"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”."