When does a set of hypotheses become a theory?

Hypotheses are statements which may or may not be true. If there is overwhelming support for such a set, it becomes a theory. In science a theory can be disproved but it can never be proven: you can only add to the weight of evidence in its support.

Mathematics is somewhat different. Although Kurt Godel proved that any non-trivial axiomatic system must contain statements whose truth or falsehood cannot be proven from within the system, most statements can be proven to be true or false. A set of hypotheses becomes a theory if every statement in it can be shown to be true, starting from the system's axioms and using any theorems already proven to be true.