"[…] evolution is only one aspect of the order of nature, of the relations of cause and effect, of continuity of space and time, which pervade the universe and enable us to comprehend its simplicity of plan, its complexity of detail." (William D Matthew, Natural History Vol. 25 (2), 1925)
"It seems clear that [set theory] violates against the essence of the continuum, which, by its very nature, cannot at all be battered into a single set of elements. Not the relationship of an element to a set, but of a part to a whole ought to be taken as a basis for the analysis of a continuum." (Hermann Weyl, "Riemanns geometrische Ideen, ihre Auswirkungen und ihre Verknüpfung mit der Gruppentheorie", 1925)
"In classical science, it was strange to find that action [...] should yet present the artificial aspect of an energy in space multiplied by a duration. As soon, however, as we realise that the fundamental continuum of the universe is one of space-time and not one of separate space and time, the reason for the importance of the seemingly artificial combination of space with time in the expression for the action receives a very simple explanation. Henceforth, action is no longer energy in a volume of space multiplied by a duration; it is simply energy in a volume of the world, that is to say, in a volume of four-dimensional space-time." (Aram D'Abro, "The Evolution of Scientific Thought from Newton to Einstein", 1927)
"In order to regain in a rigorously defined function those properties that are analogous to those ascribed to an empirical curve with respect to slope and curvature (first and higher difference quotients), we need not only to require that the function is continuous and has a finite number of maxima and minima in a finite interval, but also assume explicitly that it has the first and a series of higher derivatives (as many as one will want to use)." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)
"The course of the values of a continuous function is determined at all points of an interval, if only it is determined for all rational points of this interval."
"The most general definition of a function that we have reached in modern mathematics starts by fixing the values that the independent variable x can take on. We define that x must successively pass through the points of a certain 'point set'. The language used is therefore geometric […]." (Felix Klein, "Elementary Mathematics from a Higher Standpoint" Vol III: "Precision Mathematics and Approximation Mathematics", 1928)
"[…] the universe is not a rigid and inimitable edifice where independent matter is housed in independent space and time; it is an amorphous continuum, without any fixed architecture, plastic and variable, constantly subject to change and distortion. Wherever there is matter and motion, the continuum is disturbed. Just as a fi sh swimming in the sea agitates the water around it, so a star, a comet, or a galaxy distorts the geometry of the spacetime through which it moves." (Lincoln Barnett, "The Universe and Dr. Einstein", 1948)
"A definition is topological if it makes no use of mathematical elements other than those defined in terms of continuous deformations or transformations. Such deformations or transformations take the straightness out of planes and alter lengths and areas." (Marston Morse, "Equilibria in Nature: Stable and Unstable", Proceedings of the American Philosophical Society Vol. 93 (3), 1949)
"Topology begins where sets are implemented with some cohesive properties enabling one to define continuity." (Solomon Lefschetz, "Introduction to Topology", 1949)
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