Mathematician Who Claimed 'P Is Not Equal To NP' Says His Proof Is Wrong (arxiv.org)
Earlier this month, Norbert Blum, a German mathematician, had published a research paper in which he implied that P is not equal to NP. The abstract of the post read: Berg and Ulfberg and Amano and Maruoka have used CNF-DNF-approximators to prove exponential lower bounds for the monotone network complexity of the clique function and of Andreev's function. We show that these approximators can be used to prove the same lower bound for their non-monotone network complexity. This implies P not equal NP. Since the publication of that paper, several mathematicians have raised concerns with Blum's methodology, with some saying that there are flaws in it. Blum has now updated the research paper to add: The proof is wrong. I shall elaborate precisely what the mistake is. For doing this, I need some time.
Only if N = 1
It's refreshing to see people who will readily admit when they're wrong, since they're looking for the truth, not to prove a point.
That's always what I fall back two when people compare science to a religion: religion relies on faith - sticking to your beliefs no matter the evidence presented. Science will readily toss out everything they know and start over if something is proven to be wrong.
"People who think they know everything are very annoying to those of us who do."-Mark Twain
Seriously. This debate always comes up. Does it have a practical purpose? Once the debate is solved will anything change?
Only the State obtains its revenue by coercion. - Murray Rothbard
correction prove read
Only for NP-complete problems.
They haven't been proven to be NP-complete. There are certainly in NP.
Unfortunately, my proof cannot fit in the margins of this post.
It may look like I'm doing nothing, but I'm actively waiting for my problems to go away.
--Scott Adams
seriously, I expect better.
You must be new here.
No sig today...
Einstein was criticized for sticking to his crackpot "general" theories in later life and not jumping onto the quantum bandwagon he himself had originally piloted out of the shuttle bay. But ask yourself this: did the world actually need Einstein working on quantum physics, or were all the other brilliant people involved more than sufficient?
If the stubborn Einstein had not persisted down his stubborn path, would we now be collectively guessing what might have been in the one and only Einstein had not nestled himself in the cockpit of the alien wormhole shuttle to unimagined physics?
Instead of yammering on about this old arrogance morality tale (oh, tiresome prose!) how about bringing some actual cost/benefit to the table?
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You know, in that horrible movie, The Hobbit, I wasn't going to believe they couldn't open that stone door until there was 14 skeletons lying beneath it. If you're going to rattle the handle to the dragon's lair, the least you can do is stick to your guns (and your magic moon map).
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For anyone interested the sociology of science, or the immensity of planet earth itself, or just in it for some mind-blowing pictures, I can't recommend the following article strongly enough:
Formed by Megafloods, This Place Fooled Scientists for Decades — 9 March 2017
I often visited Drumheller and the surrounding badlands in my childhood. Amazing place. Never been to Spokane, but it's not that far away.
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Grow up. Stubbornness is a virtue every damn time stubbornness works.
The exceptions are so rare, Herzog made a movie about it, with the entire cast in character the whole wretched time.
Aguirre, the Wrath of God
The fundamental process in science is TRUTH.
Using facts and models are tools used in searching for truth. I can point to thousands of people claiming to be "Scientists" who do exactly what you claim Faith holders are doing. In fact, models which ignore facts are extremely common.
-The wise argue that there are few absolutes, the fool argues that there are no probabilities.
retracting his proof this quickly and acknowledging error takes fortitude and a type of perseverance not often seen.
Bravo in the attempt
... it is about time ... polynomial vs nonpolynomial ... but time is the same ... and u can have all the time in universe ... u can divide it infinitely ... so u c a n spend as much time u need ... u got it ?
I'm ready to accept they are not equal, but why hasn't anyone the guts to suggest which is greater than the other?
tone
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