Posted on 08/14/2010 7:57:39 PM PDT by LibWhacker
Initially hailed as a solution to the biggest question in computer science, the latest attempt to prove P ≠ NP – otherwise known as the "P vs NP" problem – seems to be running into trouble.
Two prominent computer scientists have pointed out potentially "fatal flaws" in the draft proof by Vinay Deolalikar of Hewlett-Packard Labs in Palo Alto, California.
Since the 100-page proof exploded onto the internet a week ago, mathematicians and computer scientists have been racing to make sense of it.
The problem concerns the speed at which a computer can accomplish a task such as factorising a number. Roughly speaking, P is the set of problems that can be computed quickly, while NP contains problems for which the answer can be checked quickly. Serious hole?
It is generally suspected that P ≠ NP. If this is so, it would impose severe limits on what computers can accomplish. Deolalikar claims to have proved this. If he turns out to be correct, he will earn himself a $1 million Millennium prize from the Clay Mathematics Institute in Cambridge, Massachusetts.
(Excerpt) Read more at newscientist.com ...
What does this mean in english?
In plain english, it means there are weird but smart people who worry about things so I don’t have to...
P is not equal to not-P
Yeah, well, I exploded the proof the first day it came out. Guy forgot to carry the 5.
/obvious bunkum
This mean theoretical mathematicians have nothing better to do. There is no practical application for any of this, except to build into other proofs that may have some theoretical application. Its the same as the Busy Beaver and Ackerman sequences - sort of. I’m not an egg head, but know some of this stuff. Just pretend you never heard of this story, and the world will continue to move as it always has.
HELLO! Previously useless theoretical mathematics is always getting dusted off and being applied to new applications. University mathematics degrees are frequently titled and earned in ‘theoretical and applied mathematics’— b.s. m.s. phd.
NP is nondeterministic polynomial time, not "not P."
LOL - Ok. I wondered why is wasn’t “7P”
Apropos, I have actually seen mathematicians come to blows over a proof.
“Ok, 15-minute break - everybody go outside!”
Let A=B=1
Then, it follows that AA=AB
Hence, AA-BB=AB-BB
Thus, (A+B)(A-B)=B(A-B)
Therefore, it should be obvious to the casual observer, that A+B=B
And so A=0
QED, 1=0
That's all I'm sayin'.
Is 0 odd or even?
I’ve been snooping around looking for applications. It’s considered very important for AI, quantum computing, cryptography, airline scheduling, etc. So it’s way up there in importance and not just some abstract intellectual exercise for pure mathematicians.
Yes!... :-)
Seriously, it’s even...
No, by definition, it is not. Even Numbers are defined as numbers >1, and divisible by 2.
By extension, that now includes the numeri ficti - {-2,-4,-6...}
0 is excluded.
Isn’t that what I just said...?!
That’s a different equation to my literal mind. If P is 0 and NP is any other number than 0, then P can only equal NP if other equations are applied, which is more than the stated equation asks for. Then again, I’m not even a math amateur.
If you’re right, where’s your million plus a bonus for your less than a page answer?!
Dr. Math says 0 is even.
http://mathforum.org/library/drmath/view/57132.html
Who am I to argue with this?
I forgot to thank you for the brain exercise!
Now, now... Stop that! You’ll confuse people. Zero is even. Negative numbers aren’t fictional. And you can’t divide by zero. lol
I am not right - clearly, 0<>1.
The proof is a trick. Meant to be a joke.
LOL - what, nobody gets my humor, today...
Did you know that pie are not square? But 2 pie are.
“Thus, (A+B)(A-B)=B(A-B)
Therefore, it should be obvious to the casual observer, that A+B=B”
You’d be right if division by zero were permitted. Unfortunately it’s not, QED, you’re wrong.
LOL! I never was all that good at math!
Dunno who you are, but the good Dr’s are wrong. See the Peano Axioms, and go from there.
I meant to be wrong.
Apropos, one of my favorite HS teachers - Rocky, aka MR. Rockwell, aka the math guy - died last week.
He was a vet, a pilot, and a really good influence on my life. Looked at me funny when I enlisted during the Iranian Hostage Crises, but was really supportive.
I kept meaning to go show him my degree in Math - it would have made him laugh.
But I never did.
Sigh.
Dunno who you are, but Dr. Penner isn’t buying your story:
^ Lemma B.2.2, The integer 0 is even and is not odd, in Penner, Robert C. (1999). Discrete Mathematics: Proof Techniques and Mathematical Structures. World Scientific. pp. 34. ISBN 9810240880.
“I meant to be wrong.”
I assumed so. One of my favorite HS teachers taught us the fallacy underlying this “proof.” But until he did so, it had us all baffled.
Okay, now I’m worried; I understand at least part of the concept.
Nothing yet, but if someone does send me a million dollars that I didn’t earn, all refunds are subject to a 99% service fee. : )
Well, clearly, Dr. Penner wrote his discrete maths text after I graduated. LOL.
And yes, Rocky was the one who showed my the silly 1=0 trick.
Divergence, divergence, hmmm...
Or, as Rocky used to put it, 1=2, but only for very large values of 1!
“Did you know that pie are not square? But 2 pie are.”
OK... that I got. LOL
;)
Silly wabbit, math is for twicks!
Math U Philosophy = Bi polar dude.
I had a room mate just after college that was just about to finish a MS in math at Texas Tech. He disappeared one day. The finally called and said he checked himself into a mental hospital.
Next weeks lotto number will be....
...the latest attempt to prove P ≠ NP -- otherwise known as the "P vs NP" problem -- seems to be running into trouble... The problem concerns the speed at which a computer can accomplish a task such as factorising a number. Roughly speaking, P is the set of problems that can be computed quickly, while NP contains problems for which the answer can be checked quickly... It is generally suspected that P ≠ NP. If this is so, it would impose severe limits on what computers can accomplish.
To P or not to P: ay, there is the rub.
I don’t understand why this is so hard P requires one operation.
NP requires at least two
As an engineer (not a scientist) I can’t help but feel more than a little sad every time I think of how the USA in 1984 literally threw away the pre-eminent institution of private basic research in the world....Bell Telephone Laboratories.
Had this institution and its corporate relationships and basic research been permitted to flourish as it had for decades, I have no doubt that this particular problem would have been solved years ago along with many others.
Candidly speaking I see a US government that has worked very hard and deliberative to destroy the once preeminent standing of the USA in research and manufacturing and exchange that capability so that a few crooks on Wall Street could make far too much money, and frankly I’m very ticked about it.
Today Bell Labs is just another typical corporate lab and it is owned by the French and Alcatel.
http://www.linfo.org/bell_labs.html
You just divided by zero.
Disclaimer: Opinions posted on Free Republic are those of the individual posters and do not necessarily represent the opinion of Free Republic or its management. All materials posted herein are protected by copyright law and the exemption for fair use of copyrighted works.