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 the assumption that the human conglomerate being dealt with s 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 human conglomerate be itself unaware of Psychohistory analysis in order that its reactions be truly random. The basis of all valid Psychohistory lies in the development of the Seldon functions which exhibit properties congruent to those of such social and economic forces as ...
Psychohistory is the mathematical study of the reactions of human conglomerates in response to economic and social stimuli. Psychohistory, was developed by Hari Seldon and expanded through the efforts of Gaal Dornick and other mathematicians. Using psychohistory, Seldon predicted the fall of the Galactic Empire and developed Seldon's Plan to shorten the interregnum.
Psychohistory was first thought of in 4720 AD by Auroran robotocist Han Fastolfe. He wanted to develop "Laws of Humanics", and he named them "psychohistory", but never completed the work before his death. A few mathematicians continued work on the field throughout the Galactic Era, but merely left it a vague set of axioms.
R. Daneel Olivaw kept the idea of psychohistory in his memory, however. He used it to guide humanity to the Galactic Empire, and when it was clear it was falling he convinced Hari Seldon to develop it further to figure out a plan, not for preventing the fall, but for shortening the Interregnum that would follow. He began work, along with Yugo Amaryl and other members of the Seldon Project, in 12,020, developing it across the 12,000s GE. By 12,026, some basic principles had been figured out, and by 12,028 a Prime Radiant was in development to hold it's equations. By 12,048, the science could predict basic events and a whole host of Prime Radiants existed. By 12,054, when Yugo died, the science could predict with certainty the Fall of the Empire and the following events. It was applied to create the two Foundations, who rose through the Interregnum.
Ultimately, however, psychohistory was flawed. As worked out by Golan Trevize in 499 FE, it assumed that humans were the only sentinet life in the Universe, when in fact, others existed - robots, Gaia, Memes, and Cepheids. 
The character responsible for the science's creation, Hari Seldon, established three Theorems of Psychohistorical Quantitivity:
- The population under scrutiny is oblivious to the existence of the science of Psychohistory. If aware of psychohistory then the population will alter its behavior.
- The time periods dealt with are in the region of three generations.
- The population must be in the billions (±75 billion) for a statistical probability to have a psychohistorical validity.
- Human Beings are the only sentient intelligent life in the Universe.
In order for Seldon's mathematics to be valid, he had to make certain assumptions about the Galaxy and its inhabitants. Those assumptions, as stated by Ebling Mis in 301FE, are:
- There would be no fundamental change in human society over the thousand years of the Plan.
- Human reactions to stimuli would remain constant.