In
mathematics, a
theorem is a
statement that has been
proven on the basis of previously established statements, such as other theorems—and generally accepted statements, such as
axioms. A theorem is a
logical consequence of the
axioms. The proof of a mathematical theorem is a logical argument for the theorem statement given in accord with the rules of a
deductive system. The proof of a theorem is often interpreted as justification of the truth of the theorem statement. In light of the requirement that theorems be proved, the concept of a theorem is fundamentally
deductive, in contrast to the notion of a
scientific law, which is
experimental.