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1940, in "Mathematics and the Imagination," a layman's book on mathematics written by U.S. mathematicians Edward Kasner (1878-1955) and James R. Newman, the word supposedly coined a year or two before by Kasner's 9- (or 8-) year-old nephew (unnamed in the book's account of the event), when asked for a name for an enormous number. Perhaps influenced by comic strip character Barney Google. Googolplex coined at the same time, in the same way.
The number represented in base-ten by a one with a hundred zeroes after it.
According to Webster's Dictionary, the name was coined in 1938 by Milton Sirotta, the nine-year-old nephew of American mathematician, Edward Kasner.
See also googolplex.