Numberphile - 2015-03-11
Ken Ribet - a key player in the solution to Fermat's Last Theorem - gives a taste of how real mathematics is done... piece by piece and by human beings. More links & stuff in full description below ↓↓↓ More Fermat (with Simon Singh): http://youtu.be/qiNcEguuFSA Even more Fermat (with Simon and Homer Simpson): http://youtu.be/ReOQ300AcSU Simon Singh's brilliant documentary on BBC iPlayer (UK only): http://bit.ly/TheProofDoco And his Fermat book: http://amzn.to/1jWqMTa Support us on Patreon: http://www.patreon.com/numberphile NUMBERPHILE Website: http://www.numberphile.com/ Numberphile on Facebook: http://www.facebook.com/numberphile Numberphile tweets: https://twitter.com/numberphile Subscribe: http://bit.ly/Numberphile_Sub Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): http://bit.ly/MSRINumberphile Videos by Brady Haran Brady's videos subreddit: http://www.reddit.com/r/BradyHaran/ Brady's latest videos across all channels: http://www.bradyharanblog.com/ Sign up for (occasional) emails: http://eepurl.com/YdjL9 Numberphile T-Shirts: https://teespring.com/stores/numberphile Other merchandise: https://store.dftba.com/collections/numberphile
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.
Theres whole books about it, and even they dont go into much detail on the actual proof
@mikel77 so far no, there is one proof.
Very few people actually believe Fermat had a proof
@relike868p Nonsense. Mastering Galois theory gets you no closer to understanding the proof of FLT than understanding that 1+1=2. Galois theory can be understood by most decent college math majors. The proof of FLT can be understood by only the most elite mathematicians in the world.
@anticorncob6 I'd like to see a unicorn or a golden egg laying goose.
@Bob I think you are underrating college graduates.
Fertmat, the greatest mathematical troll that there ever was.
Euler = GOAT
Huehue I gotsa proof guys but cant write it all here lolol
Well, he's no Gauss.
*fermat
Also, unoriginal comment
Euler is the greatest
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.
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.
Nobody ever talks about Fermat's second-to-last theorem.
Well there was Fermat's Little theorem which is underrated in my opinion
"second-to-last theorem".
No, "last but one theorem". Use English as American English is not sufficiently expressible.
…or his first
Ikr, nothing about the reboot (Fermat strikes back) either
@Gareth Dean only if a is not a multiple of p
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.
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
Maybe worth to note also here is that the proof of Step 3 is the part that Ken Ribet of this video did.
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!
Anybody else flinch at 14:04 when he put a big ol crease in the manuscript
It is not a manuscript, it is a preprint or copy of the journal article, he would have many copies.
I sit here in Saarbruecken, eating dinner while watching Numberphile.
Then the clip reaches minute 5:22. It's a small world ^^
One of the best Numberphile videos ever.
indeed
Totally agreed!
It can't be, it's not dr Grime #fanboyism
it doesn't have to be Dr Grime
@Szymon Harbuz Yep.
Does this guy remind anyone of Richard Feynman?
Yes, the more I listened, the more I felt I recognised Feynman.
Feynman also grew up in Rockaway, Queens, NY.
"I have discovered a truly marvellous proof of Fermat's Last Theorem, which this time slot is to short to contain."
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
What... Arch needs alot of things....Fathers personal carrier
proof Trial.....call helmsworth
been here 1 yr backside in
I can fix what Adam did
Just don't know for sure what he did, books of life are closed
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. :-)
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!
He should get the fields medal just for that
@Nissim Levy Sad that he's too old
@Käpt'n 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
@Saltire Yeah but there are so many other awards than the Fields medal. The Fields medal has the purpose to motivate younger mathematicians.
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.
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...
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)
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
arthritismutilans i laughed so hard at this
Did you just use dog's bollocks?
I never understand your videos but I love them any way
The pure enthusiasm around 11:30 is so great
literally I could see his passion through his eyes. It was really a great moment
Very interesting interview. Now when are you gonna get Andrew Wiles himself on Numberphile? Has to happen!
Pi is exactly 3.
Mitch Crane I'm so sorry to disapoint you but the true answer for pi is 42 because 42 is the answer to life the universe and everything
Of course it is ! And pi/e = 1.
pi=3=e dont @ me
The State of Indiana wants to know your location
@Thomaswarrinerr/whoosh
Andrew Wiles' proof has been verified! And he got 700,000 USD as well!
It was actually Gerhard Frey who initiated the link between Taniyama and Fermat. He didn't get anything either.
Random Guy-Next-Door --- It has been "verified" and note the quotation marks. There are mathematicians who refute Wiles' use of string theory. String theory is a gray, fuzzy area that has a lot of pushback from many theoretical mathematicians. I'm not convinced.
Dwight Turner Wiles proved FLT...according to all Specialists working in that field. Period. Paragraph. EOS.
Dwight Turner Wiles uses no string theory whatsoever in his proof.
@Dwight Turner string theory has nothing to do with his proof. In fact string theory is a physics theory... How did you even come up with that?
Greetings from the University of Saarland in Saarbrücken :)
the saarländers!
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.
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.
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.
@Gary Lewis 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.
I would love to watch a full length documentary about solved problems of modern mathematics produced by Brady.
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! :)
Lol his voice reminds me of Kermit the frog, and his head movements do a little bit too XD
hahahaha
And his name is baso ribbit
The sound frogs make
Few more days till pi day. :)
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.
@woodfur00 exactly cant eait
False. Every day is Tau Day.
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.
3:14
And would it have fit in, idunno, say, the margin of a book?
I always wondered who came up with which theories :) This was very interesting!
5:20 and a mathematician literally came around, and I say that because he was literally sitting here in this office 😂
Awesome, what a guy! I love how humble mathematicians are.
I still wanna know whether Fermat's proof for this theorem actually held up or not.
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.
Re: when you get something, as a schoolboy I suddenly 'got' differentiation and integration, when I was riding a moped at a bend in a causeway, and I nearly carried on off the road into the mud.
Watching this during math class 😎😎
You are bugging the world.
mathception
Thug life
2:10 the word "positive" is misspelled.
Ha! You're right!
@thegreatestg They misspelled maths, as well.
@James Oldfield
I see.
@David DM This channel is British, not American. We say maths here, not math.
@James Oldfield
my apologies. (in France, it is' maths' aswel, 'mathématiques')
Wonderful! I saw the Nova program on this years ago, brought back many memories. Thank you!
I LOVE THESE VIDEOS !
haha! I enjoyed the "comments" by Fermat's painting.
Great video! It's always nice and interesting to see how mathematics develops as time goes by :D Thank you so much!
27 mins!!! Yesssss
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."
23:16 what is "poised in the ballar"?
Long video! :o
I like it!
Wow, this is an amazing video!
If you had like 10 more of these, we would have an amazing minimap of Mathematics!! :D
Great interview. Really fascinating story. I highly recommend Simon Singh's book referenced above.
Proper clickbait:
"Mathematic prof. stumped by margin note!"
Abdel Armstr - 2015-03-11
I have the solution to the P - NP problem but Youtube doesn't let me post the result in the comment section
dog - 2019-04-28
NP is in P!
DILLON OLIVIERO - 2019-04-29
Problem -> No problem
Julie A. Tackett, MPH - 2019-06-10
Epsilon conjecture seems to be similar to the error term, e- sub- I which gets included in most statistical models to adjust for that which is unknown
Dwight Turner - 2019-11-15
@Subgenius -- You don't get it? Guards, take this man out and give it to him.
Timothy Morrison - 2019-12-24
Think about what type of numbers would invalidate it