Visualizing Fermat's Last Theorem

[@dvashunz7880]

So this was what things were like before 3Blue1Brown

[@cubernetes]

lmao

[@TIO540S1]

Yeah, but it’s a very nice video even today, let alone for its time.

[@vikraal6974]

This is 3b1b on steroids

[@mikeyoung3870]

@@vikraal6974 I think steroids is an understatement. More like you whole entire diet is nothing more than 200 grams of testosterone mixed with Ayahuasca

[@worndoubloon1175]

News music intensifies

[@bobsuruncle8938]

Somewhere, Fermat is laughing at all of us, saying, "Those fools fell for that joke I wrote in the margin!"

[@usurper1091]

Bob Suruncle , it's already been proved

[@hungtrumno]

The joke part is "I know how to prove but there is not enough space in the margin"

[@non-inertialobserver946]

tic toc It's better if you work on things that aren't proven, like the riemann hypothesis

[@nebilm8947]

hung trumno hahahhahaha

[@non-inertialobserver946]

@Gareth Ma I didn't say that new proofs to old theorems aren't useful, just that new proofs to new theorems are more useful

[@jaguarfacedman1365]

the music makes me feel like im in a pokemon battle.

[@eddyhans5365]

That "music" is very disruptive!

[@jaguarfacedman1365]

@@eddyhans5365 I had completely forgotten this comment.

[@memenganimation2488]

@@jaguarfacedman1365 This comment is gold

[@flyingstonemon3564]

Why does It feel like a mix of a bunch of rpgs, I feel dragon quest pokemon and final fantasy? Is is the classic feel mixed with an epic synth feel?

[@alexanderolena]

"Extends in two dimentional surface embedded in four dimentional space." Finally simple explanation I was looking for.

[@valentinsarmagal]

the ending was the nerdiest joke ever

[@believeit7818]

the fuckin.... what?

[@BENebuchadnezzar]

"If only I could explain it to you before I run out of videotape!"... and presumably die as well.

[@Stratomacaster]

This video would have been much better if I didn't feel like I had won a cheesy prize on the Price Is Right.

[@mueezadam8438]

Only a true mathematician can fully appreciate this visualization. I, unfortunately, am not one of said mathematicians.

[@wavexphonk]

hahahahaha

[@TheLegolasguy]

When my math teacher mentioned in class that he would give us extra credit for proving this, I made the mistake of taking him seriously. But, of course, that afternoon, when I looked up the theorem, I came to my senses.

[@sigmaprime4307]

I got a proof, but it's too long for this youtube comment ;-)

[@michaelpapadopoulos6054]

I got a 7 second proof too check it out

[@prototypeinheritance515]

but google+ implemented infinte comments just for you :(

[@Cyberw4y]

OOOOOoooh! Pretty shapes!

[@TrojanVirus]

same

[@prajnaprajna1923]

To prove Fermat clearly, short,absolutely, easily I use the condition xyz are integer 1^2+2^2+3^2+4^2+....+n^2=Sn=n(n+1)(2n+1)/6=2n^3+3n^2+n/6 2n^3=6Sn - 3n^2 -n n^3=3Sn-3/2n^2-n/2. Fermat had said x^3+y^3=/z^3 I supose x^3+y^3=z^3 3Sx-3/2x^2-x/2+3Sy-3/2y^2-y/2 -3Sz+3/2z^2+z/2=0 x^2+y^2-z^2=2Sx+2Sy-2Sz-x/3-y/3+z/3. Sx+S(x-1)+Sy+S(y-1)-Sz-S(z-1)=x/3+y/3-z/3. Or 2S(x-1)+2S(y-1)- 2S(z-1)+x^2+y^2-z^2=x/3+y/3-z/3 So 1^2+2^2+3^2+..+(x-1)^2+1^2+2^2+3^2+..+(y-1)^2- [ 1^2+2^2+3^2+..+(z-1)^2]= - x^2/2- y^2/2 +z^2/2+x/6+y/6-z/6 Because x(x-1)(2x-1)/6+y(y-1)(2y-1)/6- z(z-1)(2z-1)/6=/ - x^2/2- y^2/2 +z^2/2+x/6+y/6-z/6 Contrary to the assumption conclusive x^3+y^3=/z^3. General, using 1^a+2^a+3^a+...n^a=Sn Prove x^n+y^n=/z^n

[@zionjpark]

prajñā prajñā please explain how the equation under “Because” is an inequality

[@dcterr1]

Wow, that's some pretty impressive computer graphics for 1990!

[@clarekuehn4372]

Very good! I think what it's saying is: The cone in a grid cube near the beginning is a shape (model), to show visually, in a different way, all solutions for Pythagoras' theorem, a2 + b2 = c2, by where the cone hits the points inside the cube on the green dots. (Before that, it showed a circle on a two-dimensional grid. That sort of works to show which solutions for Pythagoras' theorem, but only if you project it up into three dimensions do you see how all solutions get bigger and bigger.) When the grid is changed into feactional points, or the shape to touch them is made more complex (as different curves than a cone, which is basically a circle from the top), no points still hit (green dots). This means that, despite all the shapes thought of to "hit the grid and make green dots", i.e., hit integer solutions for powers over 2, nothing has been found as of yet. To prove that nothing could be found is what the solution did.

[@naicotennis]

I have a proof but it won't fit in this comment! KZbin limits the number of words you can- ah, damn, never mind. Unlimited characters in comments... Umm, well... I would show you my proof, but I gotta go now, other stuff to do.

[@estuhyerh67ber7]

not very original

[@katherinehunter8494]

oh my god you sound just like fermat, only he says i have a proof but this margin is too small to contain ... sure the space limit is not an excuse?

[@AbhirupMukherjee10]

Loved the ending!

[@jamesyeung3286]

holy shit how the fuck did one of the easiest theorem to write out require the most abstract and difficult field of mathematics to prove.

[@boazthomassie4919]

I understand none of this

[@vishalshinde5252]

Your e not alone

[@user-hh9uc4qb8c]

Actually only less than 100 people on earth right now understand the too long and lengthy proof of Fermat's last eqn.

[@TomValedro]

this music makes me want to party.

[@neelmodi5791]

LOL I started laughing in the ending... wouldn't be surprised if that was Fermat himself

[@woot123sexyparty]

Judging by the incredible computer graphics, this video was definitely made before the proof was discovered.

[@johns5037]

That is one of the best conclusions to a youtube video I have ever seen.

[@xycubed]

Each stage of explanation in this video needs about 10x as much time devoted to it. >.

[@josegomez6549]

1. brain.exe has stopped worked 2. nah fam chill 3. you lost me at 0:47

[@TrojanVirus]

same

[@TrossachsPhoto]

x² + y² = z² If you pick any point on the surface of that cone, you'll get an x,y,z coordinate... which will satisfy Pythagoras (Fermat at n=2). So the surface of the cone is the solution which includes all non-integer numbers. However, at x=±3 and y=±4 and z=5, valid points on the cone, this is Fermat solution for n=2 (positive integers). What follows is if we rendering a shape which represents every valid solution for x³+y³=z³ (and then for subsequent higher powers), there are valid non-integer values for this equation, but conjectures (as did Fermat) that there isn't place on the shape, where all three coordinates are exact integers.

[@josegomez6549]

SnapGotYou.com / Trossachs Photography I appreciate that you tried to explain it, I really do, but I still can't really understand it beyond the basic stuff that nothing in x² + y² = z² will work out. That's all I get, the rest is just too damn complicated visually to see and understand for me as it is right now.

[@skeletonrowdie1768]

i got lost at 1:07 xD

[@APh_]

this background music makes the video sounds like its for an anime/video game rather than an a mathematical problem

[@raglanheuser1162]

i liked the final fantasy battle music

[@alkankondo89]

Side note: I like the upbeat music in septuple meter!

[@pcred567]

yeah, in retrospect that totally was 7/4 lol Never before heard a song written quite like that. Also for some reason the song artist decided to put accents on beats 1 and 4.5? so that's strange.

[@jmm1233]

lol at the end

[@MakarSvet13]

Who understood what to say at 1:30?

[@xCorvus7x]

"Just as one can raytrace a deformed solid, by following a deformed ray through the undeformed shape we can deform the integer grid instead of the Fairmont curve."

[@claus11212]

cant you tell this is an old video made before youtube existed?

[@32bikkeltje]

It's nice to see something less complicated then women..

[@eduardorivera508]

Than* ... C'mon now

[@MrArmyHusband1]

The preface of the material clearly covers that. The question is whether or not there is an alternative proof which Fermat was capable of forming with the knowledge of the era.

[@Jarmo187]

Now this was EPIC i must say. :D

[@watonearthisthat]

Pretty... What were we supposed to be looking at again?

[@alicantuncer4800]

Nice ending.

[@starrychloe]

A+++ troll!

[@sabin97]

not to be pedantic but the joke appears to be a meme of what fermat said(and i'm rephrasing in my own words as i dont remember the exact words): "i have proof but it wont fit the margin of this page" then the person in the video said "i have proof but it wont fit in this video tape" then the commenter said "i have proof but it wont fit in this comment" that's why he got all those thumbs up.

[@ChrisOrillia]

I was NOT expecting THIS narrator to do that, truly funny.

[@nikoandroman]

Bruh wdf, I’m hearing the words he’s saying but I can’t understand what he’s talking about and how he reached that conclusion. It’s like hearing a language you don’t understand

[@sixhundredandfive7123]

Mathematician solving Fermat's Last Theorem *One Winged Angel starts playing*

[@johnjackson9767]

Came for the math, stayed for the Smash Bros. music.

[@Mac2point1]

If fermat said there was a solution and that Wiles used maths not even invented in fermats time, either fermat was pissing about, or there was a much simpler way of solving this equation !!!

[@davidfalk1367]

It's thought that Fermat thought he had a proof but there was probably a mistake

[@ceskale]

No shit

[@brenden8125]

Somehow, super nintendo music seemed like the best choice.

[@venkatbabu1722]

Bridge is a sounding echo. Bridge cannot exist. Links can be five. Five circular hallow rings.

[@xypheli]

The hype music makes it soo much better

[@santircastillo]

Thank you for taking the time to write that :)

[@Thrawnmulus]

I just got here from a Numberphile vid that said Andrew Wiles and Richard Taylor fixed the proof for Fermat's theorem.

[@ta_ogboy9998]

Me: Trying understand what I'm looking at Brain: Pokemon music

[@Our_Sole_Pusch]

It really doesn't need the over-dramatic music, in fact I think it would help if it wasn't included.

[@Vextrove]

Amazing music, amazing ending

[@frostyrobot7689]

This must have been created before Andrew Wiles solved it.

[@120551DS0u2a]

Skip to 1:59 to avoid a trivial introduction to the theorem

[@StarsManny]

I remember playing this game on a 48k spectrum.

[@rowbeartow7376]

what? he didn't have another blank piece of paper ? did his marvelous proof need to be written in the damn margin? he would have had to know that such a proof would be a mathematical big deal and IF he had such a proof it wouldn't all be in his head. he'd have notes. the story is not credible.

[@ActualXJoe]

the numberphile channel says that the reason he didnt prove it, is because he dropped dead right after writing that he had solved the proof

[@tommcwilliams1072]

ActualXJoe The true story is that Fermat wasn't correct: "But this margin is too small to make a go and discover what I overlooked at first..."

[@WillToWinvlog]

The real truth behind the matter is that he suspected the conjecture was true, but didn't have a proof.

[@madvoice3703]

SUPER BRO BECAUSE OF YOUR VEDIOS I completed my research

[@EddiePortal]

If you read the description you'd see the uploader KNOWS it has already been proved. This video is not about historical accuracy / proof. It is about VISUALIZING the set of equations that are relevant to the theorem (namely x^n + y^n = z^n for differing values of n).

[@michaelcweir]

Well you can end all your speculations. Fermat's last Theorem has been solved and you can prove it for yourself. Just search on KZbin for 'Fermat's last Theorem, the original proof'.

[@likithkb8599]

Is this really 1990?

[@jennifer86010]

Every comment below makes absolutely NO reference to mathematics, geometry, or solving equations. So why did non-math people even watch this very technical, complicated video? That answer is a theorem that really needs solving !!

[@payday0023]

"video tape" haha

[@SpiderWick12]

I greatly doubt that the video is 20+ years old.

[@TheTwelfthM0nkey]

Try reading the description...

[@misticoabadaba8965]

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: kzbin.info/www/bejne/Y5vTcmCqp5trrdk

[@butteredskatoast]

How on Earth could someone making a video about something so brainy and calculating make such a fucking hilarious ending?

[@fartx211]

This is one of those times where the appropriate response is "lol wut"

[@KongofPip]

Muzak must be contagious.

[@SpiderWick12]

Of course the fact that it was a video or a video with a person wasn't what provoked my doubts, but I see I have overlooked the opening slide some-how. Never-mind that thought. I enjoyed your sarcasm, though. Sarcasm is funny.

[@seth.heerschap]

They lost me at 1:48...

[@ddorman365]

Thank you for the beautiful video, peace and love Doug.

[@jedi1357]

Historically, every time we discover a new numerical concept we begin using it for useful purposes: The number 0 in 500BC, Binary numbers 300BC, negative numbers 100BC, algebra 820AD, logarithms, calculus etc. If Fermat was wrong, then a new system would exist that we may take advantage of. Proving Fermat was right simply tells us to look elsewhere.

[@AliceYobby]

It didn’t take Fermat being wrong though. Fermat simply posing the question opened many doors

[@ybobcat]

In response to edwardowen2 ,Andrew Wiles did the prrof while he was working at Princeton

[@lamalamalex]

Omg imaginge Fermat's comment on his proof on a tweet, "I've a wonderous proof that bu alas was past 140 characters"

[@azizukman]

Can I get the music in iTunes for my wedding day.

[@santircastillo]

There is already a proof. About a hundred pages and really complex and heay mathematical topics were needed.

[@DocteurZeuhl]

1990 music adds credibility to the scientific content.

[@Ichijoumi]

@kyto the theorem states that n has to be larger than 2. Your solution is incorrect as it took more than a simple equation to demonstrate that the theorem is indeed correct. No number ^n when is above two will give you whole numbers.

[@carlkamuti]

You really, really, REALLY let yourself down at the end. You fool, this could have been so good...

[@roidkaro]

3^3+4^3+5^3=6^3, so there are infinitely many solutions to the first equation. I believe the second equation is true as well, but I'm not sure. At least there is a solution if a=0 : x=2682440, y=15365639, z=18796760 and b=20615673. However, I've no idea of the answer of your two next questions...

[@mayurkulkarni755]

Can you shut the annoying music zzzz

[@Kenneth_the_Philosopher]

Outstanding Video!

[@F.H.Machado]

My brain melted, after seeing this video.

[@xyzct]

Three fewer pixels and it would be radio.

[@afnankhokhar]

frikkin mind blasting...even though I don't know what he's talking about.

[@questforenlightenment441]

Boss fight music

[@giannisfafalios9906]

did you try reversing the polarity?

[@likeriver]

The song sounds like something out of Super Smash Bros

[@Peter-xs2mu]

I think I understoond - maybe - one word in ten. I liked Euler's proof voor n=3 much better.

[@stanlocke5547]

We woulda known if he didn't run out of video tape... NOW WE'LL NEVER KNOW HIS EXPLAINTIONS ! !!!

[@dan339dan]

the music is epic

[@cwaddle]

Did i just watch a boss battle in final fantasy 7?

[@Kyleology]

The graphics didn't help at all.

[@cartapax5077]

I had a proof but run out of mind.

[@rhysman0001]

the answer is not expliand in maths but is explaind in words

[@yotsubakoiwai1645]

trolling hard, are we now?

[@GladerDev]

No values of n would satisfy that equation.

[@OprahMemorizedPi]

I find the music selection funny.

[@Akron162]

Ok, you got to be in another plain of reality to come up with something like this.

[@01andak]

What is the sound of one nerd laughing.

[@johannesh7610]

I at least understand most of it and not only laugh at the ending joke

[@tv..6531]

Fermat's Last Theorem: 홀수 솟수 p에 대하여 x^p+y^p=z^p을 만족하는 자연수 x, y, z는 존재하지 않는다 (My Proof) 만약 자연수 x, y, z가 존재한다면 페르마 소정리에 의해, vw(v+w+2pk)F(v, w, p, k) = p^(p-1) k^p 으로 변형되며 그 해는 (x, y, z) = (v+pk, w+pk, v+w+pk) 꼴이다. 그런데 자연수 k= n인 경우 해가 존재한다면 n=1*n 이므로 k=1일 때의 해의 n배의 해를 가져야 하는데... k=1일 때 해가 존재한다면 '홀수=짝수'로 모순. 따라서 해는 존재하지 않음.