From Oxford professor Raymond Flood's 2016 lecture "Hardy, Littlewood, Cartwright and Ramanujan", anecdotes about deep mathematics, including J E Littlewood's taxonomy of discovery:

... Later on in life in an article called The Mathematician's Art of Work he distinguished four phases in creative work: preparation, incubation, illumination and verification or working out. He viewed the last phase of verification as within the range of any competent mathematician given the illumination!

Preparation was largely conscious or anyhow directed by the conscious and consisted of stripping the problem to its essentials, surveying all relevant knowledge and considering possible analogues. Following Newton he advised that the problem should be kept constantly in mind during other periods of work.

Incubation is the work of the subconscious during the waiting time which may be several years.

He says that Illumination, which can happen in a fraction of a second, is the emergence of the creative idea into the consciousness and implies some mysterious rapport between the subconscious and the conscious. He recommends
walking and the relaxed activity of shaving as helpful to the process of illumination. ...

What is this "shaving"?!

(cf Hardy Littlewood Rules (2004-06-14), ...) - ^z - 2020-09-20