  We give a proof of the Andr\'e-Oort conjecture for $\mathcal{A}_g$ - the
moduli space of principally polarized abelian varieties. In particular, we show
that a recently proven `averaged' version of the Colmez conjecture yields lower
bounds for Galois orbits of CM points. The Andr\'e-Oort conjecture then follows
from previous work of Pila and the author.
