The Banach–Tarski Paradox
Cut a solid ball into five pieces, move them around, and you have two balls the same size as the first. Nothing was stretched.
192423 min read
Hungarian-American mathematics
John von Neumann
1903 – 1957
Contributor to set theory, quantum mechanics, game theory, computer architecture and much else. In 1929 he isolated the property of a group that actually drives paradoxical decomposition — what is now called amenability — and thereby explained why the Banach–Tarski phenomenon appears in three dimensions but not in one or two.