change. Because of their extensive role in teaching service courses, the mathematical sciences will be disproportionately affected by these changes.
These conclusions were reached by the Committee on the Mathematical Sciences in 2025 of the National Research Council (NRC), which conducted the study that led to this report. The study was commissioned by the Division of Mathematical Sciences (DMS) of the National Science Foundation (NSF). DMS is the primary federal office that supports mathematical sciences research and the health of the mathematical sciences community. In recent years, it has provided nearly 45 percent of federal funding for mathematical sciences research and the large majority of support for research in the core areas of the discipline. Other major federal funders of the mathematical sciences include the Department of Defense, the Department of Energy, and the National Institutes of Health. Details of federal funding are given in Appendix C.
While the mathematical sciences community and its sponsors regularly hold meetings and workshops to explore emerging research areas and assess progress in more mature areas, there has been no comprehensive strategic study of the discipline since the so-called Odom study1 in the late 1990s. During 2008, DMS Director Peter March, with encouragement from the NSF associate director for mathematical and physical sciences, Tony Chan, worked with the NRC’s Board on Mathematical Sciences and Their Applications (BMSA) to define the goals of a new strategic study of the discipline.
For the study that produced this report, DMS and BMSA chose a time horizon of 2025. It was felt that a strategic assessment of the mathematical sciences needed a target date and that the date should be sufficiently far in the future to enable thinking about changes that might correspond to a generational shift. Such changes might, for example, depend on changes in graduate education that may not yet be implemented.
The specific charge for this study reads as follows:
The study will produce a forward-looking assessment of the current state of the mathematical sciences and of emerging trends that will affect the discipline and its stakeholders as they look ahead to the quarter-century mark. Specifically, the study will assess:
—The vitality of research in the mathematical sciences, looking at such aspects as the unity and coherence of research, significance of recent developments, rate of progress at the frontiers, and emerging trends;
—The impact of research and training in the mathematical sciences on science and engineering; on industry and technology; on innovation and economic competitiveness; on national security; and other areas of national interest.
1 National Science Foundation, 1998, Report of the Senior Assessment Panel for the International Assessment of the U.S. Mathematical Sciences. NSF, Arlington, Va.