This was written much later than the original two robot novels, the three Empire novels, and the Foundation trilogy. It and the following book, ROBOTS AND EMPIRE, link the first two robot books with the Empire series and leads up to Foundation.
There are a couple of points easy to miss here. First, psychohistory is first suggested by Dr. Fastolfe, and then advanced by the two robots. Secondly, while there is a mystery involved here, the emphasis is on the future of space exploration and who is going to be in it. The original pioneers into space have become spoiled by their reliance on their robots and no longer have the spirit of adventure necessary to continue further exploration, and yet they are fearful of the idea of generally despised Earth people colonizing planets.
So much indeed is at stake here. For full enjoyment, I suggest reading first the Susan Calvin stories and also "The Bicentennial Man" which are in Asimov's THE COMPLETE ROBOT, and then THE CAVES OF STEEL and THE NAKED SUN, the first two Elijah Bailey & R. Daneel Olivaw novels. And be prepared for this book to be more centered on mankind's future venturing into space than in the mystery element.