A conjecture is a statement believed to be true but without conclusive evidence. It differs from a hypothesis in that a conjecture has evidence to tentatively support it, and it differs from a theory because a conjecture is not an explanation of facts that has been sufficiently tested. A conjecture is more contestable than a theory but more solid than a hypothesis.
In mathematics, the term "conjecture" is used for strong guesses that unfortunately are beyond proof from the person who discovered the statement or pattern. The Goldbach Conjecture and the Riemann Hypothesis are two famous conjectures. Fermat's Last Theorem is or was a conjecture, depending on the validity of Andrew Wiles's proof.