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In 1905 "L'Enseignement Mathématique" started an inquiry into the methods of working of mathematicians. The results of this inquiry augmented and developed later by several authors, for instance Carmichael and Hadamard, can be expressed shortly as follows. The faculty of deduction belongs to the conscious mind, the subconscious being in general only able to perform very simple and trivial deductions. On the contrary the faculty of rearranging is typical of the work of the subconscious and is described by Carmichael as consisting of an extremely rapid passing over of innumerable useless combinations till a vital one or some vital ones rise to consciousness, to bring, after a severe control of the conscious mind, new truth to light. (en) |
