Is P=NP?
No synthesized answer yet. Check the discussion below.
There were many questions with no answers for literal centuries and thousands trying, and failing, to crack them. A solution was ultimately found despite that.
A new "math" might be needed, but an answer (affirming or not) will be found.
What if there exists a proof that P!=NP, but the shortest possible proof of that proposition is a googolplex symbols that long? Then P!=NP would be true, and provable and knowable in theory, yet eternally unprovable and unknowable in practice
Goodstein’s theory would take more symbols than there are atoms in the observable universe to write down in "classic" maths. To "fix" this, mathematicians had to use a "new" way of thinking about infinity known as transfinite induction.
I think if we're smart enough to detect(?) a proof, we'll find a way to express it in a finite manner.
Whether the Riemann hypotesis is true or not, is not going to have any practical effect, accept for a small group of mathematisians who are working on it. Most people do not know what a Field medal is nor care about it.
My completely unscientific hunch is someone will eventually prove that P=?=NP is independent of ZF(C). Maybe the universe just really wants to mess with complexity theorists
Or even a galactic algorithm-an algorithm for solving an NP-complete problem that is technically in P, but completely useless for anything in practice, e.g. O(n^10000000)
So it's P.
P v NP is not about ease, nor even realistic efforts.
P=NP and P=!NP are both proven nor disproven. (There is redundant information in this sentence.)
History shows us that the historical / ‘effort’ argument is not applicable to mathematics. All proofs were unproven once until proven successfully for the first time. Harder problems need bigger shoulders to stand on. Sometimes this is due to new tools, sometimes it is a magically gifted individual focusing on the problem, usually some mix of both. All we know is that all before have failed. It’s one of the beauties in math.
I recall there was a mathematician that was cataloging all the 'squaring the circle' methods people kept mailing him (it's been proven to be impossible).
I mean, if their idea were legitimately revolutionary and they had the vocabulary to express it, they could simply publish.
I agree. Computational limits become physical law, not algorithmic puzzles. Cryptography is unconditionally secure. NP-hard problems require approximation, not solution. AI must be heuristic, not exhaustive. Understanding what physics forbids, not just what we haven't achieved -> focuses effort productively.
From the original twit:
> I had a dream where P=NP.
Did this poster, in their dream, solve P=NP or they just heard it had already been solved?
Then after waking up from this dream he asked some slop slinger if P=NP?!?
From the follow up article:
> I guess by now you have a better understanding of why I thought I was crazy when I woke up thinking P=NP.
What do the details matter? Last week I had a dream that my childhood rat was the president of space. That's what dreams do.
> fun story: I still remember those “random oracles” that we used to proof cryptographic primitives in college
So someone who previously used 'random oracles' to prove 'cryptographic primitives' had to ask a slop slinger if P=NP?!?