What is the mystery of genius, still unsolved?

Could a genius of thoughts and feelings emerge from primates? The answer is obvious. This means that there are certain potencies in a person, allowing to solve the problem of genius. On the other hand, geniuses among individuals is impossible to project and grow up at all diligence in any way, and they themselves somehow manifest, but is extremely rare. What peculiar properties promote manifestation of genius and in what it is expressed?