Story where social development is an exact science

I'm looking for a book that starts with the premise that (once the population size had exceeded a certain number) the future development of mankind (revolutions and wars in so and so many years, colonization of other planets in so and so many years, and so on) could be predicted completely by applied statistics. (IIRC, they used slide rules for those exact predictions, but that is certainly owed to the time the story was written). Next, the predictability was used to take a few tiny measures that would change mankind's fate in a favourable way. After a long time, the predictive system fails(?) because a mutation occurs in some person(s).

And now is the part where I'm not sure if it belongs to this or another story: The mutation results in the ability to "beam" by thinking of a place where one has been before...

Answer

This would likely be Asimov's Foundation series, where a central premise was the idea of Psychohistory, the idea that, as a whole, humans are predictable, so you really can figure out the trends.

The Mule is a mutant who can literally change peoples' minds for them. His mutation allows him to exert a greater influence than any individual ought to be able to in the predictive model and yes, it throws the system off (although a "Second Foundation" gets it back up and running).

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