  We calculate the density of states in the half-filled Hubbard model on a
Bethe lattice with infinite connectivity. Based on our analytical results to
second order in $t/U$, we propose a new `Fixed-Energy Exact Diagonalization'
scheme for the numerical study of the Dynamical Mean-Field Theory. Corroborated
by results from the Random Dispersion Approximation, we find that the gap opens
at $U_{\rm c}=4.43 \pm 0.05$. Moreover, the density of states near the gap
increases algebraically as a function of frequency with an exponent
$\alpha=1/2$ in the insulating phase. We critically examine other analytical
and numerical approaches and specify their merits and limitations when applied
to the Mott--Hubbard insulator.
