Modern numerical analysis can be credibly said to begin with the 1947 paper by John von Neumann and Herman Goldstine, "Numerical Inverting of Matrices of High Order" (Bulletin of the AMS, Nov. 1947). It is one of the first papers to study rounding error and include discussion of what today is called scientific computing. Although numerical analysis has a longer and richer history, "modern" numerical analysis, as used here, is characterized by the synergy of the programmable electronic computer, mathematical analysis, and the opportunity and need to solve large and complex problems in applications. The need for advances in applications, such as ballistics prediction, neutron transport, and nonsteady, multidimensional fluid dynamics drove the development of the computer and depended strongly on advances in numerical analysis and mathematical modeling.
Modern numerical analysis and scientific computing developed quickly and on many fronts. Our current focus is on numerical linear algebra, numerical methods for differential and integral equations, methods of approximation of functions, and the impact of these developments on science and technology. Of particular current interest is the impact of mathematical software packages.