I think the proffesional life on an active mathematician is like that of a rock star.
How? Well, there is a time of introspective creativity where ideas and inspiration lead to theorems or songs.
After that, there is the time of crafty work (writing the paper / recording the song).
And finally, there comes the time to conquer the world, to sell the product. This is the time of academic visits and participation in congresses, the extrovert side (you know, the gigs!)