Take a ball in R^3, and partition it into a finite number of pieces. Then, carefully rotate and translate each of the pieces, without changing their form. In the end you get not one, but TWO filled balls, same size each as before.

Don't believe me? I will go in the next talk, before your very eyes, over most details of this mathematical stunt. The only magic involved will be the so-called axiom of choice, used by most mathematicians without questioning. A similar talk was given two years ago by Nick.

You will also learn why we cannot do this with the pizza, which will be henceforth cut in the same, unoriginal way (although you're welcome to try).