In mathematics, a conjecture is a mathematical statement which appears likely to be true, but has not been formally proven to be true uner the rules of mathematical logic. Once a conjecture is formally proven true it is elevated to the status of theorem and may be used afterwards without risk in the construction of other formal mathematical proofs. Until that time, mathematicians may use the conjecture on a provisional basis, but any resulting work is itself provisional until the underlying conjecture is cleared up.