"There exists a passion for comprehension, just as there exists a passion for music. That passion is rather common in children but gets lost in most people later on. Without this passion, there would be neither mathematics nor natural science." (Albert Einstein, Scientific American Vol. 182 (4), 1950)
"Mathematics, like music and poetry, is a creation of the mind; [...] the primary task of the mathematician, like that of any other artist, is to extend man's mental horizon by representation and interpretation." (Graham Sutton, "Mathematics in Action", 1954)
"Is it possible to breach this wall, to present mathematics in such a way that the spectator may enjoy it? Cannot the enjoyment of mathematics be extended beyond the small circle of those who are ‘mathematically gifted’? Indeed, only a few are mathematically gifted in the sense that they are endowed with the talent to discover new mathematical facts. But by the same token, only very few are musically gifted in that they are able to compose music. Nevertheless, there are many who can understand and perhaps reproduce music, or who at least enjoy it. We believe that the number of people who can understand simple mathematical ideas is not relatively smaller than the number of those who are commonly called musical, and that their interest will be stimulated if only we can eliminate the aversion toward mathematics that so many have acquired from childhood experiences." (Hans Rademacher & Otto Toeplitz, "The Enjoyment of Mathematics", 1957)
"There is beauty in discovery. There is mathematics in music, a kinship of science and poetry in the description of nature, and exquisite form in a molecule. Attempts to place different disciplines in different camps are revealed as artificial in the face of the unity of knowledge. All illiterate men are sustained by the philosopher, the historian, the political analyst, the economist, the scientist, the poet, the artisan, and the musician." (Glenn T Seaborg, 1958)
"Languages, literature, art, music, history: are all self-evident helps - and even mathematics and sciences, by training memory and demanding the analytical approach, are helpful by indirection." (Irene Dunne, "If You Want Success", [Screenland Interview] 1961)
"Science begins with the world we have to live in, accepting its data and trying to explain its laws. From there, it moves toward the imagination: it becomes a mental construct, a model of a possible way of interpreting experience. The further it goes in this direction, the more it tends to speak the language of mathematics, which is really one of the languages of the imagination, along with literature and music." (Northrop Frye, "The Educated Imagination", 1963)
"The question ‘What is mathematics?’ cannot be answered meaningfully by philosophical generalities, semantic definitions or journalistic circumlocutions. Such characterizations also fail to do justice to music or painting. No one can form an appreciation of these arts without some experience with rhythm, harmony and structure, or with form, color and composition. For the appreciation of mathematics actual contact with its substance is even more necessary." (Richard Courant, "Mathematics in the Modern World", Scientific American Vol. 211 (3), 1964)
"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 and yet true." (Bertrand Russell, "Autobiography", 1967)
"The fact is that there are few more ‘popular’ subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable [...]" (Godfrey H Hardy, "A Mathematician’s Apology", 1967)
"The syntax and the grammar of the language of music are not capricious; they are dictated by the texture and organization of the deep levels of the mind, so with mathematics." (H E Huntley, "The Divine Proportion", 1970)
Note: The quotes have been reordered chronologically.
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