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.

Comments

That's what's good about critical thinkers

[MBGMorden]

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.

Re:That's what's good about critical thinkers

[31415926535897]

I was about to mod you up after reading your first sentence, but then the second came. Look, we all know of people who hop on the bandwagon of science and are as stubborn as anyone. There are also plenty of religious folk who use their brains (in the voice of Inigo Montoya, "You keep using that word faith. I do not think it means what you think it means").

Re:That's what's good about critical thinkers

[Captain Splendid]

Look, we all know of people who hop on the bandwagon of science and are as stubborn as anyone.

That's like judging the artistic merit of a band by focusing on their groupies. When the faithful criticize scientists, they're not using those arguments anyway.

There are also plenty of religious folk who use their brains

Unfortunately, they're in the minority and not anywhere near as loud-mouthed as their fundie brethren.

Re:That's what's good about critical thinkers

[Anonymous Coward]

Apples and oranges in a sense though.

Religion concern itself with "why".
Science concerns itself with "how".

Re:That's what's good about critical thinkers

[sacrilicious]

Sure, there are exceptions. But the GP's point is solid: the fundamental process in science is working from facts to supporting models, and the fundamental process in faith is working from models to supporting facts. They are indeed opposites, and various degrees of exceptions to them does not change their stated missions nor their overarching patterns of practice.

Re:That's what's good about critical thinkers

[Anonymous Coward]

If the "why" is irrelevant or meaningless, then a human being has as much value as a rock, and both will be nothing more than different Lego structures.

Re:That's what's good about critical thinkers

[Strider-]

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.

That's a pretty narrow definition of religion. For a significant, but less vocal part of religious folk, faith and science are more or less orthogonal. Scientific exploration and explanation doesn't eliminate faith, and religion doesn't deny science.

For me, the main intersection between Faith and Science is in the realm of ethics. It's not whether a certain piece of research is good or bad, but whether does it help to achieve what we're commanded to do... Help the poor, feed the hungry, be good stewards of creation.

Re:That's what's good about critical thinkers

[alvinrod]

Science is still practiced by people who can be pig-headed and stick to their guns long after it has become apparent there is no basis for them or will be reluctant to accept some new information that seems to turn the field on its head. It's something of human nature to cling to an initial belief despite good evidence to the contrary.

The important part is that mathematics and science give us the means to verify our beliefs (or at least in the case of science to test and reject other possible explanations) as the universe is under no obligation to conform to a mistaken belief. Religion has no such methods.

Re:That's what's good about critical thinkers

[gweihir]

Not really. Religion is dumb. Literally. However there are quite a few people that use Science as a surrogate for religion and that corrupts science and makes it religion. For science you need an open mind. A main aim of religion is to close minds so that they do not go run off to the competition.

Re:That's what's good about critical thinkers

[jason777]

The problem with science is that it cannot get outside itself. For example, if the universe had a beginning, science cannot get outside that point. So if God created the universe (something had to), then science can never prove that. Hence faith. Science also presupposes other things in order for the scientific method to work. For example, logic.

Re:That's what's good about critical thinkers

[Archangel Michael]

Not Inigo, so answering for myself (not him/her)

Science vs Religion is framed this (GP Post) way for ego. There is no scientific reason why the two should be compared on the same plane, since they deal with totally different realms.

Lets take a well known example. The Bible says that God Created the earth, and mankind. IT doesn't say when (except "the beginning" horrible translation btw). There are people that have extrapolated out lineages and calculated the "age of the earth" at 6000 years (give or take), but I want to remind you, that the Bible itself doesn't say it is 6000 years old anywhere.

Science on the other hand is pretty much convinced it is millions of years old. I can't say "proven" because that is not something that is provable, but from a statistical point of view, it is not likely that it is only 6000 years old. ;)

My faith (biblically based) doesn't require the earth to be only 6000 years old, or millions of years old. What it has done, is proven that science cannot account for the sins of man. The story of the man and woman in the garden is instructive, because with all the knowledge we've gained over the years (6000 or a Millennia ) has itself proven true, we are technologically better off, but morally bankrupt in the process. Instead of being able to pick up a rock and kill our brother, we now have arms that can kill millions without ever seeing the destruction we inflict.

Or, to put it a different way

Your scientists were so preoccupied with whether or not they could, they didn’t stop to think if they should

For every technological achievement we have that is used for good, it is matched equally with the ability to harm to a larger and larger number of people. This lesson is buried in the beginning pages of the the book so many people have opinions of, but have never actually read.

Please read this, not as a slam against science, but rather as a defense against strawman arguments used to discredit a book, that is philosophical/moral and not scientific. Most books of faith are the same, btw, they don't usually deal with Science, but rather the moral character of man. They aren't even in the same playing space. BTW, I have the same critique of my bible thumping comrades who mix religion with science too. ;)

Science without morals is how we get Josef Mengele. Morals without truth (science) is how we get to burning witches. There is a place, side by side, for Religion and Science to co-exist.

Re:That's what's good about critical thinkers

[ag0ny]

Lets take a well known example. The Bible says that God Created the earth, and mankind.

And The Silmarillion clearly states in the Ainulindalë that Eru Ilúvatar created the Ainur, who in turn created Arda through their music.

You can't quote a book to justify your belief in an imaginary friend in the sky.

In one thing you're right: science and faith are in completely different realms. Science works with the real world and what can be demonstrated. Faith is just wishful thinking based on a delusion. It's perfectly fine to mock religion into oblivion until we finally get rid of this nonsense.

Re:Who the fuck cares?

[Myrdos]

Once the debate is solved will anything change?

Only if the solution shows that P = NP.