Rosenberg is well known by numerical analysts, in particular by those working on numerical linear algebra, for an important theorem on the convergence of the methods of Jacobi and Gauss-Seidel for solving systems of linear equations. This paper was published in 1948 with Philip Stein (1890-1974). Although the biography of Stein is well known, that of Rosenberg was almost completely unknown. This paper presents a complete biography of Reuben Louis Rosenberg (1909-1986) with an analysis of all his scientific contributions in numerical analysis and as well as in nuclear physics. Personal information are also included. The Stein-Rosenberg theorem is commented, replaced in its historical context, and a large review of its variants, generalizations, and applications is given.