A hypothesis is a proposition that is consistent with known data, but has been neither verified nor shown to be false.
In statistics, a hypothesis (sometimes called a statistical hypothesis) refers to a statement on which hypothesis testing will be based. Particularly important statistical hypotheses include the null hypothesis and alternative hypothesis.
In symbolic logic, a hypothesis is the first part of an implication (with the second part being known as the predicate).
In general mathematical usage, "hypothesis" is roughly synonymous with "conjecture."