(graph theory) A theorem stating that, among the n-vertex simple graphs with no (r + 1)-cliques, T(n, r) has the maximum number of edges.

(mathematical analysis) Any of a class of theorems which, for a given Abelian theorem, specifies conditions such that any series whose Abel sums converge (as stipulated by the Abelian theorem) is in fact convergent.

(chiefly mathematics) A theorem (or, in non-mathematical fields, a commonly accepted hypothesis) considered to be of central importance to a specified field.

(computing theory) A theorem stating that all nontrivial semantic properties of programs are undecidable.

(physics) A theorem stating that the energy eigenstates for an electron in a crystal can be written as Bloch waves.

(mathematics) A theorem that gives a lower bound on the size of a disc in which an inverse to a holomorphic function exists.

The theorem that any graph labelling (with colours) of a sufficiently large complete graph contains monochromatic cliques.

(graph theory) A characterization of the connectivity in finite undirected graphs in terms of the minimum number of disjoint paths that can be found between any pair of vertices.

(mathematics) A basic result of algebraic topology, connecting homotopy theory with homology theory via a map known as the Hurewicz homomorphism.

(number theory) A theorem stating that the sum of the reciprocals of the twin primes converges to a finite value (Brun's constant).