Problems solution This is the most simple method of progress, where someone has found a problem and as a results, solves it.
Evolutionary idea Evolutionary ideas derive from somewhere else, taking something that already exists and improving on it.
Symbiotic idea A symbiotic method of idea creation is when multiple ideas are combined, using diffirent elements of each to make a whole.
Revolutonary idea A revolutionary ideas breaks away from traditional thought and creates a brand new perspective. For example, Marxism (an evolutionary form of Hegelianism), or the writings of Copernicus (a development of classical Greek thoughts).
Serendipitous discovery Serendipitious solution are ideas which have been coincidentlly without the intention of the inventor. For example the discovery of penicillin.
Targeted innovation Creating a targeted innovation deals with a direct path of discovery. This often accompanied by intensive research in order to have a distinct and almost expected resolution. For example, linear programming.
Artistic innovation Artistic innovation disregards the necessity for practicality and holds no constraints.
Philosophical idea The philosophical idea lives in the mind of the creator amd can never[citation neened] be proven. This type of idea however cam have a vast residual effects. For example of eternal recurrence.