Music and Mathematics IV

"There are certain pleasures which only fill the outward senses, and there are others also which pertain only to the mind or reason; but music is a delectation so put in the midst that both by the sweetness of the sounds it moveth the senses, and by the artificiousness of the number and proportions it delighteth reason itself." (John Northbrooke , "Against Dicing", 1577)

"Nothing is more futile than theorizing about music. No doubt there are laws, mathematically strict laws, but these laws are not music; they are only its conditions […] The essence of music is revelation." (Heinrich Heine, "Letters on the French Stage", 1837)

"I think it would be desirable that this form of word [mathematics] should be reserved for the applications of the science, and that we should use mathematic in the singular to denote the science itself, in the same way as we speak of logic, rhetoric, or (own sister to algebra) music." (James J Sylvester, Collected Mathematical Papers, 1869)

"Music is an order of mystic, sensuous mathematics. A sounding mirror, an aural mode of motion, it addresses itself on the formal side to the intellect, in its content of expression it appeals to the emotions." (James G Huneker, "Chopin", 1900)

"Mathematics, rightly viewed, possesses not only truth, but supreme beauty - a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show." (Bertrand Russell, 'The Study of Mathematics", 1902)

"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)

"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)

"Skills are to mathematics what scales are to music or spelling is to writing. The objective of learning is to write, to play music, or to solve problems -  not just to master skills." (William Briggs, 2005)

"Mathematical ideas like number can only be really 'seen' with the 'eyes of the mind' because that is how one 'sees' ideas. Think of a sheet of music which is important and useful but it is nowhere near as interesting, beautiful or powerful as the music it represents. One can appreciate music without reading the sheet of music. Similarly, mathematical notation and symbols on a blackboard are just like the sheet of music; they are important and useful but they are nowhere near as interesting, beautiful or powerful as the actual mathematics (ideas) they represent." (Fiacre O Cairbre, "The Importance of Being Beautiful in Mathematics", IMTA Newsletter 109, 2009)

"A surprising proportion of mathematicians are accomplished musicians. Is it because music and mathematics share patterns that are beautiful?" (Martin Gardner, The Dover Math and Science Newsletter, 2011)