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ෆර්මාගේ අවසන් ගැටළුව
- Thread starter Persius
- Start date
See , I have two short PDF for the proof. FERMAT ALSO WOULD HAVE A SHORT PROOF FOR THIS THEOREM. BECAUSE FERMAT WAS ALIVE A LONG AGO. -----BUT ANDREW WILLIES PROOF IS VERY VERY LONG PROOF WITH 150 PAGES WITH COMPLEX.AT LEAST ANDREW WILLIES PROOF CAN NOT SHOW A PAPER OR WEB BECAUSE SO LONG PROOF.
First of all, saying that Fermat was "bluffing" about having a proof misrepresents what happened -- he made a note that he had a proof in the margin of a book he happened to be reading. Realistically, he wouldn't have expected anyone else to see it -- it was just a little note he wrote to himself. Most of us probably don't imagine that, after our deaths, our kids are going to publish our scratchwork.
(I should clarify that he was probably making these notes with the intention of eventually cleaning them up and publishing them, but certainly he did not expect anyone but him to look at his notes in their raw form.)
Second, he wrote this note when he was relatively young, and spent significant amounts of time in his later years just working on special cases, so by his later years he was certainly aware that he didn't have a working proof of the general case.
Now, as to what he thought was the proof, we can't say for sure, but there are a couple of arguments which work for small n that don't generalize to all n, but sort of look as though they should if you don't go over them with a fine-toothed comb. One is the flawed proof originally put forward by Lame, which relies on the "fact" that all rings are unique factorization domains, and another is the descent-based proof that Fermat himself later gave for some particular cases. Presumably Fermat came up with something resembling one of these, didn't immediately realize that it was wrong, certainly didn't think anything of the significance of the problem, and just made a little note about it.
Fermat's Last Theorem became famous because it was elementary to state and extremely difficult, but it has no real significance on its face; there are plenty of other easy-to-state problems that have remained unsolved for centuries, and there's no particular immediate application of the FLT. Fermat certainly couldn't have had any conception that the problem would become what it did.
equation (3) gaththe kalinma n=2 kiyala neda?
equation (2) c<a+b kiyala gaththeth n=2 kiyalama neda?
n=2 kiyala ganne nathuwa , c<a+b kiyanna bahane , ehema kiyanna puluwan unoth a+b -> c , equation (3) valid nahane.
Fermat's Last Theorem eka nikan katin kiyala penanna puluwan , ewunata eka mathematically prove karoth thamai piliganna puluwan wenne. eka nisa rachanawak wage liyala pennanawata wada, mathematical notations walin ma sadanaya karanla penanna. Wiles ge proof eka unath pages 108 une rachanawak liyanne nathuwa mathematically penanna una nisa wenna oni.
equation (3) gaththe kalinma n=2 kiyala neda?
equation (2) c<a+b kiyala gaththeth n=2 kiyalama neda?
n=2 kiyala ganne nathuwa , c<a+b kiyanna bahane , ehema kiyanna puluwan unoth a+b -> c , equation (3) valid nahane.
Fermat's Last Theorem eka nikan katin kiyala penanna puluwan , ewunata eka mathematically prove karoth thamai piliganna puluwan wenne. eka nisa rachanawak wage liyala pennanawata wada, mathematical notations walin ma sadanaya karanla penanna. Wiles ge proof eka unath pages 108 une rachanawak liyanne nathuwa mathematically penanna una nisa wenna oni.
That's true,
Another possibility is that he simply expressed himself in a sloppy way and intended to state that he conjectured the general result but only had a proof for the n=4 case. He is known from elsewhere to have really had a proof for the n=4 case. I think it is interesting that in his margin note he singled out the n=3 and n=4 cases before conjecturing the general case. I consider it very possible that--in a margin note intended only for himself--he just wasn't sufficiently clear that his actual proof was only for the n=4 case. He had a proof for the n=4 case and posed both the n=3 and n=4 cases as challenges to his contemporaries. But he never mentioned the general case again except that one time in the margin. This leads me to suspect he was proud of his n=4 proof--and also believed the n=3 case to possibly be within range of his contemporaries--but also believed a proof of the general case to be well beyond the reach of the mathematicians of his time.
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It is really difficult to say what exactly was in his mind when he wrote that he had a proof for his claim.
It took more than three hundred years to actually prove this so simple looking theorem. In these three hundred years, the problem was tried by several really smart minds, who,I would say were as smart as Fermat if not greater. They simply could not produce a proof. Also, over the years Mathematics grew and new techniques were introduced. Andrew Wiles, the mathematician who proved the theorem, worked for 8 odd years to produce the proof and used techniques such as elliptic curves and modular forms which simply did not exist back in Fermat’s time.
Now, it is possible that Fermat had a different and simple of way of proving the theorem. But if it had been that simple, I’m sure the problem wouldn’t have been open for three centuries. Some one would have figured it out.
That means, the solution was not so easy as Fermat had liked to believe.
Personally i believe that he wasn’t bluffing. He thought he had a way of tackling it, worked the outline of the proof in his mind and thought that the problem was just another simple puzzle and wrote the legendary note on the margin of that book that kept mathematicians wondering what the proof was. And Fermat had this habit of not really giving extensive proofs to his theorems, which by the way were proven later by other mathematicians after his death.
It took more than three hundred years to actually prove this so simple looking theorem. In these three hundred years, the problem was tried by several really smart minds, who,I would say were as smart as Fermat if not greater. They simply could not produce a proof. Also, over the years Mathematics grew and new techniques were introduced. Andrew Wiles, the mathematician who proved the theorem, worked for 8 odd years to produce the proof and used techniques such as elliptic curves and modular forms which simply did not exist back in Fermat’s time.
Now, it is possible that Fermat had a different and simple of way of proving the theorem. But if it had been that simple, I’m sure the problem wouldn’t have been open for three centuries. Some one would have figured it out.
That means, the solution was not so easy as Fermat had liked to believe.
Personally i believe that he wasn’t bluffing. He thought he had a way of tackling it, worked the outline of the proof in his mind and thought that the problem was just another simple puzzle and wrote the legendary note on the margin of that book that kept mathematicians wondering what the proof was. And Fermat had this habit of not really giving extensive proofs to his theorems, which by the way were proven later by other mathematicians after his death.
repeat same answers. a,b,c are common. so c<a+b is valid for n=any value. common means for any value of n
equation (3) gaththe kalinma n=2 kiyala neda?
equation (2) c<a+b kiyala gaththeth n=2 kiyalama neda?
n=2 kiyala ganne nathuwa , c<a+b kiyanna bahane , ehema kiyanna puluwan unoth a+b -> c , equation (3) valid nahane.
Fermat's Last Theorem eka nikan katin kiyala penanna puluwan , ewunata eka mathematically prove karoth thamai piliganna puluwan wenne. eka nisa rachanawak wage liyala pennanawata wada, mathematical notations walin ma sadanaya karanla penanna. Wiles ge proof eka unath pages 108 une rachanawak liyanne nathuwa mathematically penanna una nisa wenna oni.
equation (3) gaththe kalinma n=2 kiyala neda?
equation (2) c<a+b kiyala gaththeth n=2 kiyalama neda?
n=2 kiyala ganne nathuwa , c<a+b kiyanna bahane , ehema kiyanna puluwan unoth a+b -> c , equation (3) valid nahane.
Fermat's Last Theorem eka nikan katin kiyala penanna puluwan , ewunata eka mathematically prove karoth thamai piliganna puluwan wenne. eka nisa rachanawak wage liyala pennanawata wada, mathematical notations walin ma sadanaya karanla penanna. Wiles ge proof eka unath pages 108 une rachanawak liyanne nathuwa mathematically penanna una nisa wenna oni.
I don't think no point arguing with him , he repeated same thing over and over again without any mathematical proof. for correct proof you need to use mathematical deductions and should show it's correct for any value of " n".
And then pdf [2] and In my blog my comments also. In equation [ 3] in PDF1 at last , n=2 because left side has two terms and right side has three terms, BUT WHEN a+b tends to minimum value c , THEN a+b becomes one term c . SO n can differs from 2. ALREADY I MENTIONED IN MY BLOG WITH MY COMMENTS.
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