"[A] sequence is random if it has every property that is shared by all infinite sequences of independent samples of random variables from the uniform distribution." (J. N. Franklin, 1962)
"Mathematics is not a question of calculation perforce but rather the presence of royalty: a law of infinite resonance, consonance and order." (Le Corbusier, "Architecture and the Mathematical Spirit", 1962)
"It is paradoxical that while mathematics has the reputation of being the one subject that brooks no contradictions, in reality it has a long history of successful living with contradictions. This is best seen in the extensions of the notion of number that have been made over a period of 2500 years. From limited sets of integers, to infinite sets of integers, to fractions, negative numbers, irrational numbers, complex numbers, transfinite numbers, each extension, in its way, overcame a contradictory set of demands." (Philip J Davis, "The Mathematics of Matrices", 1965)
"The real difficulty lies in the fact that only a finite number of angels can dance on the head of a pin, whereas the mathematician is more apt to be interested in the infinite angel problem only." (Henri Lebesgue, "Mechanized Mathematics", Bulletin of the American Mathematical Society Vol. 72 (5), 1966)
"Older mathematics appears static while the newer appears dynamic, so that the older mathematics compares to the still-picture stage of photography while the newer mathematics compares to the moving-picture stage. Again, the older mathematics is to the newer much as anatomy is to physiology, wherein the former studies the dead body and the latter studies the living body. Once more, the older mathematics concerned itself with the fixed and the finite while the newer mathematics embraces the changing and the infinite." (Howard W Eves, "In Mathematical Circles", 1969)
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