Motivated by the needs of large-scale scientific applications, Argonne’s Mathematics and Computer Science Division is developing robust, reliable, efficient numerical methods and tools; delivering them to the community as portable, high-performance software and libraries; and engaging with the scientific community to expand capabilities as needed for work toward next-generation predictive simulations and analysis. Products of our research include solvers for algorithmic differentiation, differential algebraic equations, linear and nonlinear equations, numerical optimization, variational inequalities and complementarity problems, and partial differential equations. Our open-source libraries have been recognized by R&D100 awards and Gordon Bell prizes and deployed on the world’s leading supercomputers.