I really apologize if my question is not appropriate here, though I hope it is.
Let $C$ be any known conjecture in mathematics, which is still open. Let $D$ be another conjecture such that a positive answer to conjecture $C$ implies a positive answer to conjecture $D$. Now assume that one proved conjecture $D$.
Do you think that mathematicians working on conjecture $C$ will find such a result interesting?
Of course, if one has found a counterexample to conjecture $D$, then conjecture $C$ is false, but this is not the situation I am asking about.
Thank you very much!
This is discussed at some length in George Pólya's book Mathematics and Plausible Reasoning Vol. 2, Patterns of Plausible Inference. He points out, for instance, that if $A$ implies $B$, and if $B$ is quite plausible in itself, then verifying $B$ makes $A$ just a little bit more credible; but if $B$ was very improbable in itself, then verifying $B$ makes $A$ much more credible.