Big Apple
Although the history of "Big Apple " was once thought a mystery, a clearer picture of the term's history has emerged due to the work of amateur etymologist Barry Popik, and Gerald Cohen of Missouri University of Science and Technology. A number of false theories had previously existed, including a claim that the term derived from a woman named Eve who ran a brothel in the city. This was subsequently exposed as a hoax.
Big Apple
The earliest known usage of 'big apple' appears in the book "The Wayfarer in New York" (1909), in which author Edward S. Martin writes: Kansas is apt to see in New York a greedy city... It inclines to think that the big apple gets a disproportionate share of the national sap. William Safire considered this the coinage, but the "Random House Dictionary of American Slang" has described the usage as "metaphorical or perhaps proverbial, rather than a concrete example of the later slang term".