It is usual to distinguish four phases in creation: preparation, incubation, illumination and verification, or working out.… Preparation is largely conscious, and anyhow directed by the conscious. The essential problem has to be stripped of accidentals and brought clearly into view; all relevant knowledge surveyed; possible analogues pondered. It should be kept constantly before the mind during intervals of other work.… Incubation is the work of the subconscious during the waiting time, which may be several years. Illumination, which can happen in a fraction of a second, is the emergence of the creative idea into the conscious. This almost always occurs when the mind is in a state of relaxation and engaged lightly with ordinary matters.… Illumination implies some mysterious rapport between the subconscious and the conscious, otherwise emergence could not happen. What rings the bell at the right moment?
-- Littlewood (The Princeton Companion to Mathematics)
-- Littlewood (The Princeton Companion to Mathematics)