A rigorous mathematical argument which unequivocally demonstrates the truth of a given Proposition. A mathematical statement which has been proven is called a Theorem.

There is some debate among mathematicians as to just what constitutes a proof. The Four-Color Theorem is an example of this debate, since its ``proof'' relies on an exhaustive computer testing of many individual cases which cannot be verified ``by hand.'' While many mathematicians regard computer-assisted proofs as valid, some purists do not.

**References**

Garnier, R. and Taylor, J. *100% Mathematical Proof.* New York: Wiley, 1996.

Solow, D. *How to Read and Do Proofs: An Introduction to Mathematical Thought Process, 2nd ed.* New York: Wiley, 1990.

© 1996-9

1999-05-26