"It has long seemed obvious - and is, in fact, the characteristic tone of European science - that 'science' means breaking up complexes into their component elements. Isolate the elements, discover their laws, then reassemble them, and the problem is solved. All wholes are reduced to pieces and piecewise relations between pieces. The fundamental 'formula' of Gestalt theory might be expressed in this way. There are wholes, the behaviour of which is not determined by that of their individual elements, but where the part-processes are themselves determined by the intrinsic nature of the whole. It is the hope of Gestalt theory to determine the nature of such wholes." (Max Wertheimer, "Gestalt Theory," 1924)
"I recall my own emotions: I had just been initiated into the mysteries of the complex number. I remember my bewilderment: here were magnitudes patently impossible and yet susceptible of manipulations which lead to concrete results. It was a feeling of dissatisfaction, of restlessness, a desire to fill these illusory creatures, these empty symbols, with substance. Then I was taught to interpret these beings in a concrete geometrical way. There came then an immediate feeling of relief, as though I had solved an enigma, as though a ghost which had been causing me apprehension turned out to be no ghost at all, but a familiar part of my environment." (Tobias Dantzig, "The Two Realities", 1930)
"In reality the cycles we have the occasion to observe are generally not damped. How can the maintenance of the swings be explained? Have theses dynamic laws deduced from theory and showing damped oscillations no value in explaining the real phenomena, or in what respect do the dynamic laws need to be completed in order to explain the real happenings? They (dynamic laws) only form one element of the explanation: they solve the propagation problem. But the impulse problem remains." (Ragnar Frisch, "Propagation problems and impulse problems in dynamic economics", 1933)
"The unsolved problems of Nature have a distinctive fascination, though they still far outnumber those which have even approximately been resolved.(Henry N Russell, "The Solar System and Its Origin", 1935)
"It is time, therefore, to abandon the superstition that natural science cannot be regarded as logically respectable until philosophers have solved the problem of induction. The problem of induction is, roughly speaking, the problem of finding a way to prove that certain empirical generalizations which are derived from past experience will hold good also in the future." (Alfred J Ayer, "Language, Truth and Logic", 1936)
"The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future; and should analysis ever appear to be without or blemish, its perfection might only be that of death." (Eric T Bell, "The Development of Mathematics", 1940)
"We can scarcely imagine a problem absolutely new, unlike and unrelated to any formerly solved problem; but if such a problem could exist, it would be insoluble. In fact, when solving a problem, we should always profit from previously solved problems, using their result or their method, or the experience acquired in solving them." (George Pólya, 1945)
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