Andrew Wiles - The Abel Prize interview 2016

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:

Andrew Wiles is interviewed by the two mathematicians Martin Raussen og Christian Skau. Produced by UniMedia.

[DouglasHPlumb]

He is really one of the best examples for all of us in terms of the sheer value of determination.

[emanuelbranco]

Brilliant mind. Simple, humble and amazing. A privilege to watch this interview.

[harveyshirleyrose]

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! :)

[jamesmaxwell]

What a likeable, pleasant, and humble man! I wish him lots of happiness in his future life.

[tensevo]

Inspiring interview.
Hard problems are hard, precisely because we are not even sure we can ever solve them.

[hwe]

A wonderful personality, extreme persistence, very humble, a man of the 1st class human being.

[kennethflorek]

I got to see the real Andrew Wiles. Not people talking about him or him giving a talk.

[philipchief]

few men can live along with history, without fading. only the GOATS!

Professor Andrew is surely among them.

[corkkyle]

What a humble and brilliant human. Fascinating.

[teddy]

I have no clue what these brilliant minds are saying, but it is pleasantly beautiful to behold this intercourse of knowledge

[NihilistGhost]

Beautiful faces are everywhere but beautiful mind are hard to find.

[flateric]

Didn't understand ANYTHING but fascinating to watch a genius at work...

[jfjsas]

He seems like such a wise and nice gentleman

[SanderBessels]

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.

[tariqrashid]

really nice (and informative) interview with a very humble man

[siddhantritwick]

Fantastic interview ! Kudos to the interviewers. Mr. Wiles is such a great man.

[jfndfiunskj]

I get the impression this guy knows what he's talking about.

[maxdominate]

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.

[PopeLando]

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!

[ModerateObserver]

"...which this margin is too narrow to contain." The greatest troll in human history 😆