For pioneering contributions to the field of nonlinear waves and its applications to a variety of areas, most notably nonlinear optics.

For pioneering contributions to continuous optimization and variational analysis.

For deep contributions to information theory.

For contributions to optimization, stochastic variational inequalities, and nonsmooth analysis.

For contributions to computational science and engineering in the areas of numerical linear algebra and high-performance computing.

For contributions to the theory, practice, and large-scale applications of multilevel solvers and for widely used parallel software.

For contributions to the design and analysis of algorithms and their use in storage systems and computational biology.

For deep and varied contributions to mathematics, especially linear algebra, matrix theory, and matrix computations.

For contributions to dynamical systems and discrete optimization and the advancement of transfer operator methods.

For foundational contribution to the theory of robust control and to spectral analysis of time series.

For innovative contributions to computational fluid mechanics and fundamental contributions to the development and teaching of the finite element methods.

For innovative contributions to mathematical modelling in cancer biology and for the advancement of underrepresented minorities in science.

For contributions to interactive parallel computing, matrix-based graph algorithms, green supercomputing, and big data.

For contributions to modeling pathogen-host interactions and host immune response in infectious diseases and training in mathematical biology/immunology.

For leadership in applied mathematics education, especially in mathematical modeling, across the entire educational spectrum.

For contributions to the numerical solution of partial differential equations and to the development of randomized algorithms for matrix computations.

For discerning analysis of fundamental problems in partial differential equations and mathematical fluid mechanics including boundary layers, transport, and mixing.

For contributions to modeling, approximation, and control design for distributed parameter systems.

For pioneering contributions to uncertainty quantification and the use of Bayesian methods in physical modeling, with applications to combustion and far beyond.

For research and mentoring contributions spanning applied and computational mathematics and developmental cell biology.

For contributions in numerical analysis, scientific computing, and modeling of porous media.

For contributions to mathematical neuroscience, mathematical biology, and dynamical systems theory.

For contributions to sparse matrix algorithms and software.

For original, broad, and fundamental contributions to applied and computational mathematics, including conservation laws, kinetics, image processing, and social dynamics.

For contributions to scalable algorithm design, mesh generation, and algorithmic game theory, and for pioneering smoothed analysis of linear programming.

For contributions to mathematical foundations of machine learning, large-scale data science, and computational imaging.

For fundamental contributions to nonlinear optimization, including algorithm design, theory, and software.

For pioneering work on traveling waves in periodic and random media and applications ranging from signal processing to finance.

*Deceased