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Definition: theorem from The Hutchinson Unabridged Encyclopedia with Atlas and Weather Guide

Mathematical proposition that can be deduced by logic from a set of axioms (basic facts that are taken to be true without proof). Advanced mathematics consists almost entirely of theorems and proofs, but even at a simple level theorems are important.

Summary Article: theorem from The Columbia Encyclopedia

in mathematics and logic, statement in words or symbols that can be established by means of deductive logic; it differs from an axiom in that a proof is required for its acceptance. A lemma is a theorem that is demonstrated as an intermediate step in the proof of another, more basic theorem. A corollary is a theorem that follows as a direct consequence of another theorem or an axiom. There are many famous theorems in mathematics, often known by the name of their discoverer, e.g., the Pythagorean Theorem, concerning right triangles. One of the most famous problems of number theory was the proof of Fermat's Last Theorem (see Fermat, Pierre de); the theorem states that for an integer n greater than 2 the equation xn+yn=zn admits no solutions where x,y, and z are also integers.

The Columbia Encyclopedia, © Columbia University Press 2017

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