2 Different Types of Geniuses

I have decided there are two different types of "geniuses" in this world. There is the philosopher, whose perspective is so large and contemplation so vast, that he knows he's an idiot. The person who comprehends the amount of knowledge and information there is in this world. He knows that he will never really understand everything, and therefore strains to define the broader aspects of life. Theorizes in a way that can be applied to life in general; a very unspecific, objective observer.

There is the scientist, the artist, the mathematician. Who is so engulfed in his own trade that he believes he is the living and the end. This person can learn nothing from other's, but rather toils the confines of his own modest brain to solve intricate and complicated enigmas in certain genres of science (art is a science.) His ego may soar with good reason, because he is good at what he does. His concentration can be stifled to one subject at a time. He doesn't see the world as a whole, but rather a place he resides, a place he is arrogant enough to believe he can change.