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:
https://www.ams.org/journals/notices/...

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