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:*
*Please /msg me with others.*