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Thread: Could there be an error in the proof of the Poincare conjecture?

  1. #1
    MHF Contributor alexmahone's Avatar
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    Could there be an error in the proof of the Poincare conjecture?

    When Grisha Perelman submitted his proof of the Poincare conjecture, he may have been reasonably sure that it contained no mistakes. But he could not have been 100% sure as he is, after all, human. Each time it was checked, say by the referee of an academic journal, the probability that it contains no mistakes increases. But does it ever reach 100%? After all, the referees and checkers are human as well and they could theoretically have overlooked some subtle flaw in the proof.

    So, I claim that we can be almost certain that the Poincare conjecture has been proved, but in theory we can never be 100% sure.

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    Re: Could there be an error in the proof of the Poincare conjecture?

    That would be true of any theorem.

    Oh, dear, I starting to wonder if 2+ 2 is really equal to 4!
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    Forum Admin topsquark's Avatar
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    Re: Could there be an error in the proof of the Poincare conjecture?

    Quote Originally Posted by HallsofIvy View Post
    That would be true of any theorem.

    Oh, dear, I starting to wonder if 2+ 2 is really equal to 4!
    2 + 2 = 11. In base 3 anyway.

    -Dan
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    Re: Could there be an error in the proof of the Poincare conjecture?

    Mathematics is a science. It's results are considered true until someone spots a flaw, and then people work at making it all consistent again.

    Euclid's fifth postulate was generally considered "true" (and provable) until it was realised that it was neither true nor false.
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    Forum Admin topsquark's Avatar
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    Re: Could there be an error in the proof of the Poincare conjecture?

    Quote Originally Posted by Archie View Post
    Mathematics is a science. It's results are considered true until someone spots a flaw, and then people work at making it all consistent again.
    I don't quite agree. In Math it is possible to construct an actual proof. Scientific theories cannot be proved, only noted for accuracy.

    -Dan
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    Re: Could there be an error in the proof of the Poincare conjecture?

    Yes, but if a proof previously considered water-tight is found to have a flaw, it stops being valid. If there are no other proofs, the result itself might be called into question.
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