  Higher-order topological insulators are established as topological
crystalline insulators with crystalline symmetries. One celebrated example is
the second-order topological insulator in three dimensions that hosts chiral
hinge modes protected by crystalline symmetries. Since amorphous solids are
ubiquitous, it is important to ask whether such a second-order topological
insulator can exist in an amorphous system without any spatial order. Here we
predict the existence of a second-order topological insulating phase in an
amorphous system without any crystalline symmetry. Such a topological phase
manifests in the winding number of the quadrupole moment, the quantized
longitudinal conductance and the hinge states. Furthermore, in stark contrast
to the viewpoint that structural disorder should be detrimental to the
higher-order topological phase, we remarkably find that structural disorder can
induce a second-order topological insulator from a topologically trivial phase
in a regular geometry. We finally demonstrate the existence of a second-order
topological phase in amorphous systems with time-reversal symmetry.
