Abstract:
Pierre de Fermat famously claimed to have discovered “a truly marvelous proof” of his last theorem, which the margin in his copy of Diophantus' Arithmetica was too narrow to contain. Fermat's proof (if it ever existed!) is probably lost to posterity forever, while Andrew Wiles' proof has been part of the mathematical landscape for over two decades. This lecture will describe a few of the new ideas in this marvelous proof, and the remarkable impact they have had on number theory.
Professor Henri Darmon is a French Canadian mathematician specializing in number theory. He works on Hilbert's 12th problem and its relation with the Birch-Swinnerton-Dyer conjecture. He is currently a James McGill Professor of Mathematics at McGill University.
This lecture was held at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations.
Program for the Abel Lecture 2016
1. "Fermat's Last Theorem: abelian and non-abelian approaches" by Abel Laureate Sir Andrew Wiles, University of Oxford
2. "Andrew Wiles' marvelous proof" by professor Henri Darmon, McGill University
3. "What is the Birch--Swinnerton-Dyer Conjecture, and what is known about it?" by professor Manjul Bhargava, Princeton University
4. "From Fermat's Last Theorem to Homer's Last Theorem" - a popular lecture by Simon Singh, author of Fermat's Last Theorem among other achievements. This lecture will never be published because the presentation contained material protected by intellectual property.
The camera work is very unhelpful. Too often, when the lecturer is talking about a slide, we are shown the lecturer standing in the dark (very uninteresting) rather than the slide (vital). We are apparently supposed to have committed the complicated slide to memory in the few seconds before the camera shifted away from it!
As an interested non-mathematician, I haven't learnt any new skills from this talk, but the message seems clear. Wiles' proof is not just the answer to a particular question, but a technical advance that will enable more useful work by others. It also introduced me to Abel and his work, which was accomplished in a tragically short life, under difficult circumstance.
Time and space cant be understood but philosophically talking domain never ends in trillion 100 trillion it is infinity
One should keep in mind that Wiles's proof of the Fermat's Last Theorem is in reality a proof of a special case of the modularity theorem for elliptic curves. It is only in conjunction with Ribet's theorem, that it provides a proof for the Fermat's Last Theorem. In other words, Wile’s proof is not a wholly self-contained proof of the Fermat’s Last Theorem and could not stand alone, or be decoupled, from Ribet’s theorem. This in turn leads us to the key question: Is there an alternative path to a proof of the Fermat’s Last Theorem that is completely self-contained and independent of Ribet’s theorem?
Yes.THERE IS ONE! IF YOU TUBE Will Rhee and chose from his videos the one which mentions Fermat and read the the pin comment to it you will find the marvelous proof of Fermat which takes less than two pages! IF YOU REPLY DO IT BY SHOWING YOUR PRO OR CONTRA ARGUMENTS ABOUT ITS VALIDITY.NO LESS NO MORE. THANK YOU.
Interesting question. As a matter of fact there's one such approach by Jean Pierre Serre as formulated in his paper where he formulated what came to be known as Serre's Modularity Conjecture. Infact Serre deduced that if his conjectures were true then they would immediately imply Fermat's Last Theorem without having to go through the intermediate step of Shimura Taniyama Conjecture. Strangely enough , Serre's Modularity Conjecture was proven after Shimura-Taniyama Conjecture by Chandrshekhar Khare and he used a generalization of a technique developed by Andrew Wiles. So basically crux of all this is that even if you wish to take this alternative route to proof of Fermat's Last Theorem , Wiles' contribution can not be undermined.
Yes, I have come up with just such a marvelous proof, which KZhead comments are too small to contain…
The answer is: No; but don't ask me to prove my answer.
No but nearly all proofs require building blocks. Wiles own proof required many new theorems that he created along the way.
Wow these Zeta functions are very interesting!
What a fascinating lecture!
I’m very interested in Fermat but at this level, I understood 2% of your very well,presented lecture. Could you help,please? What level does one have to be to reasonably understand your talk. Not to prove it, as Wiles did but to understand what is going on. I did A Level maths and this is way way beyond me.
Zeta function it's really interesting
Ribet should be included as solution contributor.
Id assume that Andrew has been working on the Riemann hypothesis for quite a few years now. Im guessing that is the great beast he is currently trying to slay.
More on solutions’ enumeration in Diophantine or Fermat like equations : kzhead.info/sun/adajn7NsgpGOqIE/bejne.html
Sit down with 3blue1brown or aleph0 and do an in depth series of videos about each step in the proof. This is the problem with higher maths, no one is able to bridge the communication gap with “laymen”. There should be a “Great Communicator” which recognizes the advanced scientist who took the time to really help people understand what they accomplished.
Yes, but modern math is built on so much material, it is not possible for some body not in the field to comprehend it (or they have to dedicate a lot of time in learning math).
What you are asking is as if you ask some medical specialists to train you in for example neurobiology or cardiology. And I think mathematics is deeper than that knowledge: so no way my friend. Take into account that even those people that make a living working on math and physics every day, don't understand the proofs involved in these deep theorems. I would take years for some of them to catch up...
check out mathologer. does a damn good job of simplifying mathematics, apologetically.
lol OP totally disregarding why mathematicians developed their own language in the first place... this is the age we live in, "laymen" should be in on everything so they can argue forever in the comment sections about things they think they understood after some videos!
= THE GREAT! - THE GREATEST!!! Theorem of the 21st century! = !!!!!!!!!!!!!!!!!!!!! "- an equation of the form X**m + Y**n = Z**k , where m != n != k - any integer(unequal "!=") numbers greater than 2 , - INSOLVable! in integers". !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! /- open publication priority of 22/07/2022 / /-Proven by me! minimum-less than 7-10 pp. !!!!!!!!!!!!!!!!!!!!
i wanted to watch this, but unfortunately the audio is unbareable for me
try watching with the closed captions CC.
I almost came up with that same proof ... but I forgot to carry the 1.
There a lot of screwed-up people, in the comment section. Where the planet are you'll from? I don't get their logic. Wft?!
I don't understand the follow: If "x^2-x-1" has no integer solutions, and if N_p is the amount of solutions (mod p), wouldn't that be 0 or 'undefined'. I'm sure I'm wrong, but I understood that N_p is the amount of solutions (mod P) of some equation.
By doing a quick google search, I found that the polynomial 144x^5−121x^4+100x^3−81x^2−64x+49=0 has no integer solutions. But, if we reduce it mod 3, we get the equation -1x^4+x^3-x+1 = 0 mod 3. This equation has a solution, namely x=2. This example shows us that even if an equation has no integer solutions, the N_p need not to be 0. I hope this answer your question.
@@Sydshadows Well your answer gave me a clue on how to understand this. In my example: "x^2-x-1", then if you take: "x_1 = 11n + 4 and x_2 = 11n + 8", these are solution of the equation (mod 11). It has 2 solutions (mod 11). Thanks
To add a somewhat simpler example than the one Cédric supplied, the polynomial f(x)=x^2+1 clearly has no solution in the integers. However, modulo 2, we find a solution x=1, because f(1)=1+1=0.
x^2=2 has no integer solutions, but x=3 is a solution mod p=7
Smoking my pipe and saying to myself 'indeed'....
it has been rumored that fermat might have thought of this; kzhead.info/sun/eN2mhryjh4murJs/bejne.html when he wrote his margin note.
i have two elementary proofs of wiles theorem sorry he is going to see how much he is a genius and how much is a nerd.iam sort for the mathematicians which were unable to find a proof that mens that the system of teaching mathematics got to get a revolution.
lol the marvellous thousand leaf 😎
Fermat's Great Theorem NEVER! and nobody! NOT! HAS BEEN PROVEN !!! - except Me!!!
BIGGEST EVER AND FOREVER #HSCUT #COMPONENTS .
Fermat's Great Theorem NEVER! and nobody! NOT! HAS BEEN PROVEN !!! / - except me!!!
Take your meds.
"marvelous proof"😂
Did anyone understand this? Blimey.
Il est très intéressant de voir des mathématiciens de renom exposer cette théorie fort compliquée alors que la démonstration de la conjecture est toute simple et se démontre en moins de 8 lignes. Les calculs avancés étaient inconnus du temps de FERMAT. Pour ne pas me répéter, allez sur d'autres sites concernant ce sujet où je traite en détail cette conjecture tout simplement et avec des calculs plus que basiques. Cette conjecture se révèle, à l'analyse, être le plus grand CANULAR mathématiques de tous les temps. La plupart des mathématiciens, pour sauver les apparences, n'accepteront JAMAIS de s'être fait piéger par FERMAT, méprisé par ses confrères, et par entêtement, persisteront à affirmer que la démonstration de WILES est la SEULE VALABLE et à douter même de la démonstration prétendue réelle de FERMAT !.Mais, laissons le temps faire son oeuvre et les mathématiques n'en sortiront que grandies d'une pareille histoire.
Mission impossible for you I'm afraid. Too much time spent lecturing within the corridors of academia.
???
For people that has mathematics in their blood: Maybe mathematicians got tired and accepted a very complicated path and 100 pages so that only a minimum number of mathematicians understand what the proof is. Here's a different approach to the Last Theorem on a single page: kzhead.info/sun/YM6pcZGsqWhuqq8/bejne.html
Fermat's Great Theorem 1637 - 2016 ! I proved on 09/14/2016 the ONLY POSSIBLE proof of the Fermat's Great! Theorem (Fermata!). I can pronounce the formula for the proof of Fermat's Great Theorem: 1 - Fermat's Great Theorem NEVER! and nobody! NOT! HAS BEEN PROVEN !!! 2 - proven! THE ONLY POSSIBLE proof of Fermat's Great Theorem ! 3 - Fermat's Great Theorem is proved universally-proven for all numbers ! 4 - Fermat's Great Theorem is proven in the requirements of himself! Fermata 1637 y. 5 - Fermat's Great Theorem proved in 2 pages of a notebook ! 6 - Fermat's Great Theorem is proved in the apparatus of Diophantus arithmetic ! 7 - The proof of the great Fermat's Great Theorem, as well as the formulation, is easy for a student of the 5th grade of the school to understand !!! 8 - Me! opened the GREAT! A GREAT Mystery! Fermat's Great Theorem ! (not a "simple" "mechanical" proof) !!!!- NO ONE! and NEVER! (except ME! .. of course!) and FOR NOTHING! NOT! will find a valid proof of the FGT!
This is genius. Please send your paper to all the leading mathematicians asap, so we can reward you.
NOT! " -wileS" = he IS the LiEZ !!!
are you kidding?
Ion Murgu Why do you spam all these math videos