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Are Computers Ready to Create Mathematical Proofs?

Posted by michael on from the GIGO dept.

DoraLives writes "Interesting article in the New York Times regarding the quandary mathematicians are now finding themselves in. In a lovely irony reminiscent of the torture, in days of yore, that students were put through when it came to using, or not using, newfangled calculators in class, the Big Guys are now wrestling with a very similar issue regarding computers: 'Can we trust the darned things?' 'Can we know what we know?' Fascinating stuff."

8 of 441 comments (clear)

  1. Rumsfeld, anyone? by dolo666 · · Score: 5, Funny

    > 'Can we know what we know?' Fascinating stuff.

    Reminds me of Rumsfeld... "Reports that say that something hasn't happened are always interesting to me, because as we know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns -- the ones we don't know we don't know."

    1. Re:Rumsfeld, anyone? by Deraj+DeZine · · Score: 4, Funny

      Well, I had been in the don't care that I don't know category; now I'm in the don't care that I know. Great.

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      True story.
    2. Re:Rumsfeld, anyone? by jgabby · · Score: 5, Funny

      Then there's:

      My boss, who knows that he knows not;
      But pretends that he knows that he knows;
      And he's so convincing at it, that;
      People who know that he doesn't know;
      Beleive that he knows that he knows anyway.

  2. 'Can we trust the darned things?' by FFFish · · Score: 4, Funny

    Depends whether it's a Pentium with an FDIV bug, I imagine...

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  3. Wait, I know this one... by bomb_number_20 · · Score: 4, Funny

    The answer is left as an exercise for the reader.

    --
    That's ok, Jesus likes me anyway.
  4. The stack might get a bit deep, but... by Odin's+Raven · · Score: 4, Funny
    'Can we trust the darned things?' 'Can we know what we know?'

    The obvious solution is to have the computer create a new proof that shows that the algorithm it used to create the original proof is, in fact correct.

    And to prove that the proof of the proof can be trusted, have the computer create a proof of the proof of the proof.

    And to prove that the proof of the proof of the proof can be trusted, ...
    --
    A marriage is always made up of two people who are prepared to swear that only the other one snores.
  5. Re:Create vs. Verify by panaceaa · · Score: 5, Funny

    Fortunately for you software researchers haven't programmed computers to create their own long sentences with so many prepositions that human readers of the created sentences are unable to remember the subject or figure out which verb, or possibly adjective, the trailing adverb applies to by the time they have read the entire sentence yet!

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    my blog
  6. Re:Create vs. Verify by eliza_effect · · Score: 5, Funny

    Can you please tell us The Question?

    The Ultimate Question?

    Yes!

    Of Life, The Universe..

    And everything?

    And Everything.

    Yes.

    Tricky..

    But can you do it?

    ...No. But I'll tell you who can.

    Who? Tell us!

    I speak of none, but the computer that is to come after me.

    What computer?

    A computer whose merest operational parameters I am not worthy to calculate and yet I will design it for you. A computer which can calculate The Question to the Ultimate Answer. A computer of such infinite and subtle complexity that organic life itself will form part of it's operational matrix. And it will be called.. The Earth.

    What a dull name.