Nov 26, 2012
MATHEMATICAL PROOF 1_ Documented by Marsigit
In mathematics, a proof is a demonstration that, given certain axioms, some statement of interest is necessarily true.
Proofs employ logic but usually include some amount of natural language which of course admits some ambiguity. In the context of proof theory, where purely formal proofs are considered, such not entirely formal demonstrations are called "social proofs".
The distinction has led to much examination of current and historical mathematical practice, quasi-empiricism in mathematics, and so-called folk mathematics (in both senses of that term).
The philosophy of mathematics is concerned with the role of language and logic in proofs, and mathematics as a language.
Regardless of one's attitude to formalism, the result that is proved to be true is a theorem; in a completely formal proof it would be the final line, and the complete proof shows how it follows from the axioms alone.