Trivial Definition

Trivial is related to or being the mathematically most simple case. More generally, the term trivial is used to describe any result which requires little or no effort to derive or prove. Oftentimes, solutions involving the number zero are considered trivial whereas nonzero solutions are considered nontrivial. For instance, the equation 3x + 2y = 0 has the trivial solution x = 0, y = 0. Nontrivial solutions in this case include x = -2, y = 3, and x = 2, y = -3. The word originates from the Latin trivium, which was the lower division of the seven liberal arts in medieval universities (cf. quadrivium).

Overview

According to the Nobel Prize winning physicist Richard Feynman, mathematicians designate any theorem as trivial once a proof has been obtained no matter how difficult the theorem was to prove in the first place. There are therefore exactly two types of true mathematical propositions: trivial ones, and those which have not yet been proven. The opposite of a trivial theorem is a deep theorem.