  In this paper we prove that the Cesaro operator $\mathcal{C}$ in $\ell^{2}$,
the Hilbert space of square summable sequences, is essentially normal, i.e. the
commutator
$[\mathcal{C}^{\ast},\mathcal{C}]:=\mathcal{C}^{\ast}\mathcal{C}-\mathcal{C}\mathcal{C}^{\ast}$
is a compact operator on $\ell^{2}$.
