The Banach-Tarski Dupla-Shrinker recently made an appearance on an episode of Futurama. Using it, Bender got to make two, slightly smaller, copies of himself. The smaller Benders are why they added the 'shrinker' part of the name. The actual Banach-Tarski theorem allows an object to spawn a perfect copy of itself, at its exact size, just by being chopped into bits.

The paradox was first described in 1924 by Stefan Banach and Alfred Tarski. They showed that, if someone were to chop up a solid ball of any size into six very precisely-shaped pieces, those pieces could be rearranged and used to form two new solid balls, each exactly the same size as the original. The pieces would be re-positioned, but not stretched or blown up to larger proportions. Later, another mathematician reduced the number of pieces necessary to do this to five. It gets even stranger. Another version of the theory has a ball the size of a pea being chopped up and reconstructed to form a ball the size of the sun.

This seems intuitively impossible, but as an added bonus, it's theoretically impossible as well. Physics says that mass cannot be created or destroyed with nothing more than a pair of scissors. Anyone who managed to achieve a practical Banach-Tarski operation would essentially be doubling the mass of something, like magic.