For contributions in numerical linear algebra and its applications.

For contributions to dynamics, voting, and economics.

For pioneering contributions to parallel algorithms for numerical linear algebra.

For contributions to applied dynamical systems involving the computational and analytical study of pattern formation in physical and biological systems.

For contributions to the mathematics of inverse problems and for advancing the application of mathematics in industry.

For contributions to numerical ordinary differential equations and geometric integration.

For contributions to both theory and practice in the fields of image processing and computer vision.

For contributions to numerical optimization, linear algebra, and software.

For outstanding research in algorithms of discrete mathematics and in computer science applications, alongside exemplary service to mathematics.

For contributions to applied dynamical systems and the study of pattern formation.

For contributions to integration, optimization, and modeling techniques for the study of biomolecular structure and function.

For contributions to numerical optimization.

For contributions to parallel and high performance computing, and algorithms for matrix computations.

For contributions to combinatorial optimization.

For contributions to the theory and applications of spline functions, geometric design and finite elements.

For contributions to the theory and computational methods for partial differential equations.

For contributions to finite element methods and scientific computing.

For contributions to nonlinear control theory and nonlinear optimization.

For contributions in optimal control applied to the management sciences and economics.

For contributions to the numerical solution of partial differential equations, especially level set methods.

For contributions to solution methods for multiphysics systems, scalable parallel numerical algorithms, and numerical methods for strongly coupled nonlinear partial differential equations.

For contributions to dynamics and biology.

For contributions to the development of mimetic finite difference methods for nonlinear systems of partial differential equations.

For the analysis of vortices and flows.

For contributions to approximation theory, wavelet theory, and image processing.

Arthur Sherman has made fundamental discoveries using mathematics in physiology and has trained a generation of successful biomathematicians.

For contributions to the design, analysis, and application of efficient discrete optimization algorithms in scheduling, facility location, networks, and sustainability.

For the development of optimization algorithms for groundwater flow and related environmental problems.

For contributions to the numerical solution of partial differential equations including discontinuous Galerkin methods.

For contributions to the analysis of bifurcations in the presence of symmetry.

For contributions to parallel computing and computational science.

For contributions to numerical linear algebra.

For contributions to fluid dynamics, combustion theory, and their applications to propulsion.

For contributions to computational molecular biophysics and to numerical ordinary differential equations and linear algebra.

For advances in quadrature, integral equations, and approximation of functions.

For contributions to domain decomposition, developing the powerful software package PETSc, and simulating complex scientific and engineering phenomena on massively parallel architectures.

For his contributions to uncertainty quantification and materials science.

For the development of new methods in computational combustion and their application to problems involving hydrocarbon chemistry.

For foundational contributions to the numerical solution of polynomial systems and applications of algebraic geometry.

For contributions to the theory of stochastic optimal control, viscosity solutions and mathematical finance.

For contributions to control theory and mathematical biology.

For contributions to numerical linear algebra, optimization, and model reduction.

For contributions to the theory and numerical solution of both deterministic and stochastic partial differential equations and their applications.

For contributions to discrete mathematics and theory of computing, particularly random graphs and networks, Ramsey theory, logic, and randomized algorithms.

For the study of linear and nonlinear partial differential equations.

For contributions to the theory and analysis of delayed dynamical systems and their applications.

For contributions to numerical linear algebra.

For advances in numerical linear algebra, especially iterative methods.

For contributions to finite elements and wavelets as well as influential textbooks in applied and numerical mathematics.

For investigations of nonlinear waves.

For investigations of small-world networks and coupled oscillators and for outstanding science communication.

For contributions to deterministic and stochastic dynamical computations.

For wide-ranging contributions to fluid mechanics.

For advancing symbolic and numerical techniques for solving systems of nonlinear polynomial equations and inequalities and connecting computational algebraic geometry with applications.

For contributions to nonlinear control, especially in the area of differential-geometric control theory.

For contributions to nonlinear dynamics, particularly through his experimental work.

For geophysical computations and inverse problems.

For contributions to numerical algebra and matrix theory.

For contributions to the numerical analysis of partial differential equations.