Mathematics
Peano Axioms and Recursive Definition
Quick fact
The Peano axioms define all natural numbers using only the number zero and a 'successor' function that finds the next number. Surprisingly, this tiny toolkit is enough to define addition, multiplication, and order, and even to prove that the integers and rationals can be constructed from the natural numbers.
Why this is interesting
You've been counting since you were a child—but what exactly gives the numbers their meaning? The answer lies in just five simple rules you've probably never thought about.