@@vikraal6974 I think steroids is an understatement. More like you whole entire diet is nothing more than 200 grams of testosterone mixed with Ayahuasca
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.
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
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.
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
I have a proof but it won't fit in this comment! RUclips 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.
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.
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.
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.
"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."
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.
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 !!!
Well you can end all your speculations. Fermat's last Theorem has been solved and you can prove it for yourself. Just search on RUclips for 'Fermat's last Theorem, the original proof'.
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).
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.
z^n=(x+y)^n x^n+y^2≠z^n The value of the expansion of the equation that is the multiplication of different prime numbers. It does not become √ of a natural number.
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.
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.
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: ruclips.net/video/-jpA-tr68ww/видео.html
@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.
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...
x^3 + y^3 + z^3 = a^3 x^4 + y^4 + z^4 + a^4 = b^4 Are there solutions for this indefinitely for n integers to the power of n? Are there systematically no solutions for n integers to the power of (x>n)?
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.
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.
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 !!
Michael Dougan the joke was that the video was too short for his proof of Fermat's Last Theorem, just like how the margin in Fermat's paper was too small for him to write his proof.
![Gucci Mane & Sexyy Red - You Don't Love Me [Official Music Video]](http://i.ytimg.com/vi/j7IBqyFKT4c/mqdefault.jpg)
So this was what things were like before 3Blue1Brown
lmao
Yeah, but it’s a very nice video even today, let alone for its time.
This is 3b1b on steroids
@@vikraal6974 I think steroids is an understatement. More like you whole entire diet is nothing more than 200 grams of testosterone mixed with Ayahuasca
News music intensifies
the music makes me feel like im in a pokemon battle.
That "music" is very disruptive!
@@eddyhans5365 I had completely forgotten this comment.
@@jaguarfacedman1365 This comment is gold
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?
Somewhere, Fermat is laughing at all of us, saying, "Those fools fell for that joke I wrote in the margin!"
Bob Suruncle , it's already been proved
The joke part is "I know how to prove but there is not enough space in the margin"
tic toc It's better if you work on things that aren't proven, like the riemann hypothesis
hung trumno hahahhahaha
@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
the ending was the nerdiest joke ever
"Extends in two dimentional surface embedded in four dimentional space." Finally simple explanation I was looking for.
"If only I could explain it to you before I run out of videotape!"... and presumably die as well.
the fuckin.... what?
Only a true mathematician can fully appreciate this visualization.
I, unfortunately, am not one of said mathematicians.
hahahahaha
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.
OOOOOoooh! Pretty shapes!
same
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
prajñā prajñā please explain how the equation under “Because” is an inequality
This video would have been much better if I didn't feel like I had won a cheesy prize on the Price Is Right.
I got a proof, but it's too long for this youtube comment ;-)
I got a 7 second proof too check it out
but google+ implemented infinte comments just for you :(
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.
Wow, that's some pretty impressive computer graphics for 1990!
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
I understand none of this
Your e not alone
Actually only less than 100 people on earth right now understand the too long and lengthy proof of Fermat's last eqn.
Loved the ending!
I have a proof but it won't fit in this comment! RUclips 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.
not very original
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?
1. brain.exe has stopped worked
2. nah fam chill
3. you lost me at 0:47
same
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.
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.
i got lost at 1:07 xD
LOL I started laughing in the ending... wouldn't be surprised if that was Fermat himself
That is one of the best conclusions to a youtube video I have ever seen.
this background music makes the video sounds like its for an anime/video game rather than an a mathematical problem
Each stage of explanation in this video needs about 10x as much time devoted to it. >.
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.
Side note: I like the upbeat music in septuple meter!
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.
Who understood what to say at 1:30?
"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."
this music makes me want to party.
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.
i liked the final fantasy battle music
Now this was EPIC i must say. :D
lol at the end
Nice ending.
Pretty... What were we supposed to be looking at again?
cant you tell this is an old video made before youtube existed?
It's nice to see something less complicated then women..
Than* ... C'mon now
Can I get the music in iTunes for my wedding day.
I was NOT expecting THIS narrator to do that, truly funny.
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 !!!
It's thought that Fermat thought he had a proof but there was probably a mistake
No shit
It really doesn't need the over-dramatic music, in fact I think it would help if it wasn't included.
Came for the math, stayed for the Smash Bros. music.
I just got here from a Numberphile vid that said Andrew Wiles and Richard Taylor fixed the proof for Fermat's theorem.
A+++ troll!
Well you can end all your speculations. Fermat's last Theorem has been solved and you can prove it for yourself. Just search on RUclips for 'Fermat's last Theorem, the original proof'.
The hype music makes it soo much better
SUPER BRO BECAUSE OF YOUR VEDIOS I completed my research
I remember playing this game on a 48k spectrum.
Mathematician solving Fermat's Last Theorem
*One Winged Angel starts playing*
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).
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.
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
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..."
The real truth behind the matter is that he suspected the conjecture was true, but didn't have a proof.
If aliens ever abduct me and do an intelligence test in any math greater than add/sub/mul/div, earth is doomed.
z^n=(x+y)^n x^n+y^2≠z^n
The value of the expansion of the equation that is the multiplication of different prime numbers. It does not become √ of a natural number.
Amazing music, amazing ending
Somehow, super nintendo music seemed like the best choice.
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.
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.
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: ruclips.net/video/-jpA-tr68ww/видео.html
Me: Trying understand what I'm looking at
Brain: Pokemon music
@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.
Omg imaginge Fermat's comment on his proof on a tweet, "I've a wonderous proof that bu alas was past 140 characters"
They lost me at 1:48...
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...
This must have been created before Andrew Wiles solved it.
Bridge is a sounding echo. Bridge cannot exist. Links can be five. Five circular hallow rings.
Thank you for the beautiful video, peace and love Doug.
I greatly doubt that the video is 20+ years old.
How on Earth could someone making a video about something so brainy and calculating make such a fucking hilarious ending?
Skip to 1:59 to avoid a trivial introduction to the theorem
Is this really 1990?
well I was pretty interested in those shapes than in the proof of the theorem
x^3 + y^3 + z^3 = a^3
x^4 + y^4 + z^4 + a^4 = b^4
Are there solutions for this indefinitely for n integers to the power of n?
Are there systematically no solutions for n integers to the power of (x>n)?
No, check out the shortest math paper ever. It just provides a counter example for n = 5
Was just thinking we could do some rapid prodotyping and get a really cool figure.
This is one of those times where the appropriate response is "lol wut"
It doesn't work because it postulates that the origin has a definable value, while the edges don't.
The song sounds like something out of Super Smash Bros
I at least understand most of it and not only laugh at the ending joke
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.
There is already a proof. About a hundred pages and really complex and heay mathematical topics were needed.
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.
It didn’t take Fermat being wrong though. Fermat simply posing the question opened many doors
Outstanding Video!
You really, really, REALLY let yourself down at the end. You fool, this could have been so good...
I think I understoond - maybe - one word in ten. I liked Euler's proof voor n=3 much better.
Nice music, what is it?
Thank you for taking the time to write that :)
I just found a proof but it is too long to fit inside a youtube comment
How does one comment on, or rate, a video that goes from the sublime to the ridiculous?
How about this equation: *a^3 + b^3 + c^3 = d^3*
This equation has many solutions. So does a^4+b^4+c^4=d^4 and a^5+b^5+c^5+d^5=e^5.
Am not an expert at mathematics. But the features seem really like Calabi-Yau manifolds
We woulda known if he didn't run out of video tape... NOW WE'LL NEVER KNOW HIS EXPLAINTIONS ! !!!
Did i just watch a boss battle in final fantasy 7?
love the joke at the end! >_< if only i can explain to you before i run out of video tape.
call this what you might, isnt this just symmetry?
I find the music selection funny.
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 !!
did you try reversing the polarity?
"video tape" haha
Wiles is wrong. The rule for natural logs prove n can be greater than 2.
Muzak must be contagious.
1990 music adds credibility to the scientific content.
LOL What the heck happened at the end?
Michael Dougan the joke was that the video was too short for his proof of Fermat's Last Theorem, just like how the margin in Fermat's paper was too small for him to write his proof.
The graphics didn't help at all.