According to the official website of the LDS church, the very first instance of the term School of the Prophets being used by the Mormon church came in 1832 from Joseph Smith, a founder of the religion itself. (A statue of Smith is pictured above.) Prior to that, the term was used to describe seminaries at institutions like Harvard and Yale. Early on, the first LDS School of the Prophets, based in Kirtland, Ohio, trained Mormon men for missions. Examples of religious fervency common in early School of the Prophets gatherings include speaking in tongues. Soon, the Kirtland model for School of the Prophets was used by other Mormon outposts as the religion spread west.
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Brigham Young, another important figure in the early history of the Mormon church, founded a School of the Prophets in Salt Lake City, Utah in the 1880s. By the late 19th century, though, referring to secular and nonsecular education from the LDS church with the term School of the Prophets became less and less common as the Mormon church established its seminaries to fulfill that role. Already prone to fundamentalist thinking such as polygamy, the Lafferty brothers were excommunicated from the mainstream LDS church. They spent some time afterward as a part of a similarly-minded Mormon splinter sect, also known as the School of the Prophets. This one was founded by R.C. Crossfield, a self-proclaimed prophet also known as Onias. (A statement on this period from Crossfield himself is available to read online.)
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