So how does the moment of creativity occur? One explanation was proposed a century ago by the great French polymath Henri Poincaré, based on his own profound mathematical discovery in 1881. Some 30 years later, Poincaré published an analysis of his own thought process. It goes like this: After a great deal of conscious work he became stuck and put the problem aside. But his desire to solve it kept it alive in his unconscious. Illumination occurred beneath the surface, then bubbled into consciousness. From there he was able to check his result and find that it was correct. Poincaré's four-stage model - conscious thought, unconscious thought (or incubation), illumination and verification - has since been studied in depth and refined.