"The difficulty is what if the contradiction comes not from the assumption that P=NP, but rather from some error in the proof of one of the lemmas or theorems? A problem. A serious problem. Then the proof is wrong."
For a proof to be correct, every step of the proof has to be correct.
I can't see this as a problem specific to proof by contradiction. I suppose long proofs are more dangerous than short proofs because long proofs have more steps that need to be taken.
If someone really thought they had a P/=NP proof, it would be prudent for them to break it up into Lemmas which stood on their own and only at the end point out what they'd proved. But these considerations seem completely orthogonal to the method of proof.
Am I missing something (seriously, I am only an amateur myself)?
For a proof to be correct, every step of the proof has to be correct.
I can't see this as a problem specific to proof by contradiction. I suppose long proofs are more dangerous than short proofs because long proofs have more steps that need to be taken.
If someone really thought they had a P/=NP proof, it would be prudent for them to break it up into Lemmas which stood on their own and only at the end point out what they'd proved. But these considerations seem completely orthogonal to the method of proof.
Am I missing something (seriously, I am only an amateur myself)?