This week marks the 40th anniversary of the Rumble in the Jungle. A lot has been written about that fight. Movies have been made about it. People have wept and torn their hair and rolled in the grass, beating their heels against the ground, because of that fight. It was a mighty fight. A remarkable moment. Rightly recalled.

But we thought we'd take a look back, further back, to the night when The Greatest was truly born. The night Ali first beat Liston for the crown, and made his mark not only on the boxing world, but on the social, political and even the entertainment landscape, forever. (Here are rare and classic photos from the fight.)

He was Cassius Marcellus Clay then, of course — an Olympic gold medalist, undefeated challenger for the world heavyweight crown and the most charismatic (and, for some, the most controversial) athlete of the era. It was February 1964, and the 22-year-old Clay, whose professional record was an impressive 19-0, was slated to fight Sonny Liston for the heavyweight title in Miami Beach. Hardly anyone in the boxing world — and certainly very, very few in the close-knit and deeply conservative boxing media — gave the supremely self-confident Kentuckian the slightest chance of beating the hard-punching "Big Bear."

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And while no one gave him much of a chance, nor could anyone possibly ignore a fighter who recited his own comical, self-aggrandizing poetry to anyone who would listen. (One pre-fight gem: "The crowd did not dream when they put up the money / that they would see a total eclipse of the Sonny.")

But on the night of Feb. 25, 1964, Clay took the title from Liston with a 7th-round technical knockout in a performance that marked the arrival of an unmistakably formidable boxing talent. Clay — soon to announce to the world that his name was Muhammad Ali — possessed an unprecedented set of skills, including balletic footwork, lightning hand speed and bone-crushing punching power. When the referee counted Liston out in that ring in Miami Beach, it was clear that the universe of sports would never be the same.

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Ben Cosgrove is the editor of LIFE.com. Picture This is his occasional feature for The Stacks. (Photo Credit: Herb Scharfman—The LIFE Picture Collection/Getty Images)