  We provide the first unbiased evidence for a higher-order topological Mott
insulator in three dimensions by numerically exact quantum Monte Carlo
simulations. This insulating phase is adiabatically connected to a third-order
topological insulator in the noninteracting limit, which features gapless modes
around the corners of the pyrochlore lattice and is characterized by a
$\mathbb{Z}_{4}$ spin-Berry phase. The difference between the correlated and
non-correlated topological phases is that in the former phase the gapless
corner modes emerge only in spin excitations being Mott-like. We also show that
the topological phase transition from the third-order topological Mott
insulator to the usual Mott insulator occurs when the bulk spin gap solely
closes.
