Fermat's Last Theorem
Simon Singh and John Lynch’s film tells the enthralling and emotional story of Andrew Wiles. A quiet English mathematician, he was drawn into maths by Fermat’s puzzle, but at Cambridge in the ’70s, FLT was considered a joke, so he set it aside. Then, in 1986, an extraordinary idea linked this irritating problem with one of the most profound ideas of modern mathematics: the Taniyama-Shimura Conjecture, named after a young Japanese mathematician who tragically committed suicide.
The link meant that if Taniyama was true then so must be FLT. When he heard, Wiles went after his childhood dream again. “I knew that the course of my life was changing.” For seven years, he worked in his attic study at Princeton, telling no one but his family. “My wife has only known me while I was working on Fermat”, says Andrew.
In June 1993 he reached his goal. At a three-day lecture at Cambridge, he outlined a proof of Taniyama – and with it Fermat’s Last Theorem. Wiles’ retiring life-style was shattered. Mathematics hit the front pages of the world’s press. Then disaster struck. His colleague, Dr Nick Katz, made a tiny request for clarification. It turned into a gaping hole in the proof. As Andrew struggled to repair the damage, pressure mounted for him to release the manuscript – to give up his dream. So Andrew Wiles retired back to his attic. He shut out everything, but Fermat.
A year later, at the point of defeat, he had a revelation. “It was the most important moment in my working life. Nothing I ever do again will be the same.” The very flaw was the key to a strategy he had abandoned years before. In an instant Fermat was proved; a life’s ambition achieved; the greatest puzzle of maths was no more.
Thank You prof. BRAHAMAGUPTHA, I am going to publish the third Simple and short proof of FLT using simple mathematics to say that You are one of real Mathematicians.
I am going to find a simple proof to using simple mathematics of FERMAT"S TIME. What elliptic integrals. We do not know length of an ellipse.
Rewo Nhongo' i agree with you regarding the main point that Fermat had a proof of his last theorem.Your Discussion Is great. .
c^3 =a^3 + b^3 and c^2 = a^3/c + b^3/c = m+ p/c + n + q/c where
a^3/c = m + p/c and b^3/c = n + q/c. p,q<c so that (p+q)<2c and (p+q)/c 2 but (f+g)2 so that for
(f+g+1)/c = k, f+g =(kc-1)>2. This means that no such a,b,c exist so that
c^3 = a^3 + b^3. Clearly, dividing both sides of the equation
c^v = a^v+b^v twice by c gets us to the point where c^(v-2) is not an integer for
v>2. QED . Now to say Fermat did not have the proof can not be true.
Statistics is not mathematics. I am not interested. I do believe that Fermat is generous with the correct evidences at the same time he is a amateur, not a professor.
Hi all,
I have a question for the statistical test:
If we assume that the event "Fermat really had the proof" is a random variable, what probability measure would you be able to propose for the acceptance of this null hypothesis "Fermat really had the proof":
0.00001, 0.0001, 0.001, 0.01, 0.1, 0.2, 0.3, 0.4, ..., 0.90, 0.99, 1.0
I think Fermat's last theorem and the following theorem is the same.Let x,y,z be positive integers and let h=y/x, g==z/x then the following equation
g^n=h^n+1,n>2,n being an integer,has only one rational solution g=1 and h=0.
Wait a little time,I have started the second fight.
To say the least, FLT is a recursive binomial truncate operator problem solvable in three pages. That's all. Sure, it requires inspiration but I did it. Who care? Think!
Pl.read on the internet.The Simplest proof of Fermat's last theorem,University of Kelaniya
Our proof by no means under estimates the proof of Andrew Wiles.One presented understanding alone properly, both specialized in Mathematics. I do not disclose all names.
I(with two of my students) have published The proof in an international conference which should be on the Internet.
Proof of Fermat’s last theorem for n=3.
Fermat’s last theorem for n=3 can be stated thus: There are no non-trivial integer triples x,y,z satisfying the equation
z^3=y^3+x^3,(x,y)=1 (1)
Proof of the theorem. Assume that there are non-trivial x,y,z which satisfy the equation (1).Now, without loss of generality we can assume that there non-trivial y,z>x>0 satisfying (1).
Put (1) in to the form
g^3=h^3+1 (2) by dividing the equation by x^3.
Now from (2) ,we have (g-h)[g^2+gh+h^2)=1.If g-h=d ,we have d>0 and
d[(〖h+d)〗^2+h(h+d)+h^2 ]=1, which can be written as
d^3+3hd^2+3h^2d-1=0 (3) and we know that d>0 and therefore it follows from (3) that
3hd^2+3h^2d-10 (B). Hence, its discriminant should be negative. In other words 9h^4+12h0. Therefore there are no non trivial integer triples satisfying (1). I believe now, you can prove the theorem for any n>2 using binomial expansion.
The mathematicians have made mathematics difficult.Pl.read carefully in these comments inequalities are not shown properly.
For all!
I have done my D.Sc in Quantum mechanics(Theoretical) long ago.I understood that a mathematical or any problem of our fields of study can be solved using the available mathematics at the time of problem. In this regard Fermat's last theorem was published in the 17th century.Therefore I tried last(one-proof is on the internet; A simple and short analytical proof of Fermat's last theorem.) to prove theorem using mathematics available in the 17 century. Pl. note that we have already published the proofs.I want you to challenge the world by proving this type theorem or conjecture. Wish you all the best.
Proof of Fermat’s last theorem for n=3.
Fermat’s last theorem for n=3 can be stated thus: There are no non-trivial integer triples x,y,z satisfying the equation
z^3=y^3+x^3,(x,y)=1 (1)
Proof of the theorem. Assume that there are non-trivial x,y,z which satisfy the equation (1).Now, without loss of generality we can assume that there non-trivial y,z>x>0 satisfying (1).
Put (1) in to the form
g^3=h^3+1 (2) by dividing the equation by x^3.
Now from (2) ,we have (g-h)[g^2+gh+h^2)=1.If g-h=d ,we have d>0 and
d[(〖h+d)〗^2+h(h+d)+h^2 ]=1, which can be written as
d^3+3hd^2+3h^2d-1=0 (3) and we know that d>0 and therefore it follows from (3) that
3hd^2+3h^2d-10. Hence, its discriminant should be negative. In other words 9h^4+12h0. Therefore there are no non trivial integer triples satisfying (1). I believe now, you can prove the theorem for any n>2 using binomial expansion.
The mathematicians have made mathematics difficult.
Pl,read and understand this high school level proof.
Fermat wasn't joking. Of course he had a proof rendered in terms of algebra as it stood at the time. In the years immediately after Wiles' proof was published I was working for mathematician/inventor named Herbert S. Riddle Jr., of Lake Oswego, Oregon, who was dissatisfied with Wile's proof for precisely this reason, namely, that it depended on centuries of intervening developments in math that Fermat would never know. Riddle, an MIT grad, and IEEE member , who was already mutipatented in electronic circuitry & digital encoding set to work to prove the theorem using "PERIOD MATHS" and was successful, so it appears.
Riddle's approach to the solution was simply to work to prove Fermat's Last Theorem true, by proving it true FOR THE LAST DIGIT of any possible number -- and so he called his work "Riddle's Last Digit Theorem." The proof is short, about three pages in length, and at one point he reduced it to about a page -- approximating a length that might correspond to Fermat's comments regarding the margins of his book. It's simple, elegant, and tight. I published some of Riddle's work on this in 2012,
Fermat's last theorem is a joke.Follow the proof in a different way
(z/x)^n=1+(y/x )^n and show that this is not an equation for any n>2.
i wonder if this math can help the Quantum mechanic problem using the theory of Chaos as a model for a system that uses quantum mechanical experiments to prove dynamic interpretative algorithms in programming that corresponds to micro discrete component macro visual display experiment. look at complex modulations in water drop experiments that are used for De Broglie's quantum mechanic vibrations. use these complex vibrations in reference to the dance of the universe shown in the book "The Dance of the Wu Li Masters" to see if any relativistic comparison could be derived from these two sources of data. I am trying to apply these ideas using polynomial approaches to linear Isomorphisms but use bouncing of an interactive Ping Pong games as physics model verses the falling of an apple or a man jumping off a house or a spinning carousel as Newtonian physics or Einstein did with his physics. I want to use more on hands experiments like Da Vinci using art forms.
I would love it so much that it shed some light to scientific research works to me. In economics world, finding theories, making linking chains, that must be what I should reach for.
They closed with the question of whether Fermat's solution could have been Wile's. Of course it couldn't be, but they didn't ask whether Fermat might have had another solution. The assumption is that he must have been wrong or perhaps joking but could Fermat have seen something incredibly powerful that nobody has yet realized or connected to the theorem?
God exists because the Archbishop of Canterbury says so. Fermat's Last Theorem is true because Andrew Wiles says so. Mathematics or religion? So sorry to disagree with you all guys but there you all are lauding something you do not even understand. Why? The 110 page report of the proof can be downloaded from Wikipedia, so do so, read it and then tell me if you are still impressed! The truth of the matter is that Fermat's Last Theorem is true because Pierre de Fermat proved it and stated it to be so. The truth of the matter is that the mathematicians have high jacked his glory and denied Fermat the accolade to which he is due and it's time that modern day mathematicians owned up and admitted it and redressed the balance.
The marginal proof of FLT; the theorem itself being trivial and of no mathematical import; requires nothing more than high school mathematics but that's too simple for the superior intelligence of the mathematicians who like to play mind games with their abstract mathematics called axiomatic set theory. Mathematician Laucelot Hogben said that mathematicians who loose touch with the general public risk becoming a priest hood and unfortunately that in my opinion is what latter-day number theorists have become.
So the Horizon documentary whilst it was historically correct and entertaining, was in fact a miss-sell that only served to perpetuate what must be after 370 years the longest running hoax in history!
im lost... its modual? with semitres? on another world. but its a dictionary?
"Anathema to mathematics", with that I suppose you mean empirical evidence is not applicable to math.
In that aspect math may be comparable to philosophy which also totally depends on logical evidence. Maybe that is what makes it fascinating to people like me who haven't any grip on the matter the exact sciences are concerned with.
Very nice documentary.
Although the math part is way above my head, I found it interesting because it is a cosmos of its own (a sort of parallel universe, almost) and this story shows what the imagination is capable of. My respect for the hard working scientific people continues to grow by watching this kind of stuff.
Hats off to mr Wiles and the people that helped him prove Fermat's theory.
In time I suppose unknown territories in math will be discovered and explored and new theories that cannot be proved immediatly will pop up, just like in physics and other scientific disciplines.