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"I love that computer science has made mathematics into something like an experimental science. I was never all that good at proving things, but I love doing computer experiments."
- Rudy Rucker

Psychohistory  
  Branch of mathematics describes the behavior of human beings en masses.  

This is the definition of psychohistory in the novel.

PSYCHOHISTORY–...Gaal Dornick, using nonmathematical concepts, has defined psychohistory to be that branch of mathematics which deals with the reactions of human conglomerates to fixed social and economic stimuli....

... Implicit in all these definitions is the assumption that the human conglomerate being dealt with is sufficiently large for valid statistical treatment. The necessary size of such a conglomerate may be determined by Seldon's First Theorem which ... A further necessary assumption is that the human conglomerate be itself unaware of psychohistoric analysis in order that its reactions be truly random ...

The basis of all valid psychohistory lies in the development of the Seldon Plan. Functions which exhibit properties congruent to those of such social and economic forces as ...

ENCYCLOPEDIA GALACTICA

From Foundation, by Isaac Asimov.
Published by Doubleday in 1951
Additional resources -

A person who studies and applies psychohistory is a psychohistorian.

Here is another quote, taken from the second book in the series, Foundation and Empire:

"The laws of history are as absolute at the laws of physics, and if the probabilities of error are greater, it is only because history does not deal with as many humans as physics does atoms, so that individual variations count for more."

There are earlier uses of this word in science fiction. For example, in Eric Frank Russell's 1941 story Beyond All Weapons.

You made a name for yourself in the field of Psycho-History and taught at the University of Megalon...

The Director’s eyes were dangerous. But I plunged on recklessly. “Yes, mass hypnotism — that has been your secret weapon. You may have deluded most of the world, but you forget I studied psycho-history in what you are pleased to call the Barbaric Era. Earlier dictators than you fumbled around with the idea of mass hypnosis. There was a man named Hitler back in the 1930s and ’40s who used it with some crude success. But he didn’t know anything about the scientific end of it. He employed no hypnosis rays or skillful projections to break into the unconscious and the subliminal thresholds. He relied on a raucous voice and emotional reiterations. You have been far cleverer. Your Sunday Assemblies renew your contacts with all the earth, rebathing the poor dupes in hypnosis rays and sliding afresh the projectional suggestions of your voice and mind into theirs.”

I held her tight. “All eyewitness accounts are like that,” I told her earnestly. “As the wife of a man who has devoted most of his life to the application of psychology to historical data you ought to realize that.

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Additional resources:
  More Ideas and Technology from Foundation
  More Ideas and Technology by Isaac Asimov
  Tech news articles related to Foundation
  Tech news articles related to works by Isaac Asimov

Psychohistory-related news articles:
  - Paul Krugman's Asimov Inspiration
  - TASC - DARPA's Psychohistory
  - Asimov's Psychohistory May Be Possible
  - Cliodynamics: Modeling Complex Societies Mathematically
  - Google And The Psychohistorians
  - Fast Entropy, PHE And Psychohistory
  - FuturICT Knowledge Accelerator And Psychohistory

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