The Bridges to Fermat's Last Theorem - Numberphile

[@PopeLando]

I've always loved the fact that a major contributor to the proof of Fermat's Last Theorem was André Weil and then the final proof was done by Andrew Wiles.

[@captain_kadaver]

Right? That's just beautiful

[@VikeingBlade]

I noticed that and I was like

[@windrush104]

Like?What

[@emdiar6588]

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

[@Ormek70]

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

[@PrashantParikh]

Ken Ribet comes across as such a brilliant but humble person. He gave Wiles his due without overstating his own integral contributions to the proof. Salute! :)

[@Dragonblaster1]

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.

[@johnsMITHhhhhh88]

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

[@jayneryan6395]

Wiles did this

[@vanish747]

The really, really, really watered down version of how Fermat's Last Theorem(FLT) was solved. Step 1. The general equation for FLT can be put into an elliptical form. (Fact) Step 2. ALL elliptical equations can be transformed into a "modular" form. (Conjecture) Step 3. If there is an elliptical equation solution for FLT, then it is such a strange equation that it can NOT be put into modular form (Proven). What Andrew Wiles proved was step 2. By proving step 2 then he showed that step 3 can never happen and therefore there is no solution for FLT.

[@Deciheximal]

Thank you!

[@QuasiELVIS]

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.

[@JMUDoc]

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 :).

[@IronicHavoc]

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

[@abhishekarya8487]

Alder wiles

[@eushearia]

Your name to be included in the history of math and a theorem to be yours are the greatest gifts for any mathematicians. Ribet is so brilliant and genius!

[@Ал-тайДіЙ]

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!

[@tomagain]

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.

[@ryansynk7088]

A suggestion: maybe doing a video on all of the millennium problems? You've covered two out of seven, might as well make a playlist out of it!

[@asher3240]

still hasnt been done... :(

[@thezestyman9159]

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.

[@bhattaraisandesh]

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

[@JamesJoyce12]

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

[@thezestyman9159]

@@JamesJoyce12 so where’s your Fields Medal?

[@abdelarmstr5173]

I have the solution to the P - NP problem but KZbin doesn't let me post the result in the comment section

[@DiaStarvy]

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

[@MadaxeMunkeee]

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

[@betcombo7021]

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

[@keepyouright6157]

+Anthony Armstrong I see what you did there.

[@huddlespith]

Bravo haha love this comment

[@bolerie]

I really like the idea of mathematics being a series of bridges and Islands. sometimes the Islands Are really pretty (like fermat's last theorem), sometimes the Islands Are important connection points to lots of different Islands (like Riemanns Hypothesis) and sometimes the method of building a New kind of bridge is Even more important (like Wiles)

[@marsgal42]

I remember the episode of Nova. They asked a much-younger Ken Ribet for a brief lay-person-friendly explanation of what a modular form was. He laughed...

[@JMUDoc]

They asked Sarnak and Katz and Mazur as well, if memory serves... they ALL laughed.

[@matthiasries9461]

I sit here in Saarbruecken, eating dinner while watching Numberphile. Then the clip reaches minute 5:22. It's a small world ^^

[@rajarshichatterjee3281]

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!😁😀

[@jwt242]

Ever since Simon Singh's documentary about Wiles' proof, I have found the story of Fermat's last theorem utterly fascinating; thanks very much, Brady, for bringing this incredibly interesting interview and please do more like this that illuminate details of the story.

[@manishs6479]

this guy is gonna be my Discrete Mathematics Professor next semester!!!! so hyped to takes this class

[@jacobschiller4486]

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

[@LucasRodrigues-oh1jt]

That's awesome. How is it going?

[@jacobschiller4486]

​@@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.

[@soanywaysillstartedblastin2797]

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

[@jacobschiller4486]

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

[@adityaiyengar152]

Every once in a while I come back to this video and enjoy it all over again. It's always and adventure thinking about this beautiful problem that still captivates many, including myself!

[@numberphile]

Great to hear.

[@Mark-x3l]

Ken Ribet clearly has a brilliant mind but he also comes across as a thoroughly decent bloke. What a wonderful story, and how amazing to be immortalized.

[@garethdean6382]

Nobody ever talks about Fermat's second-to-last theorem.

[@ghuegel]

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

[@garethdean6382]

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

[@jamez6398]

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

[@garethdean6382]

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.')

[@jamez6398]

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.

[@1KevinsFamousChili1]

With the success of movies like a Beautiful Mind, Good Will Hunting, The Imitation game etc. I'm surprised no one has made a movie about this story yet

[@jamez6398]

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 :/

[@michaelbauers8800]

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

[@cryme5]

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

[@apacheranger9820]

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

[@apacheranger9820]

proof Trial.....call helmsworth

[@picknikbasket]

Fantastic video, Andrew. This is one of the most epic and engrossing stories in all of mathematics and I never get sick of hearing it from any perspective. Its also the most bizarre story of 'collaboration' in any research undertaking I've ever heard of. Ken Ribet must have the patience of a saint!

[@MobiusCoin]

Alright, I get it, these proofs are beyond the scope of the average math enthusiasts but one day, if you guys have the time, it would be nice, even if it took a long series of videos, to try and explain it to those of us who have a little more than the average amount of mathematical knowledge (university level calculus, linear algebra, some understanding of geometry) but aren't mathematical gods, the workings of the proof.

[@isaacc7]

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.

[@EitanLevinzon]

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.

[@NGEternal]

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.

[@davtor33]

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.

[@AD173]

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).

[@liquidminds]

One of the most amazing ways to wake up in the middle of the night: Having an Insight into a problem that was bothering you for days. Doesn't happen often, but definitely the best way to wake up. Just make sure you find a piece of paper before you forget what you wanted to write down. :-)

[@abramwestrick9790]

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

[@phampton6781]

Very interesting interview. Now when are you gonna get Andrew Wiles himself on Numberphile? Has to happen!

[@jpacker13]

Kenneth Ribet is my professor right now at UC Berkeley and I have been watching Numberphile videos for about two years. This super exciting for me. Thanks!

[@theodentherenewed4785]

It's very impressive that mr. Ribet spent years to refine his theorem. In the end, all the complex research was behind a very simple equation, that any layman can understand.

[@rogermouton2273]

It really becomes clear just what an adventure solving FLT was - so many brilliant minds working over centuries, so many highs and lows, twists and turns, until Wiles' final moment of triumph. What an incredible saga.

[@diskgrinder]

FTL is impossible too

[@paulcassidy4559]

The pure enthusiasm around 11:30 is so great

[@ameynarkhede8264]

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

[@jeffreyjefferson536]

Does anyone else get a super strong Paul Auster vibe?! But srsly, Ken Ribet seems such a nice, humble and considerate person, I could listen to him for hours! I greatly admire his work, but on a human level, the way he talks about it is equally impressive to me.

[@woodfur00]

"I have discovered a truly marvellous proof of Fermat's Last Theorem, which this time slot is to short to contain."

[@qsquared8833]

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

[@arthritismutilans]

if you are a fly on the wall, what will you see Ans:-I have a pad, a pencil, you see my pad flying at you And then you see darkness

[@TwelfthRoot2]

arthritismutilans i laughed so hard at this

[@NoriMori1992]

Did you just use dog's bollocks?

[@KayvanAbbasi]

Ken Ribet: What a great human being. I love how humble he is and never speaks low of Wiles, even though he hid his stuff from him. Thanks for the interesting talk with this fine man.

[@trajanhammonds8507]

Anybody else flinch at 14:04 when he put a big ol crease in the manuscript

[@georgefernandez7558]

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

[@Damaniel3]

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

[@zachb.4429]

I never understand your videos but I love them any way

[@Pining_for_the_fjords]

It was an interesting story, but for a 27-minute video I was hoping for just a glimmer of insight into the mathematics behind Fermat's last theorem. Now I see it's something that only a few of the most elite mathematicians can ever hope to understand.

[@MadaxeMunkeee]

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.

[@jamez6398]

***** 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.

[@nitroyetevn]

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 :) ).

[@kaizal3161]

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.

[@Bjowolf2]

Check out the brilliant BBC Horizon / Nova documentaries for more insight.

[@alexdumortier]

"... and I would say, "Well, you know, this was proved in the 1960s by Grothendieck, but it isn't quite written down in the place you expect", and then I'd have to go find an argument." Hahaha -- What a BOSS!

[@TheMarkEH]

What a wonderful interview with a wonderful person.

[@Flemagrimm]

I'd love to see a video on some higher mathematics. Maybe the construction of the real numbers? This is Numberphile, after all. Gotta know how to make the numbers.

[@jonnyhifi]

Simply superb Brady, this is the best youtube video I have seen in a long long while (from any uploader, not just yours). Seriously. Superb. In fact racking my brains, the last one I thought that of, was your Dad recounting his landmine experience, two very different videos, but totally gripping. Thank you.

[@joaovictorpalmeida]

I feel bad now. I worshiped Andrew Wiles for solving Fermat's Last Theorem, but for what I understood from this video Ken Ribet has a major role in the solution, but he doesn't have the same recognition.

[@johntate6537]

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.

[@-danR]

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._

[@canadiannuclearman]

Taylor also.

[@reshpeck]

@@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.

[@reshpeck]

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.

[@shugaroony]

Great interview that, it touches on the spirit and drive that pushes science forward. I've read a book on Fermat's Last Theorem, so heard about this before, and have seen the excellent BBC documentary for which Ken is referring to; but to hear another opinion about solving this great problem from another angle is fascinating. Good questions as well Brady, you didn't always go for the easy ones, a sign of a great interviewer.

[@tymo7777]

I would love to watch a full length documentary about solved problems of modern mathematics produced by Brady.

[@LorenzoMella]

Watching this reignites my passion for algebraic subjects. I had always thought I would pursue a career in algebraic geometry... how I ended up specialising in probability and applied maths is still a mystery to me!!

[@willk7184]

Great interview. Really fascinating story. I highly recommend Simon Singh's book referenced above.

[@Empry]

It's such a pleasure just to listen to these kinds of talks! Very relaxing :)

[@jondury9450]

The biggest surprise in this video is that Ken is 70 years old.

[@JamesJoyce12]

how can it not make you happy that yt vid about sophisticated math theorems hits a million views?

[@villanelo1987]

I always wondered... how did these ancient mathematicians managed to live in those times? Even now, it is very, very hard for a person to be paid enough money for just being an investigator (specially in a field such as mathematics, with no "immediate effects", and few ways to directly generate money for the mecenas), and I assume the situation in these days is much, much easier than in the early 1700 (or even sooner than that). Now we have universities and institutes paying people to investigate, but before that... what? Did they actually have people sustaining them economically all their life just so they could continue investigating? Or was this just a hobby for them, and they worked like everybody else besides being mathematical geniouses? Because in that case, my respect is even bigger, I got to say. I know this is totally off-topic, and not related to the video itself at all, but... with all this talk about mathematics history, it felt kind of relevant to me, and it is, indeed, something I have always wondered.

[@axelrosalewski]

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

[@j0nthegreat]

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.

[@jgmartn]

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

[@Djorgal]

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.

[@TheRandomInternetGuy]

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

[@AliBaba-xg6uw]

Amazing. Who knew how disparate, yet serendipitous, efforts would play pivotal roles in exhibiting the genius of the human mind

[@Fleshcut]

Ken is a really inspiring mathematician and a truly nice person. He contributed so much to the world, but I think that the best thing he ever did, was getting rid of that moustache. Good choice, Ken!

[@captain_kadaver]

@Nissim Levy Sad that he's too old

[@shugaroony]

@@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

[@captain_kadaver]

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

[@vtrandal]

Born in the 1960s, I am happy I lived during such an exciting time in mathematics and science. I tried dabbling, but I am a happy spectator. I enjoy listening to these people talk about their work.

[@VechtMalthos]

2^(1/n) is irrational for n >= 3. Proof: If 2^(1/n) = p/q then p^n = q^n + q^n, which contradicts Fermat's Last Theorem. Unfortunately though, Fermat's Last Theorem isn't strong enough to prove that sqrt(2) is irrational.

[@lambdaexclamationpoint]

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

[@fetchstixRHD]

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...)

[@nitroyetevn]

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.

[@pwhqngl0evzeg7z37]

@@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.

[@knlshrvstv]

I like go to Caffe Strada now and then and every time I am there I always think of this video and how this little quiet cafe has a special place in the history of Fermat's last theorem.

[@americaneric2183]

I hope there will be a new video about this coming out soon. And I'm really hoping that they will interview Sir Andrew Wiles. Much respect from the U.S.A.

[@theoryjoe1451]

"I try to be a normal guy, and not walk around with angels on my shoulder." Humility is beautiful.

[@mr.squeaky8394]

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.

[@EMI94100]

Greetings from the University of Saarland in Saarbrücken :)

[@Punkpferd]

the saarländers!

[@zacharyhall2012]

This was really great! And absolutely deserves more views.

[@jacderida]

Wow, amazing video. I've lost count of the number of times I watched Simon Singh's documentary on Fermat's Last Theorem, but Ken offers valuable details here that didn't appear in that documentary. Perhaps they might be in the book, but I've not read it yet. An interview with Andrew Wiles would be spectacular! :)

[@tahataha1408]

27:30 "I try to on more or less a normal guy ... not walk around with angels on my shoulder"

[@michaelbauers8800]

Great video, thanks. Anyone who likes books on math should read Fermat's Enigma which I have read a few times. It covers some stuff in more detail, but it's nice to hear the story direct from Ken

[@mcndev21]

Wonderful! I saw the Nova program on this years ago, brought back many memories. Thank you!

[@TheGrooseIsLoose]

Actual insight into mathematical research is a nice break from the usual stuff on Numberphile. It shows people what the subject is really about, not the stuff that just reminds them of what they did (and in many people's cases, hated doing) in school.

[@elidrissii]

You got Ribet? Great job Brady, you really did well with this channel!

[@inchinaxp8663]

Fermat was looking down like 'damn guys, relax. I was just trolling. Holy shi** you actually poved it? Well I'll be damned..'

[@leestuurmans2837]

Fascinating interview. I really appreciate these in-depth interview style stories.

[@cuentadeyoutube5903]

It seem imposible Fermat had a correct proof to his theorem but... wouldn't it be amazing if in some decades somebody came up with a simple and elegant solution and it turned out that Fermat really had had a proof?

[@georgeice4389]

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.

[@CanobeansPL]

I absolutely loved this video. I could watch this sort of history channel all day :).

[@KotaTheFemboy]

i kid you not, last night i was wracking my brain trying to remember this exact equation and who made it for about 3 hours and i woke up still trying to remember it. then i saw this video in my feed and i think i was more excited for this video than anything else i've ever seen on youtube XD

[@greg55666]

This is a truly fantastic video. Ken is such an amazingly nice guy, he's saying it, but you have to listen really carefully to hear it.

[@riggmeister]

Awesome, what a guy! I love how humble mathematicians are.

[@user-vg7zv5us5r]

1:00 This means that we can't have a simplest shape similar to the right triangle in Euclidean geometry for the n-dimensional geometry. It might be connected to the distortion in metric of the space, whilst rising the number of dimentions.

[@timgrove3927]

Does this guy remind anyone of Richard Feynman?

[@shugaroony]

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

[@Headhunter_212]

Feynman also grew up in Rockaway, Queens, NY.

[@User-ei2kw]

No

[@mikeyboy2154]

Yes spot on John

[@timrgreenfield]

Hey I

[@benf7841]

This is the best numberphile video. Extremely inspirational yet sad too

[@dizont]

I love videos about proffesors and their work.. Im not good at math, so it was always interesting to understand how a proof of something can be so long. How basic must you begin, to induce so much ?

[@j.c.7975]

Great video! It's always nice and interesting to see how mathematics develops as time goes by :D Thank you so much!

[@jasertio]

Watching this during math class 😎😎

[@Egonkiller]

You are bugging the world.

[@magicalpencil]

mathception

[@patrickmurray6567]

Thug life

[@dina-vn1ol]

This is probably my favorite video ever

[@DaveKahn]

I know I'm shouting into the wind but "hanc marginis" (from Fermat's marginal note) should not be translated as "this margin". It appears in many printed versions and has been repeated so many times, including by John Conway in Simon Singh's beautiful documentary, that it will never be displaced. It's of no real importance as the error barely alters the meaning; change "this" to "the" and it would be a perfectly acceptable free translation. But for me each repetition of "this margin" produces a slight fingernails-on-blackboard moment as it indicates a misunderstanding of the Latin sentence structure.

[@zippyman28]

Same birthday as me. Nice. Also, the connections between algebra and geometry are astounding.

[@theechelonofmars]

Andrew Wiles' proof has been verified! And he got 700,000 USD as well!

[@Scrungge]

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

[@Fex.]

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

[@theechelonofmars]

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

[@Scrungge]

Random Guy-Next-Door Thanks!

[@peterlindner3283]

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).

[@chrisrace744]

This was so well explained. Well done to all involved.

[@greg55666]

Brady, I think you missed what Ken was saying when he said he finds it strange that Wiles needed Fermat's last theorem in order to tackle the Taniyama-Shimura conjecture. He's saying that if Wiles had attacked T-S earlier, and proven it earlier, then KEN would be the one who proved Fermat's Last Theorem! It's so unfair that Wiles needed a kick in the pants to do his part only after Ken had proven the real connection. However, the timing of all this is very interesting. Ken announced he had proven the connection in 1986 but didn't publish his paper until 1990. Wiles announced his proof in 1993. But Wiles has stated that he worked on his proof for SEVEN YEARS. That means that as soon as he heard from his friend Ken that the bridge between T-S and FLT had been built, he started working in secret on his own proof, before he even actually had the proof that Ken was working on. He knew Ken was _going_ to do it. Ken says people in math don't scoop each other, but in a way that's exactly what Wiles did. I don't know, man. Maybe it's just because I like Ken so much, but there seems to be something unsavory about what Wiles did. If he had done his part first it Ken Ribet's name would still be remembered a hundred years from now. Now, Wiles's will be instead. That's pretty gigantic. What if Ken had just announced his proof but not published it until the T-S was solved?

[@michaelbauers8800]

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.

[@hjyigo4759]

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.

[@jongu71]

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

[@tombruckner2556]

This is one of the most interesting videos I ever saw on KZbin. And I am not a mathematician myself :-)

[@MATHSTHEMATIQUES]

😂👍

[@Mitch_Crane]

Pi is exactly 3.

[@HoxTop]

I think you mean 4

[@thomaswarriner2344]

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.

[@jasperkuhn2000]

actually it's 4.

[@ZumunYT]

***** you won.

[@jontebengtsson6738]

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

[@NeonsStyleHD]

Wow that must've felt amazing. There isn't a greater feeling than working out an idea and proving it to be true.

[@rawandmahmood9368]

(3987^12)+(4365^12)=(4472^12) Source: Simpson.

[@RobarthVideo]

almost, but not

[@axelrosalewski]

Computer says NO

[@ben1996123]

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

[@kumirei8715]

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

[@yousorooo]

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

[@Italiankid1029]

I saw a documentary of this from Andrew's perspective. This is great stuff. Very interesting

[@glacialvojta]

a=0 b=0 c=0, solved

[@ViernesDeCine]

No *integer* solutions

[@edvinlam200]

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

[@glacialvojta]

Viernes de Cine 0 is integer

[@einstin2]

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"

[@TheJackawock]

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

[@zuzusuperfly8363]

Can't believe I missed this video. I remember this particular mathematician from the documentary about Andrew Wiles and proving fermats last theorem. A documentary which I recommend if it can still be found on KZbin.

[@ambers123100]

27 mins!!! Yesssss

[@Neueregel]

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

[@Neueregel]

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.

[@jamez6398]

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

[@Neueregel]

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."

[@Bjowolf2]

Check out the brilliant BBC Horizon episode called "Fermat's Last Theorem" about Andrews Wiles and his work - amazing and very emotional TV. It also exists as a somewhat different Nova episode btw.

[@ThaRSGeek]

Few more days till pi day. :)

[@woodfur00]

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

[@ZardoDhieldor]

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

[@simonenoli4418]

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

[@randomasdf97]

Simone Noli 3.1416 is a better approximation than 3.1415 though.

[@woodfur00]

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.

[@PetrifiedForce]

Wow… Saarland and Saarbrücken mentioned in a numberphile video, right now I'm proud of being from Saarland :D

[@jwilbrahamford]

That was awesome thanks Brady and Ken. It was intensely interesting to hear the human stories behind these break through discoveries. I know that you have found your place on youtube Brady but I really think the ABC(aus) could give you some funding and present these videos on their education section.

[@windrush104]

A great story. Well done numberphiles and Ken Ribet

[@DudokX]

I like longer videos!

[@Jivvi]

0:28 they figured out all of the Pythagorean triples? Don't they go on forever, or is there a point where all the bigger ones are just multiples of the smaller ones?

[@briansammond7801]

Yes, they go on forever, but there is a pattern to them, so that given A, you always know what B and C will be. For all odd A, B = (A squared - 1)/2 C = (A squared + 1)/2 so 3,4,5 5,12,13 7,24,25 etc and integer multiples of all of these 6, 8,10 10, 24, 26 14, 48, 50 etc

[@tehlolzfactor]

I still wanna know whether Fermat's proof for this theorem actually held up or not.

[@Zzzip13Strike]

If it did exist it woulda been a million pages long

[@sparkzbarca]

+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.

[@thatguyfromhouse]

Andrew wiles recently won the Abel prize for it

[@NoriMori1992]

It probably either never existed, or was wrong.

[@the_mentaculus]

Awesome video! I'd love to see more from Dr. Ribet; it's fantastic to see esteemed mathematicians such as Graham or Mazar just talking about some math that is kind of fun and interesting. I want to see Ribet fill up some brown paper!

[@antonino30]

why are you writing postive instead of positive now? 2:16

[@phoeNYkx]

Arturo Fernandez He wrote that in Australian accent :p

[@explorerc607]

He is the giant whose shoulders Andrew Wiles stood on to see further and finally proved the Fermat's last theorem.

[@bambapabbi]

What is he always looking at?

[@andr101]

at the fly on the wall

[@pwhqngl0evzeg7z37]

@@andr101 Bump, underrated comment

[@topilinkala1594]

9:20 When I was working as computer analyst one of the major problems for me was tell my boss that it didn't matter where I was and what time it was I was working on the case. Because one cannot shut ones brain out without chemical coma. But he was a pencil pusher who entered numbers in speradsheet and let the computer do it's magic and forget all of it.

[@Swybryd-Nation]

SIR Andrew Wiles now

[@shugaroony]

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

[@Gna-rn7zx]

This is an amazing piece of mathematical history!!! You should seek larger-scale publication of this interview footage, perhaps through Nova or some similar program. Thank you, Numberphile, for this inspirational and elucidating video!