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A submodule S of a module M such that for any proper submodule T of M, the submodule generated by S union T is not the entire module M. S is also called superfluous submodule.

Consecutive Smith numbers. The first few Smith brothers are (728, 729), (2964, 2965), (3864, 3865), (4959, 4960), ... (OEIS A050219 and A050220).

In a network with three graph edges at each graph vertex, the number of Hamiltonian cycles through a specified graph edge is 0 or even.

A surface parameterized in variables u and v is called smooth if the tangent vectors in the u and v directions satisfy T_uxT_v!=0, where AxB is a cross product.

The 6-polyiamond illustrated above.

A surveying problem which asks: Determine the position of an unknown accessible point P by its bearings from three inaccessible known points A, B, and C.

A polyhedron with extra triangular faces, given by the Schläfli symbol s{p; q}.

Johnson solid J_(85).

The socle of a group G is the subgroup generated by its minimal normal subgroups. For example, the symmetric group S_4 has two nontrivial normal subgroups: A_4 and ...

Socrates is reported to have stated: "One thing I know is that I know nothing."