Andrew Wiles - The Abel Prize interview 2016
ฝัง
- เผยแพร่เมื่อ 13 มิ.ย. 2024
- 0:35 The history behind Wiles’ proof of Fermat’s last theorem
1:08 An historical account of Fermat’s last theorem by Dundas
2:40 Wiles takes us through the first attempts to solve the theorem
5:33 Kummer’s new number systems
8:30 Lamé, Kummer and Fermat’s theorem
9:10 Wiles tried to solve the theorem as a teenager
10:05 André Weil and number theory
11:09 When did Wiles’ interest for mathematics start?
13:36 Wiles in high school
14:35 Algebra and number theory were Wiles’ favorite topics to study
15:30 Cambridge years with John Coates
17:18 The elliptic curves would lead to the solution of the theorem, but he did not know it yet
17:58 Elliptic curves in number theory
20:54 Birch, Swinnerton-Dyer, Tate-Shafarevich, Selmer
22:05 Coates proposed studying the Birch and Swinnerton-Dyer conjunctures
23:34 When will we solve the Birch and Swinnerton-Dyer conjunctures?
24:40 The Selmer group
29:03 The Modularity Conjecture
33:14 Taniyama
35:17 There can’t be a solution to the Fermat problem
35:25 Dundas summarizing the next steps
37:51 Working with a time-consuming puzzle and having to stop
40:50 Describing the search for proof as a metaphor
43:35 Iwasawa theory
45:25 Parallels to Abel’s work
50:16 Work style
55:05 Problems in mathematics and how to work with them
57:00 On intuition
58:00 On not getting too close to mathematics
Interview in written. Notices of the American Mathematical Society:
www.ams.org/journals/notices/...
Andrew Wiles is interviewed by the two mathematicians Martin Raussen og Christian Skau. Produced by UniMedia. - วิทยาศาสตร์และเทคโนโลยี
He is really one of the best examples for all of us in terms of the sheer value of determination.
Brilliant mind. Simple, humble and amazing. A privilege to watch this interview.
Simple? His proof for Fermat's last theorem was 300 pages long. Fermat's proof took just more than the margin of his book.
I think he is referring to Wiles' simplicity, not his proof
darkmath100 read the comment a little more carefully.
And the same smile he had as an undergraduate!
@@darkmath100 Fermat never had a proof lol. He went on later in his life to try to prove specific cases of it, which wouldn't make sense if he had a proof. It's generally accepted he was mistaken.
I know this was five years ago but to me is still academically relevant as ever. I just want to say congratulations to Mr Andrew Wiles. Your achievements truly show your passionate love and dedication for both physics and overall mathematics, especially in solving numerous challenging problems. I have nothing to say accept that I think your prize is well deserved, well done! :)
Inspiring interview.
Hard problems are hard, precisely because we are not even sure we can ever solve them.
Didn't understand ANYTHING but fascinating to watch a genius at work...
What a likeable, pleasant, and humble man! I wish him lots of happiness in his future life.
It's only been 4 weeks, I'll come back and see if there's any. Thank you.
I got to see the real Andrew Wiles. Not people talking about him or him giving a talk.
Beautiful faces are everywhere but beautiful mind are hard to find.
indeed
True
did you just call him ugly?
There's nothing wrong about being attractive
@@user-nb3mq3cg8kno but it’s not everything which is what society has labeled as most desirable instead of having a beautiful mind, but I wouldn’t expect you to actually care after all you only pointed out the most simple facet of their opinion
A wonderful personality, extreme persistence, very humble, a man of the 1st class human being.
@@_batman_Fan_Yes, I'll second that, well said. His demeanor is lovely.
few men can live along with history, without fading. only the GOATS!
Professor Andrew is surely among them.
What a humble and brilliant human. Fascinating.
What an incredible man
I have no clue what these brilliant minds are saying, but it is pleasantly beautiful to behold this intercourse of knowledge
They might as well be three wizards. But magic is pretty cool even if I can’t cast spells so…
He seems like such a wise and nice gentleman
Brilliant interview - Thanks!
Wonderful in every demand.
Great interview. Thank you everyone.
Wow, he's simply amazing!!!
really nice (and informative) interview with a very humble man
Nice interview to the great A Wiles.
Fantastic interview ! Kudos to the interviewers. Mr. Wiles is such a great man.
I feel I need to correct a small “error” in the presentation of mathematical history: the unsolvability of the quintic was first solved by Ruffini, an Italian doctor, who wrote a book about it and sent it to Cauchy. He was however completely ignored by the mathematical community. He even wrote a simplified proof, thinking his arguments might be too difficult to follow and begged others to say I if he was perhaps wrong in on some way, or if it was otherwise irrelevant. No response.
Only on his deathbed, Cauchy wrote Ruffini a note saying he always thought his work was worthy enough to get more attention. So Cauchy certainly read it and it must have influenced his own work, but he and others at that time certainly didn’t realise the importance of symmetry groups related to polynomials, the way Ruffini, Abel and later Galois did.
Abel discovered a proof independently and was very proud of it and used it to prove his mathematical skills when he traveled to Europe. Gauss however was not very impressed and also never realised the importance of symmetry groups.
So, some more recognition has to go to Ruffini, who is still pretty unknown, but he definitely was the first to prove the unsolvability of the quintic.
Nice catch
truly an inspiration! that is for sure!
Wonderful! thanks...
what a wonderful human being........
What a delight!
Great and brilliant,humble as the greatest minds of human kind,like Carl Sagan!!! Beers from Uruguay!!! Thanks for your dedication and knowledge!!!
I just placed "An Introduction to the Theory of Numbers" by G.H. Hardy & Edward M. Wright mentioned by Dr. Wiles in my Amazon wish list. I'll be buying this book next pay day. The table of contents is quite breathtaking.
Did you actually buy it?
Wonderful
how passionate andrew wiles is indeed 🥳🥳🥳🥳🥳
What a delight.
Weird that Sir Andrew is the youngest winner of the Abel Prize, since when he solved the Modularity Conjecture he was already too old to win the Fields Medal for it!
he solved a special case of MC.
It says moore about the Fields.
Love this guy (Wiles); very interesting conversation.
The squirrel metaphor towards the end is simply great...
Few people who show great interest in their own work.
They should show this to students so they can see the beauty in math
I think I understand the feeling of "starstruck" now.
Amazing Wiles! Good pupil, continue like this ...
An awesome mathematician...!
WOW Harrison Ford is such a good interviewer!
I get the impression this guy knows what he's talking about.
I can't say if you're joking.
Brilliant mathematician, great interview and nice ASMR!!
He is currently very close to cracking Swinnerton-Dyer.
51:11 Intuition of final insight
Wat u mean
I have Fermats last theorem simple proof by my point of view. How do I publish it.
I have no idea what he is saying but it sounds so intellectual that I know it is important.
40:40 - "ahhh"
"We're gonna need a bigger margin!", Fermat.
確率論は中心極限定理までを定理の発表までに勉強しようと考えてます。
Pleased to know even if no progress was made on flt before Wiles, at Turing was there
What is the name of the German mathematician cited by Wiles that analysed?
Kummer
Gerhardt Frie?
Just curious, how many other papers has Wiles published?
Many, including many papers that are landmark in number theory, including the proof of main conjecture in Iwasawa theory. He was legendary among the professionals even before the proof of Fermat's last theorem.
Yes Andrew Wiles is a perfect gentleman - one of England's best - but of course he left the UK, because in the UK we do not respect Mathematicians, Scientists and Engineers, and they have poor status and pay. Not so in the USA and that is why the USA leads. When he was 10, he was naturally attracted to the Maths section in the local library. He just liked it. When I was 10, I was likewise attracted to books on Radio and Electronics. I just liked it too. Many thanks for this interview and at last Andrew has been raised to a knight.
7/19から1週間以内に発表されなかったら発表はしばらく先だと考えてます。
LOL we all suck at math, it's just that some people have greater patience because they enjoy it more.
That's my opnion.
The harder the problem, the longer the time needed thinking about it.
So the top math men are the men who are obsessed with it like Erdos, Wiles, etc...
Whereas some people enjoy it but enjoy it less.
22 years of delay for Abel's!, and we complain about politics, laws and justice being slow.
but what are the non trivial zeroes of the Riemann Zeta function?
Trivial problem, easy to solve.
-2 -4 -6 etc ; try googling 'trivial zeros' - it's quite a trivial thing to do!
@@lsbrother "non trivial" he wrote!
12月29日までに定理が発表されると考えてます。
I don't fully understand Japanese
"...which this margin is too narrow to contain." The greatest troll in human history 😆
Who would you rather spend time with, Andrew Wiles or Richard Feynman?
Wiles any day, Feynman could give a masterclass in arrogance.
7/19に発表されると考えてます。
질문하나를 2분40초동안 하네요 ㅎㄷㄷ
Thank YOu to ERIC TEMPLE BELL for having given , with his books ,a motivation to the genius of ANDREW WILES.
Why is John Major interviewing Andrew Wiles?😂
brilliant mind, but hard work is the prerequisite for success
Five degree equation is not algebraic solution. =3
❤❤❤❤❤❤❤❤
太强了
❤❤❤❤❤❤❤❤❤❤❤❤
what does curves has to do with whole numbers? please explain so a non mathdude can understand how that is related to the problem?
the curve is a set of points, the points are expressed as (x,y) coordinates so those curves describe the solution of an equation which relate x and y. In this case we look for solutions to the equation as numbers (integer, rational .. etc) and when we draw them in a cartizian space we obtain curves.
curves are on graphs, graphs are two perpendicular lines with whole numbers on them, x squared + y sqquared = r squared is fermats last theorem but is also a curve (a circle) on a graph, wiles used elliptic curves (similar to circles) to prove it
I think I'll stick with the Mr Men books and ABBA.
I have read the demanding book 'Exploring The Earth and Moon' by Patrick Moore and found out it was for a juvenile audience.
I failed GCE English from college with a D Grade in 1999 aged 24.
Does he have to talk like such a puff?!
If you have numbers a and b, you can MAKE the curve y^2 = x(x-a)(x-b) Frey proposed this way to get an elliptic curve from the supposed solution of the Fermat's problem
@ไพบูลย์ นิติตะวัน
professor wiles, number theory!
A Graphical interface expert like Grant at 3BLUE 1BROWN could easily understand how and why the picture-plane containment of logarithmic 2-ness has 2X cofactors and 2-² Tangency Space.., but this is another language required to claim "proof-disproof" of the Conjecture, the Conformal Field Condensation Correspondence of Quantum-fields in/of Logarithmic QM-TIME Completeness cause-effect Actuality. (That's why Dr Wiles gets prizes?)
Do Elliptic Curvatures correlate with logarithmic-interference?
Eg observation of the Unit Circle bubble-mode set in inclusion-exclusion log-antilog interference of the full spectrum of 1-0-infinity modulo-radial-resonance cofactors in Perspective=> Feynman type Diagrams of vertices in vortices nodal-vibrational resonance bonding.
Line-of-sight re-cognition resonance superposition identification assumes parallel coexistence i-reflection containment by default.., so all descriptions all-ways all-at-once in/of sync-duration bubble-mode coordination becomes a complex "narrative statement" containment of/by Binocular Optics in generalised Singularity-point positioning. Simple not easy.
Logarithmic Time Duration Timing Conception is i-reflection harmonic inclusion-exclusion function-spelling => instantaneous trancendental 2-²-ness spatial distances in ONE-INFINITY word-picture.
Ie Conception Totality is self-defining but not necessarily comprehensible by Flashed e-Pi-i sync-duration recognition.
A blend of meditation, memory associations and intuitive conscience are everyone's life worth.
"The somehow does this for us".
Logarithmic Time Duration Timing Modulation Mechanism at Singularity, is inside-outside local self in/of Self-defining holography, In-form-ation of memory association information.
Typical real boffin lol, his achievement was incredible it is good to see him finally rewarded {and he is British lol}
friends, there is a solution to Format's last theorem we canot disagree yes the process to get that 4 exact numbers are in the way. God is the greatest mathematician and nature is His mathematical expression
Bhai ye wiles apna krish kyo lg rha hai koi mil gya me
20 år etter at han løste et 400 år gammelt matematisk problem ved og også løse et ca. 50år gammelt problem (modularity conjecture), fikk han Abelprisen. Visste ikke Abelkomiteen om dette da det skjedde???
Bedre sent en aldri i guess
Jo da, les komiteens begrunnelse her: www.abelprize.no/c67107/binfil/download.php?tid=67059
I am happy i am learning norwegian and i understood your comment
Wisdom is alive at mathematics in south korea
No
Andrew wiles
一橋大学に定理を送るのはまだ3週間早いと考えてます。
the youngest ?!
Check out fields medal for more "young people"
The Abel Prize is a rather recent award and it has been awarded mostly to mathematicians in their 70s, or even 80s. You could say it's kinda more of a career prize, a lifetime achievement award.
Wiles was 62 when he was awarded the Abel Prize, in 2016.
USE THE CODE TO SOLVE FERMAT Always be correct (x^1/a+y^1/a)^na=(z^1/a+x^1//a+y^1/a - z^1/a)^na. Call d=x^1/a+y^1/a - z^1/a =>(x^1/a+y^1/a)^na=(z^1/a+d)^na. They are composed of two groups One group contains x^n,y^n and z^n and the other contains all irrational numbers. z^n=x^n+y^n. Impossible!
宇宙空間から太陽光より強いエネルギーを持つ光を連続に1点に集中して当てたら金縛りが出来ます。
the latin sound like german, is that what latin sounded like?
Latin with a Norwegian accent. If a non-English speaker heard the two interviewers speaking English, they would likely think it was Norwegian. Of course, it isn't.
i dont think so
as a german who learned latin: yes it is!
@@soyokou.2810 I believe that's a Danish accent.
@@Andreas4696 I believe both interviewers reside in Norway, though I guess that's not unfeasible.
27:05 I see, I see... loll
He has a PhD in mathematics, so he's not just some random journalist.
Lord Byron. 🤓🤓
Godel expresses wff's in odd numbers
every number is prime relative to its own base n = n(n/n)=n(1_n) (primes do not include division by other numbers)
Goldbach's Conjecture "every even number is the sum of two primes" n + n = 2n
Godel's expression does not include even numbers in his defintion of wff's - they are therefore "undecidable"
(o + e) = o is always odd so is undecidable because of the existence of even numbers (e+e) = e
(o and e are sets of numbers).
Proof of Fermat"s Theorem for Village Idiots
c = a + b
c^n = [a^n + b^n] + f(a,b,n) (Binomial Expansion)
c^n = a^n + b^n iff f(a,b,n) = 0
f(a,b,n) 0
c^n a^n + b^n QED
Pythgoras is wrong, Fermat is correct even for n = 2. Someone go tell the physicists (Especially Einstein and Pauli)
and also for multinomials (tell the cosmetologists..)
(Hint: Wiles had to use modular functions, which are only defined on the positive half of the complex plane.)
there are no negative numbers: -c= a-b, b>a iff b-c=a, a >0, a-a = 0, a=a
if there are no negative numbers, there are no square roots of negative numbers. The ""complex" plane is affine to the real plane (1^2 1, sqr(1^2) = 1 2qr(1) (Russsell's Paradox; a number can't both multiply and not multiply itself).
more on this on the physicsdiscussionforum (dot org)
Wow maths in interesting, if only it wasn't too much hard work and technical grunt...
If Wiles had hired a PR agency he would have won more awards and sooner than when he did win. Fortunately, I'm not into awards.
So is this guy smarter than Fermet then since he couldn't prove his own equation?!
It doesn't have much to do with being more or less smart. Fermat back then didn't have the mathematical tools to solve it, and he didn't devote THAT much attention to it anyways.
but, does he know what are sine and cosine ?
Stop going off on a tangent.
That's beside the point...
I don't believe Fermet lied about his proof, for he would have put his reputation at stake if confronted about the proof.
I am an amateur mathematics hoppyist myself. There are many techniques I use for solving problems. There is one technique (much different from my usual techniques) I use for creating integrals, but I can only apply it to quadratic form, for now. It is very clever (marvelous) and if asked about it, I can produce an example.
Obviously, the work Andrew Wiles did is great and required extreme affort. Fermet's approach may have been more direct, something totally different from his usual techniques.
Fermat never claimed that no one ELSE could ever prove his conjecture. He only said it was too inconvenient for him at the time to spell out the details of HIS proof. His reputation as a brilliant amateur mathematician would remain intact either way. If someone during Fermat's lifetime proved Fermat's claim , it would simply confirm the veracity of it. If no one , on the other hand , ever found a proof it would remain an unsolved mystery . During Fermat's life , he teased professional math experts by sending them problems that seemed intractable , then humiliated them by showing the actual solution. I think it's possible he strongly SUSPECTED there's no solution for N3 or greater and let everybody else go crazy trying in vain to find it. Andrew Wiles has such a gift, that i think he could discover a true pathway , however circuitous , to connect any two exotic dots however far removed from one another. He's a facinating man and his peaceful demeanor is the PROOF of his wisdom. He must be a wonderful parent too.
I agree with your idea that Fermat possibly had a very DIRECT demonstration of the proof - something fundamentally true for the case N2 set , to make it unique from all the others N3 & higher-- some subtle piece of logic commonly ground underfoot and ignored but right there all the time.
Fermat's last theorem is a fact.
Fermat's did not claim that there are no whole solutions to equation.
Fermat's claim that are no solutions to the equation in whole numbers.
You better call it "Wiles' Theorem".
For / according to Fermat it was just a "conjecture" (hypothesis)
@@scp3178 th-cam.com/video/nChQtxftPQw/w-d-xo.html
You wrong
meet the equations of yehuda bitton's.
Giant
INTELLECTUAL
I like to believe that somehow this problem can be solved in a simpler, more elegant way. I have huge respect for these brilliant mathematicians and their advanced techniques, but why shouldn't there be an easier way? After all, Fermat was a great mind too, and in his comprehension of mathematics perhaps he did understand a means to solve the problem in his own way. Either that, or he a liar or he is wrong
Fermat was indeed brilliant but almost certainly wrong. Elements of Wiles's proof have been simplified but not to the extent that methods available to Fermat are known to be sufficient to construct a proof. Entire branches of mathematics have grown from failed attempts to solve it. Lame proposed a proof that failed because he assumed unique factorization in extended rings of integers where the property doesn't hold. This led to the theory of ideals in rings which recovers something of unique factorization....but not a proof of Fermat.
There is actually enormous elegance in Wile's proof. FLT falls out not as a result of using a sledgehammer to crack a nut but because Wiles proved a hugely more general result- the modularity theorem.
Feel free to have a go! if you can you will become extremely famous and I'm sure Andrew Wiles would be among the first to congratulate you.
@@mcmanustony There is no way you could assume that he was almost certainly wrong. Unless you yourself know all of maths. There are new relationships being constantly formed between previously considered disparate areas of maths. The idea that Wiles' proof cannot be simplified, is also a vast assumption.
@@reachforthesky1576 I didn't assume. I concluded- that there is only a very small possibility that Fermat had a correct proof. There is no known pathway from the mathematics of Fermat's time to a proof of FLT. There are also several plausible looking arguments from before during and after Fermat, any one of which could have been the guts of his lost "proof", that are nonetheless erroneous.
"The idea that Wiles' proof cannot be simplified, is also a vast assumption."- I made no such assumption. Where do you think I did? I also KNOW that not only COULD Wiles proof of FLT be simplified- it HAS BEEN simplified.
@@mcmanustony I would love to see the working behind such a conclusion.
Only Fermat-Murgu Impossible Equations ca CERTIFY - FERMAT'S LAST THEORE AND ALREADY DID IT #EARTHPROUDDAY
3 up one down four up one down five up two down. ..
三角平方和
Cwwhoaa! Bit math-y this fella, int'it?
Maff iz rayshish