Some words from Selberg

Atle Selberg, who recently died, was one of the great mathematicians of the twentieth century. His long career spanned more than half of that century. Here are some quotes from a recently published interview which took place soon before his death. These quotes may have some resonance with Math 411 students.

A quote near the beginning of the interview

Then I started to read more advanced mathematics. I discovered Störmer's lecture notes in mathematics. My father had a fairly old edition which was hand written. I often leafed through the book and I found the formula

   π       1   1   1 
   — = 1 – — + — – —  + ...
   4       3   5   7
which I thought was very strange, because I knew already what π was in connection with the circle. So I made up my mind to find out how this could be, and I began to read the book carefully from the start. It was a wonder that I did not give up because the book started with introducing the real numbers by using Dedekind cuts. I read through it and I could not comprehend what this should be good for. I thought I had a pretty clear concept of real numbers, which I thought of as decimal numbers, perhaps infinite decimals. I must say that Euler undoubtedly had a clear concept of what a real number was, so there is no reason to think that it originated with Dedekind. I could not understand the purpose or usefulness of this introduction of real numbers in Störmer's lecture notes, but I did read through it. After I had finished that section of the book the material began to be interesting to me ...

A quote at the end of the interview

Question We want to end our interview with you by asking the following question: What in your opinion is it that characterize mathematicians of high and exceptional quality?

Imagination, resourcefulness and a feeling for relations and patterns are important ingredients. It is also very important to have a whole lot of perseverance, combined with patience. Needless to say one needs a lot of energy as well. Finally, I think that quite simply some luck is part of it. Yes, some people are lucky many times, and others are lucky only one time, while some perhaps are not lucky any time. What I mean is that I have seen good ideas, even brilliant ideas, that some people have had, but which in the end did not lead anywhere. And I have also seen examples of people with ideas that did not seem good or exciting, but which strangely enough led to interesting results. I have known people that seemed to have lots of ideas and that knew a lot of mathematics, but that never obtained really exciting results. I have also met people, whom I did not consider to be particularly intelligent when I talked to them, but who came up with things, often in a clumsy and inelegant way, which turned out to lead to results of great importance. No, I dare not define what is the essence of a mathematical talent. It is too multifaceted and of such great variety.

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