[tdiddy]

Just because there is a theorem, doesn't mean a proof exists

Excuse me, but by definition a theorem is proposition that can be proved from accepted premises. So, actually if there is a theorem, there must also be a proof of a theorem. If there is no known proof of the proposition, then it is called a conjecture even if it is widely believed to be true. Of course, Fermat's Last Theorem was called a theorem before it was proven, but it was actually only a conjecture until it was recently proved true.