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The course of mathematical invention and investigation reveals itself, broadly speaking, as a series of upward hitches. For long periods of time the current mathematics is discussed, worked with, smoothed out, and gradually perfected. Then suddenly some one sees a connecting linkage which conveys an inner wholeness, an unsuspected simple basic similarity pr even sameness, to several and various parts of the subject. With one fell stroke the science is lifted (almost by its own bootstraps) to a higher level on which a further and greater polishing and perfecting process may be carried out. Each of these lifts is essentially a unification of hitherto apparently unrelated pieces. Each is an amalgamation under one head of the apparently many and diverse. Each is a stride towards generality in that isolated problems become one and the one answers the many.

Gaylord Merriman
American mathematician
To Discover Mathematics, 1942