For every positive integer $N$ we can find integers $a,b,c,d$ such that $N = a^2 + b^2 + c^2 +d^2$. This statement is naturally in interpreted in four dimensional Euclidean space and we will give a classical geometric proof. The ideas of the proof are at the heart of much of classical algebraic number theory and have arisen more recently in the pioneering work of Bhargava et al. on the ranks of elliptic curves.