Interview conducted and edited by Wylder Green of the HLFF Communications Team.
How did you become aware of the Heidelberg Laureate Forum?
I heard of your initiative first from my colleagues in Norway and was of course aware of the analogous Nobel activity.
With your career already firmly established, was receiving the Abel Prize expected?
I have through the years served on so many prize committees that I well understand how many good candidates exist and how many different points of view. There are exceptional situations with obvious candidates but not often. For these reasons a prize is always a surprise and that was certainly the case for my Abel Prize.
What drives you?
I now use my remaining time to think about mathematical problems that are too hard to be cost efficient, i.e. where the chances of success are very small.
Was there a specific point in your life that led you to pursue a career in mathematics?
I was a slow starter in mathematical research. My family had no academic tradition but I was early interested in problem solving. At the University of Uppsala I was lucky to find a professor who was a world leading analyst, Arne Beurling. He is well known in the computer science community for his reconstruction (based on authentic telegrams) in 1940 of the German Geheimfernschreiber. I spent my first 10 years at Uppsala solving not very significant problems and reading papers in journals often way outside my own field. This possibility is now being lost when you get your information on a computer screen. In my opinion we should keep a certain number of general printed journals and these should be read widely. Too much specialization is an obvious danger today. The difference between problem solving and creation of new mathematics became only slowly clear to me. When you are young it all may seem so easy because you ask conventional questions.
Where are your sights set now? Where do you expect the next breakthrough in mathematics to occur?
Mathematics becomes everywhere more important for modern society and is an area with no language barriers. The prospects for the future therefore seem excellent. You can think of it as the machine that drives society. A factory needs engineers and inventors and similarly we need also so called pure mathematicians who analyze the structure of the mathematical fabric. So nobody should hesitate to study mathematics for its own sake.
If you are not prepared to spend a long time (years) on the same question you will never achieve anything deep. But at some point you must throw in the towel.
What advice would have helped you as a young researcher?
You ask me what advice from my teacher Arne Beurling would have helped me and what I can pass on to a new generation. Probably he gave good advice that I immediately forgot or ignored as is natural when you are young. Let me nevertheless volunteer two general ones.
When you work on a problem be persistent but be prepared to give up (perhaps to come back later). The balance between these two opposite attitudes is crucial for a successful mathematician. If you are not prepared to spend a long time (years) on the same question you will never achieve anything deep. But at some point you must throw in the towel.
My second point is: spend much time on trying to produce counterexamples to your proposed statement. To achieve victory you should know your enemy. Counterexamples are much less attractive than theorems but looking for them is always very helpful (especially if they exist).