These observations by noted visual artists, mathematicians and scientists are ones with which we feel great sympathy. They may help begin to articulate the spirit that motivates our efforts. (And rather than emailing us to complain that we only quote men, why not send us your suggestions, we're looking for great quotes from women too.)

	Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree. - Aristotle (384 - 322 B.C.), Metaphysics, Bk. XIII, Ch.3, 1078a, 33 ff.
	It is more important to have beauty in one's equations than to have them fit experiment... If one is working from the point of view of getting beauty in one's equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one's work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor features that are not properly taken into account and that will get cleared up with further development of the theory. - Paul Adrien Maurice Dirac (1902 - 1984) Scientific American, May 1963
	The ideas in the Large Glass are more important than the actual realization. The "Large Glass" constitutes a rehabilitation of perspective. For me, it's a mathematical, scientific perspective, based on calculations and on dimensions. Everything was becoming conceptual, that is, it depended on things other than the retina. What we were interested in at the time was the fourth dimension. Simply, I thought of the idea of a projection, of an invisible fourth dimension, something you couldn't see with your eyes. "The Bride" in the "Large Glass" was based on this, as if it were the projection of a four-dimensional object. I called "The Bride" a "delay in glass." A tactile sensation which envelopes every side of an object approaches a tactile sensation of four dimensions. Consequently the act of love as tactile sublimation could be felt as a physical interpretation of the 4th dimension. - Marcel Duchamp (1887-1968)
	Sane judgment abhors nothing so much as a picture perpetrated with no technical knowledge, although with plenty of care and diligence. Now the sole reason why painters of this sort are not aware of their own error is that they have not learnt Geometry, without which no one can either be or become an absolute artist; but the blame for this should be laid upon their masters, who are themselves ignorant of this art. - Albrecht Dürer (1471-1528), The Art of Measurement. 1525 Geometry is the right foundation of all painting. - Albrecht Dürer (1471-1528), Course in the Art of Measurement
	The most beautiful thing we can experience is the mysterious. It is the source of all true art and science. - Albert Einstein (1879 - 1955), What I Believe
	It is possible to know when you are right way ahead of checking all the consequences. You can recognize truth by its beauty and simplicity. - Richard Feynman (1918 - 1988), The Character of Physical Law, M.I.T. Press, Cambridge and London,1965
	I am interested in mathematics only as a creative art. - Godfrey H. Hardy (1877 - 1947) A Mathematician's Apology, London, Cambridge University Press, 1941 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. - Godfrey H. Hardy (1877 - 1947) A Mathematician's Apology, London, Cambridge University Press, 1941
	If you scorn painting, which is the sole imitator of all manifest works of nature, you will certainly be scorning a subtle invention, which with philosophical and subtle speculation considers all manner of forms: sea, land, trees, animals, grasses, flowers, all of which are enveloped in light and shade. Truly this is science, the legitimate daughter of nature, because painting is born of that nature; but to be more correct, we should say the granddaughter of nature, because all visible things have been brought forth by nature and it is among these that painting is born. - Leonardo da Vinci (1452 - 1519), in M. Kemp, ed., Leonardo on Painting, Yale University Press, New Haven and London, 1989 That mental discourse that originates in first principles is termed science. Nothing can be found in nature that is not part of science, like continuous quantity, that is to say, geometry, which, commencing with the surfaces of bodies, is found to have its origins in lines, the boundary of these surfaces. Yet we do not remain satisfied with this, in that we know that line has its conclusion in a point, and nothing can be smaller than that which is a point. Therefore the point is the first principle of geometry, and no other thing can be found either in nature or in the human mind that can give rise to the point.... No human investigation may claim to be a true science if it has not passed through mathematical demonstrations... The principle of the science of painting is the point; second is the line; third is the surface; fourth is the body which is enclosed by these surfaces. And that is just what is to be represented...since in truth the scope of painting does not extend beyond the representation of the solid body or the shape of all the things that are visible. - Leonardo da Vinci (1452 - 1519), in M. Kemp, ed., Leonardo on Painting, Yale University Press, New Haven and London, 1989
	A scientist worthy of his name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. - Jules Henri Poincaré (1854 - 1912) in N. Rose, Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988 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. - Jules Henri Poincaré (1854 - 1912)
	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. - Hermann Weyl (1885 - 1955) quoted in an obituary by Freeman J. Dyson in Nature, March 10, 1956