
-
Jane Muir, Of Men & Numbers, Dover, 1996.
Gauss: You have no idea how much poetry there is in
the calculation of a table of logarithms!
-
F.Dyson, in Nature, March 10, 1956
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))
-
O.Spengler, in J.Newman, The World of Mathematics,
Simon & Schuster, 1956
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."
-
O.Spengler, in J.Newman, The World of Mathematics,
Simon & Schuster, 1956
"A mathematician," said old Weierstrass, "who is not
at the same time a bit of a poet will never be a full mathematician."
-
Jakob Bernoulli, Tractatus de Seriebus Infinitis,
1689 (quoted in From Five Fingers to Infinity, F.J.Swetz (ed), Open
Court, 1996)
So the soul of immensity dwells in minutia.
And in narrowest limits no limits inhere.
What joy to discern the minute in infinity!
The vast to perceive in the samll, what divinity! |
-
S.Lang, The Beauty of Doing Mathematics, Springer-Verlag,
1985
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
answred: "The manipulation of notes?"
Manifesto
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