6. Borel's monkeys
Variations go back to Aristotle, but the modern version of the infinite-monkey theorem was introduced in 1913 by French mathematician Émile Borel. You know the deal: An infinite number of monkeys pecking at typewriters for an infinite length of time will "almost surely" produce the complete works of Shakespeare. Seems unlikely, because our minds have a hard time grasping the infinite. Mathematically, it's true.
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