alt Hacker NewsYou're looking for the practical answer, but philosophically it isn't possible to translate an informal statement into a formal one 'correctly'. It is informal, ie, vaguely specified. The only certain questions are if the formal axioms and results are interesting which is independent of the informal formalisation and that can only be established by inspecting the the proof independently of the informal spec.
Philosophically, this is not true in general, but that's for trivial reasons: "how many integers greater than 7 are blue?" doesn't correspond to a formal question. It is absolutely true in many specific cases. Most problems posed by a mathematician will correspond to exactly one formal proposition, within the context of a given formal system. This problem is unusual, in that it was originally misspecified.