Comment by novaRom
11 hours ago
For me, this result is significant. It basically adds much more hope P is equal NP (that majority seems being against). I believe one day AI will explain a major flaw in modern mathematics, so a kind of correction in axioms will be suggested to prove Rieman's hypothesis (or a completely new apparatus)
I don't know if that's a "flaw". It's what Godel Incompleteness guarantees.
Would be funny if the most famous problem turns out be an example though
That's not that how that works btw. The incompleteness is a property of the algorithm which does the proofs, not the theorems. If a theorem is true it has a proof and a program which proves it (printf("the proof verbatim")). But no computer program can successfully prove all theorems. The space of potential proofs is too big to search systematically, but you can still get lucky.
That is also not how it works. The theorem says that there exist some true statements for which there is no proof. This is assuming the axioms are consistent.
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Godel says that there are statements that are true but have no proof within that system. It's not about algorithms.
I'm saying it'd be funny if Riemann were true but not proveable.
Though I guess it's actually funnier. If Riemann were false then there would be a counterexample, so it's clearly within existing axioms.
So if one can prove that Riemann isn't proveable in our current axioms then it has to be true.
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Why do you "hope" P=NP? It would be a catastrophe
Either P=NP or not. Hoping one way or the other changes nothing. Nor does it change how efficient computing is, nor does it have any effect on cryptography. Discovering a vastly more efficient means of factoring primes--perhaps via quantum computing--would do that. But just learning that P=NP does nothing to further such a discovery. Almost certainly, if P=NP, the exponents and/or constants in a polynomial factoring algorithm would be galactic. (FWIW, Knuth believes that P=NP and that it has no practical consequences.)
Not really. P=NP but the degree of the polynomial is Grahams number doesn't let people into your bank account
it could make lots of compute way more efficient, not sure why it is catastrophe..
Why? Nature doesn't care if people are making financial transactions based on flawed cryptography.
Have you been in nature? It's cold and full of bugs and disease.