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Mathematician Who Claimed 'P Is Not Equal To NP' Says His Proof Is Wrong (arxiv.org)

Posted by msmash on from the end-of-debate dept.

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.

6 of 234 comments (clear)

  1. That's what's good about critical thinkers by MBGMorden · · Score: 5, Insightful

    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
    1. Re:That's what's good about critical thinkers by Anonymous Coward · · Score: 5, Insightful

      Apples and oranges in a sense though.

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

    2. Re:That's what's good about critical thinkers by Anonymous Coward · · Score: 5, Interesting

      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.
      That's why MBGMorden used "science" and "religion" not "scientists", and "religious people". People can be stubborn and non-corrective, but science as a whole corrects itself. In the same vein, Religion (western at least) sticks to ideas like nothing else. How many hundreds of years did it take for the Catholic church to admit that maybe it shouldn't have punished Galileo?

      Look no further than the books of each craft. Science books change all the time. Go find some Geology books from the 1940s, and you'll see crazy explanations we now know are wrong about what causes Earthquakes. Those ideas died out after Plate Tectonics took over in the 1950s or so.

      By contrast, the Bible was canonized long, long ago and can't change. Religion changes very, very, very slowly. Much of the change is do to splinter groups forming and going off and doing their own thing. That's the perfect example of inflexibility. Splinter factions don't really happen much in science, and when they do, it's temporary until there's more data available, and consensus forms. Try that in religion!

    3. Re:That's what's good about critical thinkers by alvinrod · · Score: 5, Insightful

      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.

    4. Re: That's what's good about critical thinkers by Anonymous Coward · · Score: 5, Interesting

      Objectively, that is true. Human beings and rocks are basically the same thing, from a universal context.

      To he human beings themselves, though, it's clearly not true.

      But we, the ones having this conversation, are human beings. Thus, human beings matter a great deal more than rocks in the only context that matters, our own. That importance is not hinged on any sort of "why" we exist. In fact, any hypothetical "why" that involves god(s) actually would reduce our importance. See Christians whose whole world view is based on how awful and useless we are as creatures.

  2. Re:Who the fuck cares? by Myrdos · · Score: 5, Insightful

    Once the debate is solved will anything change?

    Only if the solution shows that P = NP.