  Higher-order topological insulators are established as topological
crystalline insulators protected by 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 secondorder 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.
