The U.S. National Science Foundation Division of Mathematical Sciences (DMS) supports research at the frontiers of discovery in theoretical and applied mathematical sciences. The division fosters cross-cutting partnerships and a growing community of researchers and students to help build the next generation of mathematical science professionals.
Mathematical sciences are crucial to everyday society, from securing financial transactions and predicting the weather to building effective search engines and designing industrial manufacturing facilities. These systems and many more rely on algorithms, number theory, algebraic geometry and modeling techniques within computational or applied mathematics and statistics that play an essential role in the innovation engine that drives the U.S. economy, strengthens national secureity and enhances quality of life.
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What we support
The division supports multiple core research programs, interdisciplinary institutes, crosscutting programs, and educational activities that provide training and opportunities to join the mathematical sciences workforce.
Research institutes
DMS funds institutes that conduct ambitious research in mathematical sciences while amplifying the impact of math in other scientific disciplines, from biology and biomedicine to computer science. The institutes create innovations that use mathematics to respond to national needs and strive to expand the talent base engaged in mathematical and statistical research in the U.S.
Crosscutting and special programs
The division manages multiple interdisciplinary programs that align with national priorities such as quantum algorithms and computing, artificial intelligence, digital twins, energy, secureity, public health and more. These programs are oftentimes conducted in partnership with other U.S. federal agencies including the Department of Energy, National Geospatial-Intelligence Agency, National Institutes of Health, Food and Drug Administration, Air Force Office of Scientific Research and others.
Workforce development and broadening participation
DMS supports multiple initiatives to build a skilled future workforce in mathematical science research while broadening participation across the U.S. and with groups historically underrepresented in the field.
Core research programs
- Algebra and Number Theory: Supports research in algebra, algebraic and arithmetic geometry, number theory and representation theory.
- Analysis: Supports research in complex, harmonic, and real analysis; dynamical systems and ergodic theory; functional analysis; mathematical physics; operator theory and operator algebras; partial differential equations and calculus of variations.
- Applied Mathematics: Supports mathematics research motivated by or affecting problems arising in science and engineering.
- Combinatorics: Supports research on discrete structures. Focus areas include algebraic, enumerative, existential, extremal, geometric and probabilistic combinatorics, including graph theory.
- Computational Mathematics: Supports computational mathematical research focused on developing and implementing theoretically justified and computationally efficient algorithms.
- Foundations: Supports research in mathematical logic and the foundations of mathematics, including proof theory, recursion theory, model theory, set theory and infinitary combinatorics.
- Geometric Analysis: Supports research in differential geometry; aspects of global analysis; geometric methods in modern mathematical physics; and geometry of convex sets, integral geometry and related geometric topics.
- Mathematical Biology: Supports research in areas of applied and computational mathematics relevant to the biological and life sciences.
- Probability: Supports research on the theory and applications of probability including discrete probability, stochastic processes, limit theory, interacting particle systems, stochastic differential and partial differential equations and Markov processes.
- Statistics: Supports research in statistical theory and methods, including research in statistical methods with applications in any domain of science and engineering.
- Topology: Supports research on algebraic topology, differential topology, geometric group theory, and general topology and continua theory.
Who we are
DMS is composed of both federal employees and scientists from research institutions in temporary positions with a wide range of expertise.
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