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"Mad men" was a slang term coined in the 1950s by advertisers working on Madison Avenue to refer to themselves. The only documented use of the phrase from that time may have been in the late 1950s writings of James Kelly, an advertising executive and writer.
See also: List of Mad Men episodes, Mad Men (season 1), Mad Men (season 6), Mad Men (season 7), List of Mad Men characters, and Mad Men (season 2).