African-Americans invented cool as a stylistic defiance against racism during World War II. This is simply well-documented social, historical, and linguistic fact. To be cool in the 1940s referred to the ability to be relaxed in one's own style in any environment, an act of courage and mental strength for any Black person during the Jim Crow era. Whether meaning high praise ("Cool!"), vetting someone to others ("she's cool"), or referring to a relaxed state of mind ("I'm cool, man") -- our modern usages all began in jazz culture. Jazz fan Jack Kerouac caught the new word at clubs and wrote of his "theory of cool" to Neal Cassady in 1950 and William Burroughs registered this "new word in the hipster vocabulary" in Junky (1952). By the time The Jazz Lexicon came out in 1963 -- the definitive dictionary of jazz jargon -- Robert S. Gold called cool "the protean word" of jazz culture. There were two pages of citations from magazines and a page each for "uncool" and "cool it," as well as for "hip" and "unhip." Jazz was the dominant subculture of the post-World War II era in NYC and jazz musicians' slang became the first rebellious code of cool.
from The Jazz Lexicon (1963)
Jazz legend Lester Young was the first to spread this underground gospel of cool. To be cool meant you would not Uncle-Tom -- i.e., produce a fake smile -- to show white Americans you knew your place. Young then added stylistic markers to defy the white gaze: a personal, impenetrable slang; wearing sunglasses at night; inhabiting a smoky alcohol haze for insulation. Both black and white jazz musicians put on their shades, torqued up their slang, smoked dope or shot heroin, and became cool cats. Within a decade, sociologists began writing about cool, Norman Mailer became obsessed with the concepts of hip and cool (in his Village Voice columns on "The Hip and the Square") and Leonard Bernstein registered its presence in national consciousness with "Cool" in West Side Story (1957). White appropriation and dilution of "cool" and "chill" continues, then as now. (Read more in chapters one and five of The Origins of Cool in Postwar America.)