"Pure mathematics is a collection of hypothetical, deductive theories, each consisting of a definite system of primitive, undefined, concepts or symbols and primitive, unproved, but self-consistent assumptions (commonly called axioms) together with their logically deducible consequences following by rigidly deductive processes without appeal to intuition." (Graham D Fitch, "The Fourth Dimension simply Explained", 1910)
"The scientific imagination devises a possible solution - an hypothesis - and the investigator proceeds to test it. He makes intellectual keys and then tries whether they fit the lock. If the hypothesis does not fit, it is rejected and another is made. The scientific workshop is full of discarded keys." (John A Thomson, "Introduction to Science", 1911)
"A false hypothesis, if it serve as a guide for further enquiry, may, at the right stage of science, be as useful as, or more useful than, a truer one for which acceptable evidence is not yet at hand." (William C Dampier, "Science and the Human Mind, Science in the Ancient World", 1912)
"It is experience which has given us our first real knowledge of Nature and her laws. It is experience, in the shape of observation and experiment, which has given us the raw material out of which hypothesis and inference have slowly elaborated that richer conception of the material world which constitutes perhaps the chief, and certainly the most characteristic, glory of the modern mind." (Arthur J Balfour, "The Foundations of Belief", 1912)
"Without hypothesis there can be no progress in knowledge." (Max Verworn, "Irritability", 1913)
"In the complete absence of any theory of the instincts which would help us to find our bearings, we may be permitted, or rather, it is incumbent upon us, in the first place to work out any hypothesis to its logical conclusion, until it either fails or becomes confirmed." (Sigmund Freud, "On Narcissism", 1914)
"The great difference between induction and hypothesis is that the former infers the existence of phenomena such as we have observed in cases which are similar, while hypothesis supposes something of a different kind from what we have directly observed, and frequently something which it would be impossible for us to observe directly." (Charles S Peirce, "Chance, Love and Logic: Philosophical Essays, Deduction, Induction, Hypothesis", 1914)
"Theory is the best guide for experiment - that were it not for theory and the problems and hypotheses that come out of it, we would not know the points we wanted to verify, and hence would experiment aimlessly" (Henry Hazlitt, "Thinking as a Science", 1916)
"A good hypothesis in science must have other properties than those of the phenomenon it is immediately invoked to explain, otherwise it is not prolific enough." (William James, "Selected Papers on Philosophy", 1918)
"An indispensable hypothesis, even though still far from being a guarantee of success, is however the pursuit of a specific aim, whose lighted beacon, even by initial failures, is not betrayed." (Max Planck, [Nobel lecture] 1918)
"It must be gently but firmly pointed out that analogy is the very corner-stone of scientific method. A root-and-branch condemnation would invalidate any attempt to explain the unknown in terms of the known, and thus prune away every hypothesis." (Archie E Heath, "On Analogy", The Cambridge Magazine, 1918)
"A science cannot be played with. If an hypothesis is advanced that obviously brings into direct sequence of cause and effect all the phenomena of human history, we must accept it, and if we accept it, we must teach it." (Henry Adams, "The Degradation of the Democratic Dogma, The Tendency of History", 1919)
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