"The object of pure mathematics is those relations which may be conceptually established among any conceived elements whatsoever by assuming them contained in some ordered manifold; the law of order of this manifold must be subject to our choice; the latter is the case in both of the only conceivable kinds of manifolds, in the discrete as well as in the continuous." (Erwin Papperitz, "Über das System der rein mathematischen Wissenschaften", 1910)
"As systematic inquiry into the natural facts was begun it was at once found that the accepted ideas of variation were unfounded. Variation was seen very frequently to be a definite and specific phenomenon, affecting different forms of life in different ways, but in all its diversity showing manifold and often obvious indications of regularity." (William Bateson, "Problems in Genetics", 1913)
"The validity of demonstrably wrong law cannot conceivably be justified. However, any answer to the question of the purpose of law other than by enumerating the manifold partisan views about it has proved impossible - and it is precisely on that impossibility of any natural law, and on that alone, that the validity of positive law may be founded. At this point relativism, so far only the method of our approach, enters our system as a structural element." (Gustav Radbruch, "Rechtsphilosophie", 1932)
"We know, since the theory of relativity at least, that empirical sciences are to some degree free in defining dynamical concepts or even in assuming laws, and that only a system as a whole which includes concepts, coordinating definitions, and laws can be said to be either true or false, to be adequate or inadequate to empirical facts. This 'freedom', however, is a somewhat doubtful gift. The manifold of possibilities implies uncertainty, and such uncertainty can become rather painful in a science as young as psychology, where nearly all concepts are open and unsettled. As psychology approaches the state of a logically sound science, definitions cease to be an arbitrary matter. They become far-reaching decisions which presuppose the mastering of the conceptual problems but which have to be guided entirely by the objective facts." (Kurt Lewin, "Principles of topological psychology", 1936)
"The true physician cannot remain outside the manifold of the events he observes." (Alan Gregg, "Humanism and Science", Bulletin of the New York Academy of Sciences Vol. 17, 1941)
"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-distinguished 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", 1949)
"[...] our purpose is to give a presentation of geometry [..[.] in its visual, intuitive aspects. With the aid of visual imagination we can illuminate the manifold facts and problems. [...] beyond this, it is possible [...] to depict the geometric outline of the methods of investigation and proof, without [...] entering into the details [...] In this manner, geometry being as many-faceted as it is and being related to the most diverse branches of mathematics, we may even obtain a summarizing survey of mathematics as a whole, and a valid idea of the variety of problems and the wealth of ideas it contains. Thus a presentation of geometry in large brushstrokes [...] and based on the approach through visual intuition, should contribute to a more just appreciation of mathematics by a wider range of people than just the specialists." (David Hilbert, "Geometry and the Imagination", 1952)
"The historian's special contribution is the discovery of the manifold shapes of time. The aim of the historian, regardless of his specialty in erudition, is to portray time. He is committed to the detection and description of the shape of time." (George Kubler, "The Shape of Time", 1982)
"People are deeply imbedded in philosophical, i.e., grammatical confusions. And to free them presupposes pulling them out of the immensely manifold connections they are caught up in." (Ludwig Wittgenstein, "Philosophical Occasions 1912-1951", 1993)
"Direct experience is inherently too limited to form an adequate foundation either for theory or for application. At the best it produces an atmosphere that is of value in drying and hardening the structure of thought. The greater value of indirect experience lies in its greater variety and extent. History is universal experience, the experience not of another, but of many others under manifold conditions." (Basil L Hart, "Why Don't We Learn from History?", 2015)
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