Atle Selberg

"... It is true — certainly in mathematics; what I say now will not apply to the School of Historical Studies where people tend to make their main contributions at a much later age — in mathematics and physics, the prime period in one's life in probably over by, say, 45 or so. That's a bit conservative. Some might put it a bit earlier. Of course one can continue to work, and do very good work afterwards, but certainly the most productive period would be before that, between 25 and 45."

"I think in some sense much has to do with luck. If you are lucky many times, then you are a genius, of course. You may be lucky just a few times or some people might not have any great luck at all. I don't know really what is the reason for this. I think what lies behind having luck is first of all if you have a background that is a bit different from what everybody else has so that you are not encumbered with precisely the same knowledge and are not thinking exactly the same way. It also helps if you can benefit by accidents, facts that you come across quite accidentally and start thinking about and see there is something more. I would say that most of the better things I have done all came about not because I set out from the beginning to do them. Something shifted the focus of my attention completely and I ended up doing something rather different. One has to be able to see opportunities and learn to utilize them. Real, original work, I think, comes about in this way."

"Selberg’s work in automorphic forms and number theory led him naturally to the study of lattices (that is, discrete subgroups of finite covolume) in semi-simple Lie groups. His proof of local rigidity and, as a consequence, algebraicity of the matrix entries of cocompact lattices in groups such }}, n > 2, marked the beginnings of modern . His results were followed by proofs of local rigidity for cocompact lattices in all groups other than the familiar , where its failure reflects the well-known local deformation theory of Riemann surfaces. These results inspired to find and prove his celebrated “strong rigidity” results for such lattices in groups other than . From his work on local rigidity and algebraicity, Selberg was led to the bold conjecture that, in the higher rank situation, much more is true; namely, that all lattices are arithmetic (i.e., they can be constructed by some general arithmetic means). He was able to prove this conjecture in the simplest case of a non-cocompact irreducible lattice in the product of at least two ’s. The full Selberg arithmeticity conjecture in groups of rank at least two was established by , who introduced measure- and p-adic theoretic ideas into the problem, as well as what is now called “super-rigidity”."