What is Fermat's Last Theorem?

Professor Sir Andrew Wiles of Oxford University has been awarded the 2016 Abel Prize - one of the highest honours in mathematics - for his proof of Fermat’s Last Theorem. But what was this famous theorem, and why did it exercise the greatest minds for more than 300 years? Marcus du Sautoy, Simonyi Professor for the Public Understanding of Science at Oxford University, explains.

[@vieuxfouvines2914]

1:26 !! that is immortality !!

[@jangofet555]

the ultimate prize isnt the opinion and praise of others, its math it self and for the love of math in you and in others, and for love.

[@Tsouki67]

OKAY BUT FFS HOW DID HE PROVE IT

[@thesimen13]

+Tsouki S. Are you willing to study every day for more than 10 years?

[@sannyver]

+Tsouki S. i leave a comment for the answer

[@oxforduniversity]

Hi +Tsouki S. It's pretty long, but if you've got the time, see if you can dig up a copy of Annals of Mathematics 142 (1995), Sir Wiles's proof is on pages 443-551. You can find it online in various places. Enjoy!

[@Tsouki67]

+University of Oxford It's alright, he said it, it's a simple and elegant proof

[@offchan]

+Tsouki S. The proof is 150 pages long.

[@ArnobAlam]

I have discovered a truly marvelous proof of this, but this youtube comments box is too narrow to contain it

[@nabeelkhan4910]

Fact :- Wiles proved what fermat said and had been working on it since he himself was of 10 years old

[@MegaMementoMori]

I don't know about you guys, but after watching a Japanese rapper make a commercial about Arabic coffee, I had this sudden urge to type Fermat's last theorem into the yt search engine and listen to some history of mathematics for a change :D

[@platostien189]

Does this apply to roots also? N√x+n√y never equals n√z????

[@rogerramjet4316]

From UPI By Eric DuVall | u pdated March 17, 2016 at 5:45 PM " Andrew Wiles, 62, was a professor at Princeton in 1994, when he and a protege, Richard Taylor, a student at the school, submitted their proof of the math problem, known in math circles for centuries." Why does not Taylor get some credit also ? The article used the word "their" proof. Why doe Wiles not acknowlede Taylors contributation?

[@MrSilki2]

amazing how this guy fails to mention integers, not any numbers

[@harrychode6935]

Genius.

[@carlorossi2788]

I solved it for n > 3

[@BogusNotions]

At 40 seconds you seem to be saying it's more difficult to prove you can't find three numbers than actually finding three. But surely Andrew Wiles has managed the former whilst later is impossible?

[@AJsarge1]

+BogusNotions For clarification, in the formula, there's a common exponent between X, Y, and Z. No matter what numbers you use for X, Y, or Z, their exponent, N is the same for all three. This is most commonly used as the Pythagorean Theorem, where the exponent N = 2. The theorem created by Fermat is that the formula can't be solved, no matter which numbers you use for X, Y, or Z, when N > 2. In order to prove Fermat's Theorem, Wiles would have had to solve the equation with every number conceivable up to infinity. I assume that this would be as impossible as trying to calculate the last digit of pi. Instead, what he did is theoretical math, where he actually found the reason why you can't solve the formula when n>2.

[@SuperYtc1]

+AJsarge No you're missing his point. He's saying if it's easier to prove something by finding three numbers then why has the opposite been proven first in this case. The answer to that is because in THIS case, proving you can't find three numbers is the only solution as it's impossible to find three integers. When we say that it's easier to prove things are possible by using an example, we mean in general, when the answer is that it is possible. If it is not possible, then it obviously wouldn't be possible to prove as it's not true.

[@TheAbd1233]

then there people like me who fail at simple maths at school

[@Awesomecutss]

who els cried. i cant believe one of my dream goals has just died. man. 350 years it would be a privilege to have broken that streak.

[@vaclav222]

Isnt that the simplest question in algebra tho i saw harder equations in calculus

[@Backseatsman84]

So you're saying Andrew Wiles was motivated by fame?

[@forinyto]

+Backseatsman84 Wiles wanted to solve that problem his whole life, from 10 years old. that bald guy is slightly delusional. I bet it's his personal dream.

[@ElFudgeMusic]

+Backseatsman84 To be fair, most scientists are motivated by fame. Who wouldn't want to write/publish an article that will be referenced to for years to come? They are driven by both scientific advancement as well as personal gain.

[@Backseatsman84]

+Nick Even if it were true that most scientists are motivated by fame, to speculate that Wiles' motivation was to win a historical brain-measuring contest detracts from the significance and beauty of his achievement.

[@Kaozorier]

+Backseatsman84 Some degree or form of fame, at least, I'm guessing. To be honest, I wouldn't mind being an unsung hero when it comes to solving this neither, especially if it's taken this long. Think fame, but to yourself, i guess? The self-induced prestige, even? Not quite sure how to aptly describe it, glory, perhaps?

[@toussi69]

+Backseatsman84 scientists and mathematicians and stuff are motivated by fame in a way but it's a different kind of fame. It's not fame in the way we traditionally think of it with hollywood and stuff. no, this is a different kind of fame that involves having your name linked to major scientific achievement and often having your discovery being named after you so it may live on as long as humans exist. That to me is a different kind of fame. However, not all are like this. There are many who turn their back on this sort of thing. Nobel prizes and other such academic achievements as well as the monetary compensation that comes with it. They see finding the solution as the prize and such.

[@charlessmyth]

Really?? From my reading of the subject, as someone who is neither a rocket scientist, nor Terrence Tao, Andrew Wiles provided a proof for the Taniyama-Shimura conjecture, which, via an argument by Gerhard Frey has been popularly presented as the léger de main of a proof for Fermat's Last Theorem.

[@avinoamatzaba9853]

A mathematical argument that only awaits refutation (it can not be proved) Green number + green number = number that is not green A green number is a natural number that has a third root . Refutation will appear if a green number is found to the left side of the equation Aetzbar

[@Nothing_serious]

Meh. I have a better proof but it's too long to type it.

[@guedemedebremartin5081]

I have a new proof of this. It is much more simple than the wiles' proof and it is general. 😮😮😮😮

[@mohmd252]

where is the solution of Fermat's last theorem????????????????

[@juckun4578]

How is it 5 square? Am I dumb

[@peterpuleo2904]

Oh, of course ! LOL !

[@azizukman]

Amazing talker on a dry subject.

[@craigs6045]

+___ ____ Dry? Dry subject? What could possibly be more interesting than the rules and precepts that govern the world we live in?

[@azizukman]

I get what your saying but be honest more people have heard of the kardishinas (however you spell it) than Fermat's last theorem or have interest in it.

[@salmansaeed4039]

1+1=3 I proved but I can't say so starting research and after 300 years it will prove some one and then u realize and I become popular 😉

[@DistortedFaiths]

The goal of this is very shallow.