A rigorous mathematical argument which unequivocally demonstrates the truth of a given proposition. A mathematical statement that
has been proven is called a theorem.
According to Hardy (1999, pp. 15-16), "all physicists, and a good many quite respectable mathematicians, are contemptuous about proof. I have heard Professor Eddington, for example, maintain that proof, as pure mathematicians understand it, is really quite uninteresting and unimportant, and that no one who is really certain that he has found something good should waste his time looking for proof.... [This opinion], with which I am sure that almost all physicists agree at the bottom of their hearts, is one to which a mathematician ought to have some reply."
To prove Hardy's assertion, Feynman is reported to have commented, "A great deal more is known than has been proved" (Derbyshire 2004, p. 291).
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. There are several computer
systems currently under development for automated theorem proving, among them, THOREM.
A page of proof-related humor is maintained by Chalmers.
OREM
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