Theorem: Given any ham sandwich, there is always a knife that cuts it so that the ham, cheese, and bread slices are all divided into two equal parts.

This theorem is really called the "ham sandwich theorem". It was proved by mathematicians Arthur Stone and John Tukey in 1942, and is of great importance in measure theory.

The ham sandwich theorem can be extended to the n-dimensional case: if there are n objects in n-dimensional space, then there is always an n - 1-dimensional hyperplane that divides each object into two equal parts of equal "volume". These objects can be of any shape, can be disconnected (e.g., slices of bread), and can even be oddly shaped sets of points, as long as the set of points is measurable.