[timwiseman]

You make fine points and I agree.

But if I may, it can be expanded on. In mathematics, a theorem is an idea combined with proof. In short, the idea is combined with the knowledge that it is a true and accurate fact (at least within the domain you are working in. Things are true in C that are not true in R), along with some idea why it is true emboddied in the proof. It is this combination of the idea with knowledge it is right that makes it valuable.

To be slightly more concrete, the idea that P = NP is not overly valuable. It is not yet proven either way and it could be true or false. A full proof would be tremendously valuable, and very surprising to many who are very confident P != NP. Creating a proper proof seems much more akin to writing the novel than it is to having the idea for the novel.