I never accepted the proof of the original, because in my view a proof needs to be convincing as well as correct. Not every mathematician has this view, but language-wise I'd prefer to call the original proof a "verification of correctness" rather than a proof. The new proof is similar - more of a formal correctness verification.
What is the point of proof if not to actually convince the reader that the statement is correct? After all, most modern pure math is not terribly relevant to solve practical problems anyway, so if it's not convincing, then what?
I have this same discussion with folks applying formal methods to prove the correctness of software where I work. Often the "proof" is harder to read than the original code and I certainly don't feel anyone has proven anything to me.
this reminds me of a debate about science education - somewhere in elementary school we had to study various proofs that the world was round, mostly with historical context. some people now argue that we don't need this to be part of the curriculum any more - the answer is "we have gone to space and seen it, here are the photos!"
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I never accepted the proof of the original, because in my view a proof needs to be convincing as well as correct. Not every mathematician has this view, but language-wise I'd prefer to call the original proof a "verification of correctness" rather than a proof. The new proof is similar - more of a formal correctness verification.
What is the point of proof if not to actually convince the reader that the statement is correct? After all, most modern pure math is not terribly relevant to solve practical problems anyway, so if it's not convincing, then what?
I have this same discussion with folks applying formal methods to prove the correctness of software where I work. Often the "proof" is harder to read than the original code and I certainly don't feel anyone has proven anything to me.
this reminds me of a debate about science education - somewhere in elementary school we had to study various proofs that the world was round, mostly with historical context. some people now argue that we don't need this to be part of the curriculum any more - the answer is "we have gone to space and seen it, here are the photos!"