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/201703/rnoti-p197.pdf Andrew Wiles is interviewed by the two mathematicians Martin Raussen og Christian Skau. Produced by UniMedia.