As others have noted, finding the truth of a theorem is important and elegance has to be secondary in most people's book. Or at least, the truth of a proposition is never not going to be important.
But oppositely, I don't think anyone's demonstrated "proof mining" to be practical in any general sense. Huge proofs have been produced by brute-force, yes, BUT ONLY after the original theorem claim was altered in a clever and important fashion (for 4-color theorem, for Ramsey's theory and so-forth).
But oppositely, I don't think anyone's demonstrated "proof mining" to be practical in any general sense. Huge proofs have been produced by brute-force, yes, BUT ONLY after the original theorem claim was altered in a clever and important fashion (for 4-color theorem, for Ramsey's theory and so-forth).