Hilbert-Waring Theorem

Theorem
For each $k \in \Z: k \ge 2$, there exists a positive integer $g \left({k}\right)$ such that every positive integer can be expressed as a sum of at most $g \left({k}\right)$ $k$th powers.

Also known as
The Hilbert-Waring Theorem is often referred to as Waring's problem, which was how it was named before proved it in $1909$.