The Bridges to Fermat's Last Theorem - Numberphile 

Right? That's just beautiful

I noticed that and I was like

Like?What

Not only that, they also resemble each other quite a bit.

I am glad, that the names are written out in the video.

He was at Wiles’ series of lectures, and applauded exceptionally enthusiastically when Andrew announced that he had proved TSC for semistable elliptic curves, and that therefore, largely from Ken’s work, FLT was true. A true gentleman and seeker of knowledge. I have met Andrew Wiles, and he is also pretty self-effacing and humorous. But I would love to meet Ken Ribet.

He talked about how he shared what he was working on with his colleagues and had no worries about getting his work stolen or anything. It makes sense that mathematicians don't have much ego when they are dealing with these huge concepts and would be completely lost without heavily relying on the work of others

Wiles did this

I have proved on 09/14/2016 the ONLY POSSIBLE proof of the Great Fermat's Theorem (Fermata!). I can pronounce the formula for the proof of Fermat's great theorem: 1 - Fermath's great theorem NEVER! and nobody! NOT! HAS BEEN PROVEN !!! and NEVER!!!! 2 - proven! THE ONLY POSSIBLE proof of Fermat's theorem 2A - Me opened : - EXIST 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 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! Mystery! Fermat's theorem! (not "simple" - "mechanical" proof) !!!!- NO ONE! and NEVER!

I guess most working pure mathematicians have discovered a result or two. But rarely is the proof 50 pages of very advanced stuff. Even rarer to have it widely known under one's name.

Thank you!

That's enough detail for a non math person. I did a couple of 2nd year math university papers and it didn't cover modular forms or anything like that.

Can be watered down even more - Wiles didn't prove the modularity theorem for all elliptic curves, only semi-stable ones. It's just that Frey's equation WOULD have been semi-stable, so that was enough :).

@Douglas Sirk They're saying their comment is the watered down version, not the video.

Alder wiles

still hasnt been done... :(

Three so far on Numberphile: Navier-Stokes Equations, Riemann Hypothesis, and Poincaré Conjecture. One on Computerphile: P vs. NP Only three to go: Yang-Mills and Mass Gap, Hodge Conjecture, and Birch and Swinnerton-Dyer Conjecture. The last of these is what I am most looking forward to on this channel.

Progress is going to be really slow on those, we got 1 in 22 years so far. Also the folks they have on are mostly English or based off of the UK, where most of the theorems did not originate. Hard to fight experts in those specific fields. Hoping to see at least one more cracked in this lifetime

@@thezestyman9159 i proved [p v ~p] when I was in first year

@@JamesJoyce12 so where’s your Fields Medal?

And guess what mate...am gonna apply for msc mathematics course of Saarland university this upcoming summer semester 2022, really wanna study there. It's a small world indeed!😁😀

Maybe if they called it "Fermat's penultimate theorem". Enough people think "penultimate" means something like "super-awesome" that it could get some traction.

ghuegel This is valid. I must go now, to rebrand!

Gareth Dean It's boring (to people that are at the point whereby they understand all of the stuff in this video)

James Oldfield I dunno; a^(p − 1) − 1 being an integer multiple of p has some intriguing results. It even has a similar history to the last theorem. ('I'd send you the proof of this but it'd be too long,so I won't.')

Gareth Dean It's not the length, but the complexity. If it was a chemistry paper, I'd be in fighting chance of understanding it unless I've not covered the topic.

Same! The material looks a bit intimidating to me, but I am certain we will do well!

That's awesome. How is it going?

​@@LucasRodrigues-oh1jt Our final was in mid-May (from 7 to 10 PM!). I took the class with Manish, and I got a B+. I'm not actually enrolled at UC Berkeley; when I took the class, I was in 12th grade.

What school has 3 hour long finals. Did you make that entire thing up Jacob?

@@soanywaysillstartedblastin2797 No. I was very tired by the end of it, even though there were less than 15 problems.

P = NP if and only if P = 0 or N = 1.

Must be all those swear words in your proof. Try rephrasing it without them.

Anthony Armstrong may be u also know in (a^x+b^x=c^x) the result x=x(a,b,c)? ]]]

+Anthony Armstrong I see what you did there.

Bravo haha love this comment

I'm sorry Mario, but, your theorem is in another castle.

1KevinsFamousChili1 Because Beautiful Mind and Good Will Hunting has a clear goal, whereas even understand the goal of this video would require a degree in maths :/

there's a documentary or two. better than a movie which would get it wrong

There's a book called The Parrot's Theorem, a movie called Fermat's Room. Both are fictional though, and the last is about Goldbach's conjecture

What... Arch needs alot of things....Fathers personal carrier

proof Trial.....call helmsworth

After seeing the NOVA program on this I don't think explaining it to laymen is in the cards. Judging by their "dumbed down" explanation, this is highly technical stuff and you need to be well into it to even get the rough outline. Didn't he say the proof was over 300 pages? Yikes! One things for sure, there's no way Fermat had this in mind.

It won't be possible, it would take so many videos, explaining so many different subjects, it would take to long and they would need to teach us so many subjects.

My friend, this is not at all practical. I'm not sure if you know this, but mathematics, just like any other subject, has a large variety of sub topics that in some cases barely resemble the rest. Not exactly particular to this idea, group theory (abstract algebra) is very, well, abstract and theoretical. Thus, someone accustomed to algebra or calculus would not get any sort of intuitive tie between these subjects. Not only are these subjects content heavy, but there a lot of them and are probably not that open to lay person translation.

MobiusCoin I don't believe any Calculus/Linear Algebra is necessary to the understanding of Modular Curves (or at most elementary amounts), and hence the epsilon conjecture. To have a more in depth conversation about this, you'll probably need at least a little group theory, familiarity with fields and Galois Theory.

Well, calculus and linear algebra would not really help much. We are talking about abstract algebra which is very different. Abstract algebra is just a rephrasing of addition, multiplication and their inverses. Technically, undergraduate abstract algebra is easy enough for a highschooler to understand (however, the level of abstraction can be too high. Higher than other mathematics). The only advantage you have is knowing about complex numbers and their subsets, and some proof theory (I guess you know proof by induction, contrapositive proofs and the like).

I think that the logical structure of the related problems definitely counts as significant insight. The bottom line is that the proof of Shimura-Taniyama is hundreds of pages long, and that's without the epsilon proof which we could see was easily 30 pages on its own. Even at the graduate level, it's not something an experienced mathematician could read unless they were an experienced algebraist.

***** It is something that few elite mathematicians can ever hope to understand, but at least you can understand the goals behind and some of the maths and theorems if you have a degree in maths.

I'm just a random grad student and I'm sure I'll understand all of it in the next few years. Yes, it's slow going, but it's not reserved for the most elite mathematicians. I think it's more about the enormous amount of time required, although of course for the elites the time will be a bit shorter. But point taken about it being inaccessible. But you never know! This is still a relatively new result in terms of the history of mathematics. People may find a way to distill/reorganize everything in a way that shortens the time needed to understand it all. I doubt it will ever be "simple" or "short" but there will likely be some improvement (it would be too strong a position to claim that there could _never_ be any improvement :) ).

That's like saying playing a Mozart piece it's only achievable to the best composers, any mathematician who puts enough time into understanding some proof can do it, the tricky thing is creating one.

literally I could see his passion through his eyes. It was really a great moment

That was John Von Neumann summed up: just waking up to solutions left and right.

Great to hear.

It is not a manuscript, it is a preprint or copy of the journal article, he would have many copies.

I was too busy trying to decipher the words on the first page of the manuscript to notice the crease.

arthritismutilans i laughed so hard at this

Did you just use dog's bollocks?

Then why do I get the impression this guy is secretly seething inside? He keeps saying things like "Well, that's what Wiles said..." implying Wiles wasn't being honest. That he somehow stole the idea.

@Nissim Levy Sad that he's too old

@@captain_kadaver It is a silly rule that. As someone post-40 myself hoping to one day make my mathematical mark, I know I'll never win it! :D

@@shugaroony Yeah but there are so many other awards than the Fields medal. The Fields medal has the purpose to motivate younger mathematicians.

I don't think you should feel bad. Even in the video, Ken Ribet acknowledged that Wiles' contribution to the solution was a bigger piece of mathematics - something which seems borne out by the fact that most people, Ribet included, did not think even after his epsilon proof that Tanayama-Shimura-Weil was accessible to then known mathematics. It's quite common for the solutions to longstanding mathematical problems to be the culmination of work by many mathematicians, but it doesn't mean that the contribution made by the person who makes the final proof isn't still something special. I think the point with Ribet's theorem is that it exists within a very specialised corner of one particular problem in mathematics - its importance appears to be completely contingent on the importance of the work of Tanayama, Shimura, Weil, Serre and Frey. Wiles' proof, on the other hand, laid the foundations for the proof of the modularity theorem; so yeah, don't feel bad. I don't think Ribet feels bad about it at all, and it's not as if his name and contribution are ever going to be forgotten - his proof is named after him.

Ribet built a bridge between two subjunctive islands; This established trade and commerce between them, but their goods had very little value to anyone else. Wiles built a bridge from the mainland to them and thus realized them. This is _huge._

Taylor also.

@@canadiannuclearman I rather think Taylor's role was like a very talented film editor who, along with the director, was able to knuckle down and piece together a Best Picture-worthy film after the director finished production but somehow neglected to shoot a crucial scene, without which the film made no sense. Heroic work on his part to be sure, but only possible and necessary because of the genius but accidentally incomplete work of the director (and let's call Ribet the director of photography or some other analogue whose work on the film was extraordinary and crucial to the film's success). It would be like if David Lean had somehow forgotten to get any shots of Peter O'Toole during the attack on Aqaba in Lawrence of Arabia. And it makes me think: if written properly, this whole story could make for a great movie.

Here's a better film analogy: What if when Llewellyn Moss (Josh Brolin) gets killed in No Country for Old Men, it was originally supposed to be shown on screen, but the Coens just screwed it up somehow and never filmed the actual shootout. And yet the final version where we never see it somehow actually makes the film even better, because it carries a deeper meaning (which is true). This analogy suffers from the fact that the Coens edit their own films. I need to stop watching numberphile vids and go put in a DVD.

the saarländers!

Fermat himself had maths just as a hobby. I can't quite remember his original job from the top of my hat tho...

i bet it was that they were wealthy enough to spend the time thinking and didn't have to worry about getting paid for it.

Fermat was a lawyer. He did mathematics in his spare time.

There's often been an entire (although small) part of society that didn't work to live. A noble man would have had nothing but freetime and could have done mathematics in his freetime or even spend his fortune for his hobby (I'm thinking about Lavoisier who was a chemist). There's also the possibility to find a mecene. that's the situation most scientists and philosophers found themselves in (mathematics used to be a branch of philosophy). The king may not be himself gifted in maths, and he may also have other matters to attend to, but he can have an interest and sponsor scientists. For example king George III of England was passionated by astronomy and financed the well known astronomer Herschel who discovered Uranus (and initially called this planet George). And I realize that I didn't give any example of a mathematician. I don't know if Bagdad's caliph Abd Allah al Mahmoun was himself interested in science or rather that he knew (with the example of the Library of Alexandria) that knowledge was extremely important for a city to shine. In either case he did sponsor Al Khwarizmi (in latin he's called algorithmi....^^) and asked him to write a mathematical treaty aimed to the commoner, this book would become one of the most influencial book of all time, the first ever book to have a traduction both in latin and chinese : "Kitab Al jabr w'al mouqabala" this treaty fathered the algebra (al jabr), no less. By the way, arabic numerals are also due to Al Khwarizmi, who wasn't arab but persian and took this numerals from the hindus.

***** Djorgal These are both really good answers

The theorem is for x^n + y^n = z^n, as n>2

Damn, pretty neat, I see what you did there! (Of course, the proof of the irrationality of sqrt(2) is one of the "typical" ones, but that's nice to see...)

One worry is that because we are unable to trace all of the steps involved in proving FLT, we can't be certain that something equivalent to "2^(1/n) is irrational" wasn't used somewhere along the way, which would mean this proof doesn't work. Vladimir Voevodsky's fears live on.

@@lambdaexclamationpoint This isn't a problem, unless you mean to say that a condition of FLT is x ≠ y ≠ z ≠ x (I don't know, actually), in which case OP's proof is incomplete.

You are bugging the world.

mathception

Thug life

Yes, the more I listened, the more I felt I recognised Feynman.

Feynman also grew up in Rockaway, Queens, NY.

No

Yes spot on John

Hey I

YES! GEORGE ICE,AN AMERICAN AMATEUR DISCOVERED FERMAT'S PROOF!! WHATCH THE VIDEO Fermat marvelous FLT proof and read GEORGE ICE'S COMMENTS TO IT.

Almost every single discovery is dependent on what came before. Of course Ken provided a very important prerequisite. As did all the abstract algebrists Wile's used theorems from. And those people needed the work of the people before them, and so on. Wiles proved T-S, no one else had that claim so he's the one who gets the most press as always. You can wish it worked differently, but it doesn't. I don't see how Wiles did anything underhanded based on what I have read.

I think Wiles' aloofness didn't help. Ribet seems annoyed by his lack of collegiate spirit. By working as he did Wiles does give the impression that he did it all himself, which he clearly didn't. I think it's more shyness and an awkward personality over maliciousness though.

Don’t pity Ribet. He has a mathematical theorem officially named after himself. How many living mathematicians can claim that?

No *integer* solutions

I know you are joking, but the theorem states that a, b and c are positive integers, which 0 is not.

Viernes de Cine 0 is integer

That is called the trivial case. The actual question is "excluding the trivial case, there are no integer solutions to the equation a^n + b^n = c^n for n greater than 2"

x^0 + y ^0 = 1 + 1 = 2. Nothing raised to the power of 0 is 2.

405" seconds (6.75 mins) actually. I watch in 4x speed. Full comprehension

James Oldfield Can you actually read basic English sentences? I said I watched this very fast. I didn't say it was easy or hard.

Neueregel No, I can't. Do you feel bad now? :/

Are you the cousin of Mike Oldfield? If yes, then yes, feel bad. His techno-ambient and pop music was rather lame and basically only 1 or 2 hit-wonder. "Tubular bells and moonlight shadow."

I think you mean 4

No. More like: 3.14159265358979323846264338327950288419716939937510. I can recite 50 decimals of pi. Yeah what do. If you don't believe me, I'm so sorry.

actually it's 4.

***** you won.

Pi is infinite,meaning we have to say it's approximately 3.14. We can't say it's 3 or 4, because it's not. The only way to write it exact is to write its symbol:π

Which isn't a big thing really unless the receiver of a knighthood is pompous about it like 'Sir' Ben Kingsley.

+Random Guy-Next-Door Do you have a link for the explanation??

+Random Guy-Next-Door Meaningless, besserwisser correction - he got 720,000 USD. :)

+z8_GND_5296 just Google it my friend, you'll find PDF documents.

Random Guy-Next-Door Thanks!

It is sad that Ken Ribet got no money. Ribet seems like an intellectually great guy who is also humble. And unrecognized -- like I can't recall hearing about him prior to this, and I've been following this since I read about it in the NY Times (circa 1994).

almost, but not

Computer says NO

3+9+8+7+4+3+6+5-4-4-7-2 is not divisible by 3 => false

Rawand Mahmood Not exactly, but close. It's an irrational number, 4472 is correct to 8 decimals. (3987^12+4365^12)^(1/12)=~4472.000000007

krokodile dundee Everyone knows it's not. It's a prank made by the makers of The Simpsons.

Forget Pi Day, I'm excited for the conclusion of Harry Potter and the Methods of Rationality.

woodfur00 Forget that, what about the penumbral solar eclipse on the 20th of march? :D

Its gonna be 3 14 15 so best day for pi ever in one hundred years :D

Simone Noli 3.1416 is a better approximation than 3.1415 though.

randomasdf97 No, but at one point it will be 3-14-15 at 9:26:53. Two points, in fact. You can't do that when you round up.

If it did exist it woulda been a million pages long

+tehlolzfactor If Fermat himself had a "proof" with the amount of mathematicians that looked at this and didn't solve it for a long time using lots of after developed math. If he had actually written down a proof it's likely it was simply false. I mean yes he ended up being correct in his assertion but if he wrote down a mathematical reason why it was almost certainly wrong in the sense that it alone would have proved his theory.

Andrew wiles recently won the Abel prize for it

It probably either never existed, or was wrong.

at the fly on the wall

@@andr101 Bump, underrated comment

Arturo Fernandez He wrote that in Australian accent :p