Mathematics
The Axiom of Choice and the Well-Ordering Theorem
Quick fact
The axiom of choice is logically equivalent to the well-ordering theorem, which claims every set can be ordered so that every subset has a least element. This equivalence allows mathematicians to prove the existence of a well-order for any set, even though no explicit well-order can be described for most infinite sets.
Why this is interesting
You've probably picked one item from each of several boxes without thinking twice. But what if there were infinitely many boxes, each containing infinitely many items? Could you still make a choice?