"The function of a mathematician, then, is simply to observe the facts about his own intricate system of reality, that astonishingly beautiful complex of logical relations which forms the subject-matter of his science, as if he were an explorer looking at a distant range of mountains, and to record the results of his observations in a series of maps, each of which is a branch of pure mathematics. […] Among them there perhaps none quite so fascinating, with quite the astonishing contrasts of sharp outline and shade, as that which constitutes the theory of numbers." (Godfrey H. Hardy, "The Theory of Numbers", Nature 1922)
"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)
"Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers; the law of revolution is not a social law, but an immeasurably greater one. It is a cosmic, universal law - like the laws of the conservation of energy and of the dissipation of energy" (entropy)." (Yevgeny Zamiatin, "On Literature, Revolution, Entropy, and Other Matters", 1923)"
"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)
"Revolution is everywhere, in everything. It is infinite. There is no final revolution, no final number. The social revolution is only one of an infinite number of numbers; the law of revolution is not a social law, but an immeasurably greater one. It is a cosmic, universal law - like the laws of the conservation of energy and of the dissipation of energy" (entropy)." (Yevgeny Zamiatin, "On Literature, Revolution, Entropy, and Other Matters", 1923)
"Number knows no limitations, either from the side of the infinitely great or from the side of the infinitely small, and the facility it offers for generalization is too great for us not to be tempted by it." (Émile Borel, "Space and Time", 1926)
"The fundamental laws of chemistry which are well known to you and which are laws of discontinuity" (discontinuity between chemical species, and discontinuous variation according to the 'multiple proportions' in the composition of species made from the same simple bodies) then become immediately clear: they are imposed solely by the condition that the molecule constituting a compound contains a necessarily whole number of atoms of each of the simple bodies combined in this compound." (Jean-Baptiste Perrin, "Discontinuous Structure of Matter", [Nobel lecture] 1926)
"Number theory is useful, since one can graduate with it." (Edmund Landau, "Vorlesungen über Zahlentheorie", ["Lectures on Number Theory"], 1927)
"The mystery that clings to numbers, the magic of numbers, may spring from this very fact, that the intellect, in the form of the number series, creates an infinite manifold of well distinguishable individuals. Even we enlightened scientists can still feel it e.g. in the impenetrable law of the distribution of prime numbers." (Hermann Weyl, "Philosophy of Mathematics and Natural Science", 1927)
"The difference between commensurable and incommensurable in its strict sense" (and hence also the concept of irrational number) belongs solely to precision mathematics." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)
"Numbers are not just counters; they are elements in a system." (Scott Buchanan, "Poetry and Mathematics", 1929)
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