theorem

theorem 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.

theorem general proposition demonstrable by argument. XVI. — F. théorème or late L. theōrēma — Gr. theṓrēma speculation, theory, proposition to be proved, f. theōreîn look at, f. theōrós spectator (see THEORY).
So theoretic(al) †speculative, contemplative; pert to theory. XVII. — late L. theōrēticus — Gr. theōrētikós. Hence theoretician XIX.