Mathematics
The Banach-Tarski Paradox and the Nature of Sets
Quick fact
The Banach-Tarski paradox demonstrates that, assuming the axiom of choice, a solid ball in 3D can be split into five pieces and reassembled into two perfect copies of the original ball, seemingly doubling its volume without any stretching or overlapping.
Why this is interesting
Imagine taking a solid ball, cutting it into a few pieces, and rearranging them to create two identical balls, each the same size as the original. This sounds impossible—yet mathematics says it can be done.