"As every mathematician knows, nothing is more fruitful than these obscure analogies, these indistinct reflections of one theory into another, these furtive caresses, these inexplicable disagreements; also nothing gives the researcher greater pleasure." (André Weil, "De la Métaphysique aux Mathématiques", 1960)
"In fact, the construction of mathematical models for various fragments of the real world, which is the most essential business of the applied mathematician, is nothing but an exercise in axiomatics." (Marshall Stone, cca 1960)
"Nothing in our experience suggests the introduction of [complex numbers]. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius." (Eugene P Wigner, “The Unreasonable Effectiveness of Mathematics in the Natural Sciences”, Communications in Pure and Applied Mathematics 13 (1), 1960)
"Nothing is more fruitful - all mathematicians know it - than those obscure analogies, those disturbing reflections of one theory on another; those furtive caresses, those inexplicable discords; nothing also gives more pleasure to the researcher. The day comes when this illusion dissolves: the presentiment turns into certainty; the yoked theories reveal their common source before disappearing. As the Gita teaches, one achieves knowledge and indifference at the same time. Metaphysics has become Mathematics, ready to form the material of some treatise whose cold beauty has lost the power to move us." (André Weil, "De la métaphysique aux mathématiques", 1960)
"It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better." (Paul Dirac, "The Evolution of the Physicist's Picture of Nature", 1963)
"Mathematics is a creation of the mind. To begin with, there is a collection of things, which exist only in the mind, assumed to be distinguishable from one another; and there is a collection of statements about these things, which are taken for granted. Starting with the assumed statements concerning these invented or imagined things, the mathematician discovers other statements, called theorems, and proves them as necessary consequences. This, in brief, is the pattern of mathematics. The mathematician is an artist whose medium is the mind and whose creations are ideas." (Hubert S Wall," Creative Mathematics", 1963)
"A theory with mathematical beauty is more likely to be correct than an ugly one that fits some experimental data. God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe." (Paul Dirac, Scientific American, 1963)
"[…] it is more important to have beauty in one's equations that to have them fit experiment. […] It seems that 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." (Paul Dirac, Scientific American, 1963)
"The mathematicians and physics men have their mythology; they work alongside the truth, never touching it; their equations are false But the things work. Or, when gross error appears, they invent new ones; they drop the theory of waves In universal ether and imagine curved space." (Robinson Jeffers," The Beginning and the End and Other Poems, The Great Wound", 1963)
"It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together." (Richard Courant, "Mathematics in the Modern World", Scientific American Vol. 211, 1964)
"When the problems in physics become difficult we may often look to the mathematician who may already have studied such things and have prepared a line of reasoning for us to follow. On the other hand they may not have, in which case we have to invent our own line of reasoning, which we then pass back to the mathematician." (Richard Feynman,"The Character of Physical Law", 1965)
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