History For Finite Simple Groups
There are two threads in the history of finite simple groups – the discovery and construction of specific simple groups and families, which took place from the work of Galois in the 1820s to the construction of the Monster in 1981; and proof that this list was complete, which began in the 19th century, most significantly took place 1955 through 1983 (when victory was initially declared), but was only generally agreed to be finished in 2004. As of 2010, work on improving the proofs and understanding continues; see (Silvestri 1979) for 19th century history of simple groups.
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“Whenever a person strives, by the help of dialectic, to start in pursuit of every reality by a simple process of reason, independent of all sensuous information—never flinching, until by an act of the pure intelligence he has grasped the real nature of good—he arrives at the very end of the intellectual world.”
—Plato (c. 427–347 B.C.)
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