Innovation and enterprise depend for their success on the development of new ideas. But from where do new ideas come? How do they arise? Finding solutions to such questions is at the heart of creativity research and the solving of novel problems. Reflection, not only in cognitive processes but also in the non-cognitive ones used in solving novel mathematics problems, is uncovering a way in which the origins of new ideas occur. A study involving protocol analysis of five expert problem solvers identifies three critical elements. These elements have been employed to construct a framework of creative problem solving which may be used to foster creativity among young people under instruction and provide a cognitive explanation of the origin of new ideas. (Contains 3 figures and 1 footnote.)