One of the classic books in this area is "The Psychology of Invention in the Mathematical Field", written by Jacques Hadamard of Princeton University in the mid 1940s, and published by the Princeton University Press. It concentrates upon creativity at the highest possible level, in an individual rather than a group context, and examines the roles of the conscious and the subconscious in solving a problem.
Among many other things, Hadamard lists the phases through which mathematical creativity often passes.
Preparation. This is when the subconscious is "primed" for the problem. It is usually intense (perhaps the more so the better), and often protracted.
Incubation. This is when the subconscious actually does its thing: cross-linking ideas, synthesising, sifting, sieving, etc. It is generally assisted by a state of relaxation (sometimes only physical, sometimes only mental, sometimes both).
Illumination. This is when the subconscious "delivers the goods". It happens suddenly, and the answer tends to be complete rather than partial. Illumination is sometimes preceded by another phase that Hadamard calls Intimation.
Verification. Self explanatory. This phase is necessary because the process is not infallible.
Hadamard does not claim that these are ever sufficient, and he does not claim that they are always necessary. But he does claim that at the very least they appear to be conducive to creativity.
A couple of years ago I saw a newspaper article quoting Nobel laureate James Watson (of DNA fame) as having said, "It is necessary to be slightly underemployed if you are to do something significant." This is totally consistent with Hadamard's comments on the incubation phase.
And totally at odds with most modern corporate cultures, with or without any consultant-driven acronymic fad.
