To be a genius is to understand, to understand is to have appropriated to the imagination.
And this appropriation is not so much 'mastery' as being-mastered-by that which is understood.
Most people's 'understanding' on most (or all) topics is at the level of accepting. Accepting what people say, accepting rules or laws or maxims - and applying them.
Everyday so-called-understanding is passive, submissive, sociable, empathic, ego-denying: moves from the outside inwards.
Hyper-intelligent people are typically no exception - they simply grasp, memorize and apply instructions more rapidly - they don't understand them.
But for the genius in relation to the thing about which they are a genius: understanding is an act of internalizing; making of the thing a part of themselves - no, it is more than this - it is to bring that thing within them, and give that thing life (or allow it life).
To understand a thing is, therefore, to have it inside the imagination and in connection with the mind and body - to observe and feel its growth and workings.
To understand is therefore to-be-possessed-by that thing.
Extreme 'understanding' of one's imagination is therefore psychosis: when a person is possessed by the reality of their own thoughts and hears the thoughts as objective voices, believes ideas as delusions - but genius is also to be possessed by (for instance) thoughts and ideas, but in a manner which can be moved-into and out-from.
And this is the basis of creativity.
To be creative is first to understand in this inner, imaginative and real sense - to feel the thing at work within and to have a relationship with it, indeed to be mastered by it - and then to perceive the implications of this real, lively, living, dominating thing within: to see what it means.
Thus the genius is at root a type of personality, and personality is a way of thinking.
The genius is rare because balanced between externally-dominated normality and the internally autonomous state of psychosis.
Compared with normality, a genius is possessed by his imagination, and this inner life is independent from normal social influence; but compared with a psychotic the mastering imagination of a genius retains significant communication with the external world.
(All of which is to re-state HJ Eysenck's perception that genius is a state of moderately-high Psychoticism; midway along the scale; where Psychoticism is a trait with the socially submissive, socially-engaged empathic, conscientious rule-follower is at the low extreme and an egotistical, psychopathic psychotic is at the highest extreme.)