Fermat's Last Theorem - Numberphile
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- čas přidán 31. 05. 2024
- Simon Singh on Fermat's Last Theorem.
Simpsons book: amzn.to/1fKe4Yo Fermat book: amzn.to/1jWqMTa
More links & stuff in full description below ↓↓↓
EXTRA FOOTAGE: • Video
FERMAT IN SIMPSONS: • Homer Simpson vs Pierr...
Interview with Ken Ribet, who played a big role: • The Bridges to Fermat'...
Wiles' proof: bit.ly/FermatProof
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"The proof is trivial and left as an exercise to the reader."
The proof:
Typical 🤣
this hits so hard ... literally my EM physics lecturer use to do this for half the course
Fr lol 😂
Well there can be other proofs which just require creativity that's probably 2-3 pages long and simple.
Ye
fermat was the ultimate troll of academia
+Alex Trusk Or a psychopath and a master in manipulation !
Alex Trusk lol
Yeah, because 3987^12 + 4365^12 = 4472^12
TheMoonRover It isn't correct, it is ALMOST correct, but it isn't
I know. It was a joke as to *why* Fermat was trolling (see original comment).
Had Fermat never heard of the concept of GETTING ANOTHER PIECE OF PAPER?
It seems that concept was far too complex during his age. It's probably harder than the Theorem itself.
I thought they used vellum back then not paper
Wooooosh
Of course he heard the concept. Bet you never heard of this another concept of "Maybe he's lying all along and it's just a conjecture of his and relies on other people to prove it because he has no proof all this time"
There just wasn't enough brown paper.
Truly a travesty.
I have a most wonderful proof of the Reimann Hypothesis. Sadly, this comment box is too small to fit it in.
+jaxxstraw Aww man.... I was really looking forward to seeing an ASCII zeta function
Damn, there goes my free time for the next 7 years :/
Don't die on us now!
+Squilliam Fancyson not sure what a ASCII zeta function is but it sure sounds sexy
This aint twitter, you aren't limited. Do tell lol.
Fermat was also right in that the margin was too small to contain the proof.
69th like
This is the most underrated comments of all. Fantastic!
Quite a fellow Fermat was. Right about everything.
Mdmerajshaikh
17th century proofs are mostly non mathematical they prove it mostly using geometry that must have been beautiful .
"For seven years Andrew Wiles worked on this problem in complete secrecy."
DID YOU NOT LEARN WHAT HAPPENS WHEN YOU WORK ON PROBLEMS IN SECRECY THE FIRST TIME?!?
+++
Then he finally found the proof, so he wrote on a piece of paper "paper too small for proof" and tragically passed away.
I was also a sleeping person for solving this three-letter problem. Fermat ask question in the 3-letter disequation :x^n+y^n=/z^n. I answer:
x^(n/2)+y^(n/2)+delta=z^(n/2 ) Because they are not the same so
there is no solution about integer.
@@prajnaprajna1923 WHY do you have this exact comment posted SO MANY times in the comments’ section of this video?
Probs wanted all credit for himself
When i was 17 years old, my mathematician bought me a book called : Fermat's Last Theorem. It was by far the best book I 've ever read to this day. Today i see this video from Numberphille, and i realize that the author of that very book, is the guy in the video above : Simon Singh. Needless to say that I am speechless.
You had your own mathematician? Nice. :)
Have you read his book about the mathematical references in the Simpsons. I never quite finished but it is still sitting on my shelf
thodkats is legendary
Same thing happened to me, I realized it today.
Needles to say...
LIFE HACKS: next time you get an exam saying "show your work" write "this paper is too small to contain it".
Tried that, teacher didn't get it...
I'VE GOT THE PROOF!! ... but I gotta go return some dvds to blockbuster :(
***** strange the answer was easy, but I am lost on how to post it. so please click on my name.
v
"I have to return some videotapes"
i got it, but i can't explain it. to complex for you mortals to understand
Be careful when you cross the street.
i am so shocked at how well this guys pulls off that hair
spartnstarcraft2 He reminds me of the main antagonist from Outlast: Whistleblower , Eddie Gluskin 😂😂 I still love him though 😊
Literally pulling it off.
Taxi driver style mohawk.
LOVE YOUR COMMENT KIND OF FAMILY GUY LIKE.
Not gonna lie, I thought it was Maynard James Keenan at first
Fermat would really suck at twitter.
First reply after 8 years
@@nikolairahat2782second reply after three weeks
I like it when n=1. :-)
1 + 1 = 1 right noooob
+robin van Sint Annaland n=1 results in the formula a+b=c....
+robin van Sint Annaland n=1 makes a^1+b^1=c^1. I bet I can find a solution, like a=3, b=4, c=7. 3+4=7. :-) Of course I'm just being silly, the mathematicians here are real geniuses and I totally respect them.
+robin van Sint Annaland n is the index...
+Colonel Mustard i know but is abc is 1 as well aaaaa........
The correct explanation is always the easiest one. Fermat was an alien/time traveller who used his superior knowledge in mathematics to spark human curiosity and help our primitive civilization to discover new branches of mathematics. He didn't show the proofs to not interphere too much with human history. Thats why all their hyphotheses were correct. Occam's razor, guys.
+jmiquelmb What a conspiracy !
Thanks for this, now i can die in peace
+
(thats the joke)
Rina the joke
your head
Rina You're welcome,moron
Take a bow Andrew Wiles. He found his passion so early and worked hard and didn't stop until he solved the problem. A true inspiration
Agreed. I like to think he's a distant relative - my grandfather, a decorated D-Day veteran, was named Thomas Wiles. I understand the mighty mental magnitude of what he did but consider myself to be a mere muppet in comparison to both of the aforementioned.
@@adzaaahhh wow that's something! You must have so many stories from your grandfather about the war. Huge respect for both of them!
@@soumyasishbhattacharyya2805 Unfortunately he passed away when I was 2 years old so never got to know him or hear any of his war stories firsr-hand. According to my parents, he never liked to talk about it anyway as he was quite traumatised by the memory. In truth, I doubt there's any close link between the two men other than the same surname, and their sheer dogged determination (in different ways of course).
all his efort to proof FLT was in vain.HE lack the genius and chose the nerd way to find a proof. if i can present my two
elementary proofs of fLT the world would see that his efort was in vain.
with a lot of perspiration
Wiles provided the correct proof to Fermat's Last Theorem which was the greatest achievement in modern mathematical history. Yet, outside of academic circles , no one knows who he is. It was still one hell of an accomplishment as far as I'm concerned.
Matthew Jackson but he was wrong
Did you not watch until the end? He found the proof eventually.
What do you mean different? In the video both the flawed attempt of proof was talked about as well a the correct one Andrew Whiles delivered.
@Matew Jackson : you say:"the greatest achievement in modern mathematical history". I am saying so much overrated
After Fermat's death he said "It's just a prank bro"
hAHAHAHAAA best comment here!
Sofus Jejlskov Brandt Andrew wiles: Get rekted bro
AFT"OR"BEFOR-E
Well jokes on him
Yes, in fact he wrote that note on April 1st according to historians. Do some research bro!
That is one hell of a compelling story, and this Simon tells it so well!
"I was sitting at my desk examining the Kolyvagin-Flach method. It wasn't that I believed I could make it work, but I thought that at least I could explain why it didn’t work. Suddenly I had this incredible revelation. I realised that, the Kolyvagin-Flach method wasn't working, but it was all I needed to make my original Iwasawa theory work from three years earlier. So out of the ashes of Kolyvagin-Flach seemed to rise the true answer to the problem. It was so indescribably beautiful; it was so simple and so elegant. I couldn't understand how I'd missed it and I just stared at it in disbelief for twenty minutes. Then during the day I walked around the department, and I'd keep coming back to my desk looking to see if it was still there. It was still there. I couldn't contain myself, I was so excited. It was the most important moment of my working life. Nothing I ever do again will mean as much."
- Andrew Wiles
He showed one can do anything he likes if he possesses the proper passion, perseverance, determination. This guy literally wasted(irony intended) half of his life to prove the theorem and he succeeded. What a legend!
He is a legend!
Brady, I've just realized, I've probably seen most of the videos you've posted and I've never commented... Thanks for making videos, dude.
I was also a sleeping person for solving this three-letter problem.
Fermat ask question in the 3-letter disequation :x^n+y^n=/z^n. I answer:
x^(n/2)+y^(n/2)+delta=z^(n/2 ) Because they are not the same so
there is no solution about integer. yes, Fermat is crazy
Haha, and in Star Trek TNG, they were talking about how it still had not been proven in the 24th century. I guess they should have waited a few years.
+Aeroscience ...Or this proof will be found to be wrong and unfixable.
In March 2016, Wiles was awarded the Norwegian government's Abel prize worth €600,000 for "for his stunning proof of Fermat’s Last Theorem by way of the modularity conjecture for semistable elliptic curves, opening a new era in number theory."
The two papers were vetted and published as the entirety of the May 1995 issue of the Annals of Mathematics. These papers established the modularity theorem for semistable elliptic curves, the last step in proving Fermat's Last Theorem, 358 years after it was conjectured.
i know its copy paste(my statement was taken from wikipedia) but its already proven which mean that from conjecture to theorem... u get it??? the theorem had already being checked... he even got award for it... zzz
You are driven by wishful thinking. There is only a handful of mathematicians worldwide who may have what it takes to understand the proof. Even they don't have much information about the new knowledge invented in the proof. So little manpower and so much area for errors warrants suspicion.
I'd like humanity to progress as much as the next guy, but having the hegemon solved single-handedly by an unknown professor is just not something I will buy into in a hurry.
This guy looks so steampunk.
Or cyberpunk
Hahaha hes like a cyborg to me😂
You have got an anti prime number of likes
Wiles's original paper was a bit of a Parker square.
I was also a sleeping person for solving this three-letter problem.
Fermat ask question in the 3-letter disequation :x^n+y^n=/z^n. I answer:
x^(n/2)+y^(n/2)+delta=z^(n/2 ) Because they are not the same so
there is no solution about integer. yes, Fermat is crazy
@@prajnaprajna1923 your method and statement is wrong. There are solutions when n=1 and n=2.
Few years ago, BBC television (UK) made a programme with him explaining all about the humongous amount of work and isolation he endured to solve this problem, truly astonishing programme.
The programme in question is an episode of the "Horizon" series called "Fermat's Last Theorem", and it was directed by some bloke called Simon Singh.
At the time of writing (2022-09-25), it's available on BBC iPlayer.
@@WebeloZappBrannigan Great!
he came to my school, and he signed my fermat book
+Vamshi Darisi Fermat died in January....... of 1665. Someone call Guiness World records, we have a new world's oldest person!!
+Thomas Pallister no i mean simon singh
+Thomas Pallister u dun fukked up.
+Vamshi Darisi L
Thomas Pallister lol, dumbass
I have proof that we're living in the matrix but I'm not suppose to texting while driving.
@@jenilb420
Lol
The terrible grammar makes this even better
I still think Fermat had a simpler proof.
Who knows!?
I have simple proof
Hahaha. What a torturous rabbit hole to ponder.
But like what video said, there might be a edge mistake in that proof.
It could be the same as Lamé's incorrect proof, which was wrong for subtle reasons.
I had the proof, but when writing it down I took an arrow to the knee...
+Tomasz Wota (Xupicor) wow first arrow in the knee joke that isn't funny
Il XIHill Yesss. Job done, internet, job done. No need to thank me, I'll see myself out. ;)
I had the proof, but a settlement needed my help.
Let's have some style and change the comment to "arrow notation" to the knee :)
I used to work on Clay Institute problems like you, but then I took an arrow in the digit.
I'm so sad the bonus footage seems to have been made private, would love to see it.
I have always been amazed about how Wiles fully dedicated so much time and effort into his passion. In my opinion, it is even beyond the dedication of olympic athletes and self-made millionaires. Within the realm of math Wiles showed that with enough determination you can solve a problem that 358 years worth of professional mathematician's could not. It has been a great motivation for me ever since i was 7 years old and read the news.
His perseverance, passion, determination were in another level. A true legend!
Took him 28 years, but by George, he did it
Makes you wonder how many worked on lifelong projects secretly but died before it was revealed. 3 decades years is plenty of time for things to go downhill.
He didn't do it from ground up though, the 358 years of failed attempts by others helped him in some way
Do you really compare being a millionaire to being a full time Mathematician? That's an embarassment to Mathematics. Mathematics is way harder than being a self made millionaire
I can solve world hunger, but the world is too small.
I can solve that one too! But in my case the world is too big.
Mridul Tiwary underrated comment cause f the world was bigger and had more resources That would solve world hunger
James Evans comment of gold !
@@LevatekGaming have you ever heard of production? Theres already more food in the world then needed for everyone
We could solve it easily if people weren't so greedy.
An extraordinary true story, well told by Simon Singh. He conveys he excitement and tension of the events.
This is far and away my favourite Numberphile video. The narrative is such a fascinating one which is told with such clarity and enthusiasm.
Exactly right. We all know the end of the story but he tells it with such economy and passion. A win for the internet.
Simon Singh is a good story teller. Sometimes 9 minutes seem long for a video but he really was telling the story in a way that you wanted to know the end.
Simon Singh is quite possibly one of my favourite academics of all time.
I read his book on Fermat's Last Theorem on a whim and ever since then have been a huge fan of his.
Saw Simon do this speech in a lecture this evening! Absolutely fascinating... amazing stuff!!
Professor Vaas teaching:
"Have I ever told you the definition of a mathematical theorem??"
I've read his Simpsons book, it's incredible
My favourite Numberphile yet. Always good to hear someone as passionate as Simon Singh on a subject they know.
I could listen to this guy talk about Maths and History non stop. Why don't we have teachers like him?
My grandmother gave me his book when I was 12 years old. 8 years later I'm watching a video on which I found out to be the very author of the book being interviewed. This is so cool. Thank you for making videos Numberphile. You are awesome.
Sounds like Fermat was just trolling "oh, I can prove this, but I'm not gonna write it down" yeah right :P
Come to think of it; Hey guys I figured out the meaning of life, but I have to go feed the cat. Bye.
Well the meaning of life isn't such a big deal, in fact is quite lets say uninteresting, but i won't write it down :D
ybra Plot twist: The meaning of life is feeding cats.
I know the meaning of life :) 42 and the question is. Brb
+ybra You got it. I think Pierre de Fermat was trolling people way before it became trendy.
+myguy200inventions That's the answer, but what is the _real_ question?
Why isn't there a movie about this?
people cannot understand the movie
+amirul farhan or director cant understand the script ;)
+Snakeyes244 There was a documentary made on Andrew Wiles' proof.
because a dvd would be to small to contain it....
"La habitación de Fermat" (Fermat's room in spanish)
I know pretty much nothing about the complex math you guys do on this Chanel but this video was awesomely entertaining and well worth the watch !
This guy is so good an explaining complex things in simple ways that’s understandable to a laymen. This video is testament to that and so is “The Code”. Really great communicator
His Book about Fermat is one of the best books I've ever read. Can't recommend enough. Extremely easy to read, engaging and packed with information, I read it in two days.
i just realised this guy came to do a lecture at my school but me being the stubborn 11 year old didn't go. I regret it
To be fair, at eleven years old, you probably wouldn't have gained much mathematical insight anyway. He was probably doing a motivational lecture.
Still my favourite video on this channel and I'm sure I'm gonna come back again and again.
I remember reading his book on this subject and how absolutely immersed i was in it. Still one of my favourites although it's been 10 years and although I'm in Humanities now.
my aunt had a cat she named after fermat. the spelling? furmatt
+
No.
Wiles' proof involved mathematics not known to Fermat. So if Fermat did have a proof, it was not the same proof that Wiles came up with. I tend to agree with the idea that Fermat thought he had a proof but probably it was invalid. Some of the great minds of math who came after Fermat all tried and failed to find a proof until Wiles.
they did not find the elementary way to prove pell's equation and how fermat splita 4k+1 primes in two squar numbers.
i like you to be present if i ever meet wiles to see how fun i make of him and his efforts .yes i envied him since he does not merit to be the one who discovered a proof.what about mr. ribet.?
I've been following the literature of the Last Theorem for 40 years. I have chills.
HE LOOKS LIKE VAAS IN FAR CRY 3 !!!
lol. he does
except much more intelligent
racist
have i ever told you the definition of Fermat’s Theorem?
simon singh is british of indian origin.... vaas in far cry 3 looks like east european
Wow! I cant believe, you actually got Simon Singh on your channel. The guy who wrote the book 'Fermat's last theorem' , 'The Code Book' and a person who actually owns an enigma machine. Brilliant Brady, keep them coming!!
You know, if I squint a bit, I can imagine it's Wez from "Mad Max 2" telling me about numbers, and that somehow makes it awesome....
+theproplady or Vaas from Farcry 3
Start by taking the partial derivative with respect to each variable and then...one second brb.
"It started with a ten year old child"
I immediately thought of Gauss 😂😂😂
I've read Simon's book years ago on this and its a gripping read, fun and informative. There is also a Horizon BBC documentary here on CZcams with Sir Andrew WIles retelling the story, and its one of the best Horizon's ever made to this day as its a wonderful insight into the process of how a scientific mind works through sometimes abstract problems.
"we cant prove Fermat's Last Theorem"
Andrew wiles : hold my beer
Ha ha ha ha ha
Great stuff, Simon! Thanks!
I just finished Simon’s book. It was great! I took it from my father’s book shelf. I enjoyed it very much.
At 9:30, the subtitled has “loathed (?)” in fact it should read “lauded.”
Stark Trek brought me down this rabbit hole of over my head maths.
Edit: i'm in tears that was the best joke i've heard in weeks.
"Ayo finish your proofs"
"Aight gotta finish these legal paperworks doe"
*Last heard of 4 centuries ago*
"Lauded," not "loathed" (quite the opposite, actually.)
"Slain," not "slained."
"Piet Hein," not "Pete Hines."
I'm suddenly wondering the following:
In order to get the length of the hypotenuse of a one-dimensional line, you just measure it. a = a
In order to get the length of the hypotenuse of a two-dimensional triangle, you take the two other sides, square them, add them together, and take the square root. a^2 + b^2 = c^2
Now, what would you do in three dimensions? Simply tack on a third variable, and change those squares and square roots to cubes and cube roots. So now you have a^3 + b^3 + c^3 = d^3.
My assumption is that somewhere, there exists some sets of four integers for which this is true. Am I matching the pattern wrong?
Wrong. For three dimensions you get a third variable but the power stays 2. So a²+b²+c²=d²
The case for a^3 + b^3 + c^3 = d^3 has numerous solutions.
Probably the simplest is 3^3 + 4^3 + 5^3 = 6^3, which you can readily check.
Very similar to the 3,4,5 solution for the Pythagorean equation.
What I would like to see is a proof of the minimum number of terms required for a given power n for the equation to be true.
I saw him today in my College doing a presentation he is amazing. I bought the The Simpsons and their mathematical secrets, and it was signed!
This channel is a gem.
Thanks !happy new year !
I find it likely that he thought he found the proof, but found a mistake.
+andrewxc1335 If it were me in Wiles' shoes, I'd probably go "yeah, but if you ignore that part, it makes total sense!"
+andrewxc1335 Yes, that is what I think too.
Piet Hein's Grooks are my favorite.
Stomach ache may be a curse,
Heartache may be even worse
So thank heaven on your knees
If you have but one of these
Don't know how I have managed to live my last 10 years without this episode. Thanks!
Well explained and entertaining! Tough to do on this kind of subject.
Recomendo a leitura do livro o Último Teorema de Fermat de Simon Singh.
É um livro excelente com uma linguagem clara e fácil não necessitando de matemática avançada.
the dude bragged about having the proof when he didn't actually have one and made a silly reason of not having enough paper and when people found it was an excuse he just died
he looks like someone from fallout
I met Simon Singh yesterday - he gave a talk in my university in Bristol and I got my book signed. Really nice person, he is...
Make a video on the taniyama shimura conjecture pls!!!
I have NO IDEA what it is, but it sounds complicated.
Me neither that's why i want them to make a video lol
Yeah, make a video, that sounds quite like a challenge !
basically: prove Taniyama -Shimura and you got Femat covered too. Wiles used Taniyama-Shimura for his approach on Fermat's Theorem and solved both. :)
There is a video with the guy who proved the link between Taniyama-Shimura and Fermat's Last Theorem, where he talks about that conjecture and how they were connected.
SOLVED! Do another video on it please :)
i love numberphile videos, they are so understandable
this channel is amazing
HEY NUMBERPHILE
can you do a video on season 6 episode 10 of futurama"The prisoner of benda" the professor makes a machine that switches minds but once you switch you cant switch back. I would love to see the mathematics of how many other people it would take to return everyone to their original bodies.
+Alex Kasantsidis 2 more, both if 'the body' can't switch again AND if 'the mind' can't switch again
It's an amazing coincidence that Fermat's Last Theorem requires Andrew Wiles' Final Proof to be completely unlocked.
TOTAL BS
Over the multiple calculus courses I took and other classes as well, I have probably learned several theorems and other such things. But I never really thought about how they came to be. After watching this video I started to understand I little bit about how proofs are so necessary in the process of developing a theorem. I remember that in geometry class, my teacher discussed proofs and theorems, I was able to make some connections here.
Simon Singh came to my school to give us a lecture, and it was amazing
He worked with the Simpsons for a bit
7:53 I think he says "lauded" rather than "loathed"
I believe fermat had a simple proof. I think he reduced to the rational numbers ==> xexpn +yexpn = 1, where x,y in Q. if you graph this, it is bounded by a 1x1 square and a circle of radius 1, getting more squarish as n increases. then if you slice it into 2 parts, use integration to find the area under the 2 parts. go ahead - draw it on paper...
Excellent story! And well told.
thank you for making this video...the best explanation and history.
I've been working on a proof but sadly I've hit some roadblocks. It deals primarily with prime numbers and rotational bases. I don't know if I'll ever finish it though.
And this is a great example of how mathematics can be fascinating
I want to sit and have a beer and a chat with Simon Singh so badly it actually hurts. Great video!
He speaks so passionately about the subject!!!!
English is not my native language, so can somebody tell me if i figured out what the problem is: you can't find 3 whole numbers x, y and z, which verify x^n+y^n=z^n where n>2 ?
If n=3, It means a number, which cubic root is a whole number, can't be the sum of 2 other such numbers?
yes, thats the problem. not a single group of 3 integers can fulfill a^n+b^n=c^n. however, in math this isnt enough proof. Who knows, there might be an almost infinate group of numbers that fulfill this equation. Thats why an equation of geometric proof is required to prove all theorems
What if x=1 and y=0?then z=1 which means theres a solution..
Have an answer for you? Yes. But you're not going to like it... 42
hitchhikers guide to the Galaxy 😁😁
what an inspiring story! really hope that we can also find our places in the world, like sir wiles did.
I really like how he explains things.
Plot twist: The statement "I have a marvelous proof of this theorem, which this margin is too narrow to contain." actually mathematically proves Fermat's Last Theorem. I don't know how, but Fermat must've known what he was talking about.
You are so right!
Im reading Simon Singh's book now :) It has already been translated to brazilian portuguese
really well made and interesting video!
this videos are great. thanks for sharing.