"It is the intuition of pure number, that of pure logical forms, which illumines and directs those we have called analysts. This it is which enables them not alone to demonstrate, but also to invent." (Henri Poincaré, "The Value of Science", 1905)
"Architecture is geometry made visible in the same sense that music is number made audible." (Claude F Bragdon, "The Beautiful Necessity: Seven Essays on Theosophy and Architecture", 1910)
"In the beginning of algebra, even the most intelligent child finds, as a rule, very great difficulty. The use of letters is a mystery, which seems to have no purpose except mystification. It is almost impossible, at first, not to think that every letter stands for some particular number, if only the teacher would reveal what number it stands for." (Bertrand Russell, "Mysticism and Logic: And Other Essays", 1910)
"Mathematics abstracts from all the particular properties of the elements hidden behind its schemata. This is achieved by mathematics with the help of indifferent symbols, like numbers or letters. Tektology must do likewise. Its generalizations should abstract from the concreteness of elements whose organizational relationships they express, and conceal this concreteness behind indifferent symbols." (Alexander Bogdanov, "Tektology: The Universal Organizational Science" Vol. I, 1913)
"The way to enable a student to apprehend the instrumental value of arithmetic is not to lecture him on the benefit it will be to him in some remote and uncertain future, but to let him discover that success in something he is interested in doing depends on ability to use numbers." (John Dewey, "Democracy and Education: An Introduction to the Philosophy of Education", 1916)
"Through and through the world is infected with quantity: To talk sense is to talk quantities. It is not use saying the nation is large - How large? It is no use saying the radium is scarce - How scarce? You cannot evade quantity. You may fly to poetry and music, and quantity and number will face you in your rhythms and your octaves." (Alfred N Whitehead, "The Aims of Education and Other Essays", 1917)
"It is not surprising that the greatest mathematicians have again and again appealed to the arts in order to find some analogy to their own work. They have indeed found it in the most varied arts, in poetry, in painting, and in sculpture, although it would certainly seem that it is in music, the most abstract of all the arts, the art of number and of time, that we find the closest analogy." (Havelock Ellis, "The Dance of Life", 1923)
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