In mathematics, a proof is a series of statements ordered in such a way so as to show that something is true without exception. There have been many false proofs over the years (most notably, Fermat's Last Theorem and 1=2), but there have also been new and correct proofs recently (again, Fermat's Last Theorem).

Some of the first proofs were made by Euclid and deal in Euclidean Geometry. Other early theorems include the Pythagorean Theorem and the Chinese Remainder Theorem, although many of the "old" theorems were not proven satisfactorily until recently.

Most mathematical proofs are based in logic and depend on implications, inverses, converses and contrapositives. Often, the most desirable kind of implication is the iff statement. Every proof must be founded on axioms or definitions, statements which cannot be proven by any means but which can be assumed true. In fact, an axiom can be changed and there can still be logical consistency in many cases; compare Euclidean geometry with non-Euclidean geometry and their basic but mutually exclusive axioms: "Parallel lines never meet"; "Parallel lines meet at infinity".
Some items which have proofs here: