0:07 The Index Theorem - the history
2:16 Both of you contributed to the index theorem with different expertise and visions. Could you describe this collaboration and the establishment of the result a little closer?
5:37 You worked out at least three different proofs with different strategies for the Index Theorem. Why did you keep on after the first proof? What different insights did the proofs give?
7:36 The role of collaboration in mathematics
10:46 The interplay between physics and mathematics
18:16 Has the mathematical problems solved and the techniques that arose from physics been the lifeblood of mathematics in the past; or at least for the last 25 years?
20:43 Can we move to newer developments with impact from the Atiyah-Singer Index Theorem? I.e., String Theory and Edward Witten on the one hand and on the other hand Non-commutative Geometry represented by Alain Connes. Could you describe the approaches to mathematical physics epitomized by these two protagonists?
27:22 Which mathematical areas will witness the most important developments in the coming years?
32:42 Mathematics has become so specialized, that one may fear that the subject will break up into separate areas. Is there a core holding things together?
37:46 On the continuity of mathematics. Rephrasing slightly a question that you, Prof. Atiyah are the origin of, let us make the following gedanken experiment: If, say, Newton or Gauss or Abel were to reappear in our midst, do you think they would understand the problems being tackled by the present generation of mathematicians - after they had been given a short refresher course? Or is present day mathematics too far removed from traditional mathematics?
40:17 Communication of mathematics
43:58 Could you tell us how you work best, how do new ideas arrive?
48:40 Is mathematics a young man’s game?
52:50 Prof. Atiyah, you have been very much involved in the establishment of the European Mathematical Society around 1990. Are you satisfied with its development since then?
55:43 Interests beside mathematics
The interview exists in written, published in Notices, published by the European Mathematical Society: www.emis.de/newsletter/curren...
The Abel Prize Interview 2004 with Isadore Singer and Sir Michael Atiyah.
Interviewed by mathematicians Martin Raussen og Christian Skau.
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