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Fermat's Last Theorem.

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    Fermat's Last Theorem.

    Read a book about this over the weekend.

    Just looked up some of the mathematical ideas behind the proof.



    Stone me, I can't understand the stuff from the 19th century.

    Ideal number - Wikipedia, the free encyclopedia

    Much less the 20th.

    #2
    The modern proof is pretty mind boggling, and is pages long.

    Fermat's comment though, written just before he died, was good, sort of "the proof is quite simple, but it doesn't quite fit in the margin"

    The modern proof isn't what Fermat was thinking of so it would be interesting to work out what it actually was. I reckon there's a big prize waiting for anyone who can come up with it.
    Last edited by BlasterBates; 11 April 2011, 11:53.
    I'm alright Jack

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      #3
      I reckon our very own sasguru would have beaten Fermat easily.

      Good thing he is dead.

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        #4
        Originally posted by AtW View Post
        I reckon our very own sasguru would have beaten Fermat easily.

        Good thing he is dead.
        Sasguru is dead?!?



        Tests needed on man found dead in shed - Telegraph

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          #5
          Originally posted by BlasterBates View Post
          The modern proof is pretty mind boggling, and is pages long.

          Fermat's comment though, written just before he died, was good, sort of "the proof is quite simple, but it doesn't quite fit in the margin"

          The modern proof isn't what Fermat was thinking of so it would be interesting to work out what it actually was. I reckon there's a big prize waiting for anyone who can come up with it.
          There isn't a prize AFAIK but you would probably make a name for yourself. There are some prizes on offer from the clay maths institute for some other unsolved problems.

          It seems likely that if a simple proof existed Fermat would have written it down somewhere else and/or it would have been found already. A lot of very smart people had a crack at it in the intervening 300 odd years. So my guess is that he realised his idea was flawed.
          Last edited by doodab; 11 April 2011, 12:30.
          While you're waiting, read the free novel we sent you. It's a Spanish story about a guy named 'Manual.'

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            #6
            I don't like posts that spoil my illusion that I am a genius.

            Although obviously I could easily understand all that if I could be bothered.
            bloggoth

            If everything isn't black and white, I say, 'Why the hell not?'
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              #7
              Originally posted by doodab View Post
              There isn't a prize AFAIK but you would probably make a name for yourself. There are some prizes on offer from the clay maths institute for some other unsolved problems.

              It seems likely that if a simple proof existed Fermat would have written it down somewhere else and/or it would have been found already. A lot of very smart people had a crack at it in the intervening 300 odd years. So my guess is that he realised his idea was flawed.
              Mathematics Prizes -- from Wolfram MathWorld
              I'm alright Jack

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                #8
                Originally posted by xoggoth View Post
                I don't like posts that spoil my illusion that I am a genius.

                Although obviously I could easily understand all that if I could be bothered.
                Didn't threaded explain the proof of Fermat's last theorem to us in layman's terms a couple of years ago?

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                  #9
                  Originally posted by BlasterBates View Post
                  That's slightly out of date now, the poincare conjecture was solved by some Russian guy the other year.

                  You are unlikely to get the Cole prize, as they already gave it to Wiles. The prize for Beal's conjecture might be worth a crack though. Something to do in the evenings when you're working away from home anyway.
                  While you're waiting, read the free novel we sent you. It's a Spanish story about a guy named 'Manual.'

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                    #10
                    Originally posted by BlasterBates View Post
                    The modern proof is pretty mind boggling, and is pages long.

                    Fermat's comment though, written just before he died, was good, sort of "the proof is quite simple, but it doesn't quite fit in the margin"

                    The modern proof isn't what Fermat was thinking of so it would be interesting to work out what it actually was. I reckon there's a big prize waiting for anyone who can come up with it.
                    The comment wasn't written just before he died, quite the opposite in fact.

                    He first became interested in Diophantine Analysis (finding or ruling out integer and rational fraction solutions of underdetermined polynomial equations) when he read a copy of Bachet's commentaries on Diophantus as a student, or not long after, and that was when he scribbled the comment.

                    It was one of many other comments he scribbled in the margins, and for most of the other equations he claimed to have proved he did indeed later provide proofs or sketches. So given that he never mentioned FLT again, it is very unlikely he had a valid proof and equally likely he soon realized this.

                    Probably he assumed one could factor x^n + y^n (for prime n) into linear factors x + w^i y, where w is a complex n-th root of unity. If this factorization can be proved to be unique, then the result follows. Unfortunately (or fortunately, given how many advances have followed from the study of this and related equations), the factorization is not unique for all values of n.

                    However, at least two distinguished mathematicians, Sir Peter Swinnerton-Dyer and Doron Zeilberger are on record as not completely ruling out an elementary solution; but they both say this would almost certainly be extremely subtle and intricate in the unlikely event it exists.

                    Kummer's original theory of ideals, which he developed in the 1840s, is fairly tough to get one's head round, as is Kronecker's related theory of primary decomposition. But in the 1880s a guy called Dedekind greatly simplified the theory, and it's his definition of ideal that is used today. It's actually quite easy to explain and understand how it works, in everyday terms and examples, and if anyone is interested I will; but I won't waffle on any more now.
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