1. That which is considered and established as a principle; hence, sometimes, a rule. "Not theories, but theorems, the intelligible products of contemplation, intellectual objects in the mind, and of and for the mind exclusively." (Coleridge) "By the theorems, Which your polite and terser gallants practice, I re-refine the court, and civilize Their barbarous natures." (Massinger)

2. <mathematics> A statement of a principle to be demonstrated.

A theorem is something to be proved, and is thus distinguished from a problem, which is something to be solved. In analysis, the term is sometimes applied to a rule, especially a rule or statement of relations expressed in a formula or by symbols; as, the binomial theorem; Taylor's theorem. See the Note under Proposition. Binomial theorem.

<mathematics> A theorem which extends to any quantity without restriction.

Origin: L. Theorema, Gr. A sight, speculation, theory, theorem, fr. To look at, a spectator: cf. F. Theoreme. See Theory.

(01 Mar 1998)