| Mathematical Sciences in
the FY 2005 Budget
Samuel M. Rankin III,
- Federal support for the mathematical sciences is slated to grow from an estimated $362.41 million in FY 2004 to an estimated $374.45 million in FY 2005, an increase of 3.3 percent. This rate of increase is less than half of the rate of increase from FY 2003 to FY 2004.
- The National Science Foundation's (NSF) Division of Mathematical Sciences (DMS) would receive only a 0.9 percent increase to $202.25 million in FY 2005 from an estimated $200.41 million in FY 2004.
- The Defense Advanced Project Agency (DARPA), a Department of Defense (DOD) agency, would grow by 7 percent while the Army Research Office (ARO) mathematical sciences budget would increase by 5.3 percent. The National Security Agency (NSA) budget, although small compared to other DOD agencies, would grow by 16.7 percent.
- The Department of Energy (DOE) Applied Mathematics division would receive a 29.6 percent increase, the largest percentage jump of all the agency budgets for the mathematical sciences.
The mathematical sciences are funded through the National Science Foundation, the Department of Defense (including the NSA), the Department of Energy, and the National Institutes of Health (NIH). In 2005, the majority of support for the mathematical sciences from all these agencies would come from NSF, contributing 54 percent of the total. DOD accounts for 21.3 percent of the total, with the NIH supplying 16.9 percent, and the DOE 7.8 percent. NSF accounts for the majority of the support for academic research in the mathematical sciences and is the only agency that supports mathematics research broadly across all fields. DOD, DOE, and NIH support research in the mathematical sciences that contributes to the research and development missions of these agencies.
Several other agencies have small amounts of funding for mathematics research as it relates to agency missions, including the Environmental Protection Agency, the National Aeronautics and Space Administration (NASA), and the National Institute of Standards and Technology.
Table 1. Federal Funding for the Mathematical Sciences (millions of dollars) #
* This figure is estimated based on language in the FY 2004 omnibus appropriations bill (Public Law 108-199).
** Estimates based on conversation with program manager. The NIGMS FY 05 number is the author's best guess based on a conversation with an NIGMS representative last year.
# Budget information from agency documents and conversations with program managers. DOD FY 2004 and FY 2005 figures are estimates.
TRENDS IN FEDERAL SUPPORT FOR THE MATHEMATICAL SCIENCES
The FY 2005 estimated aggregate spending for mathematical sciences research
and related activities would be $374.45 million, a potential increase
of 3.3 percent over FY 2004. The increase for the NSF would be the lowest
in several years, severely impacting the overall federal support for the
mathematical sciences. The increase at DOE for FY 2005 would be a healthy
29.6 percent increase over the FY 2004 level. Other pleasant surprises
would be the 7 percent increase at DARPA, the 5.3 percent increase at
ARO, and the 16.7 percent increase at NSA.
The mathematical sciences are making major contributions to the country's intellectual capacity and the need for the mathematical sciences in scientific discovery and technological innovation is accelerating. Yet, many mathematical scientists performing excellent research and who submit grant proposals deemed of very high quality are either not funded or are under-funded. According to 2002 Science and Engineering Indicators, only 28.3 percent of full-time academic mathematicians receive federal research support, much lower than most fields of science.
National Science Foundation (NSF): For FY 2005, the mathematical sciences would continue to be an NSF-wide priority area. The Foundation has budgeted $89.11 million to carry out the priority area activities in FY 2005, with $67.39 million of this amount coming from the Division of Mathematical Sciences (DMS) and the remaining $21.72 million coming from throughout NSF. The NSF-wide allocation depends on cooperative funding opportunities with other NSF directorates and requires matching funds from the DMS. The mathematical sciences were first designated an NSF priority area in FY 2002 and this designation is planned to go through FY 2007. In FY 2006, the priority area would receive approximately $90 million and in FY 2007 $92 million.
The DMS is slated to receive a budget of $202.25 million in FY 2005, only a 0.9 percent or $1.84 million increase over FY 2004. This low increase is quite surprising, given that the mathematical sciences are a priority area and given that advances in science and engineering rely more than ever on the mathematical sciences.
The FY 2005 increase in DMS would maintain the investment in focused mathematical sciences research teams, interdisciplinary training groups, and other collaborative mechanisms related to advancing science and engineering. It would also enhance the national institutes in the mathematical sciences that address the growing interface with other disciplines and the mathematical and statistical problems whose solutions will contribute to both fundamental knowledge and national needs. In FY 2005, support for mathematical sciences research institutes would increase by $1.5 million to a total of $16.6 million. The increase would also enhance research training activities in the mathematical sciences and mentoring activities aimed at increasing the number of U.S. students choosing careers in the mathematical sciences. This would be achieved by a redistribution of funds from other targeted investments in people.
Air Force Office of Scientific Research (AFOSR): The Directorate of Mathematics and Space Sciences provides funds for research in the mathematical sciences in support of the Air Force mission. Current program emphases include cooperative control, quantum computing, and Maxwell's equations. Beginning perhaps as early as FY 2005, a new initiative in nanoscience is anticipated. The AFOSR Mathematics program includes specific portfolios in dynamics and control, physical mathematics and applied analysis, computational mathematics, optimization and discrete mathematics, systems and software, electromagnetics, and signals communication and surveillance.
Army Research Office (ARO): The Mathematical Sciences Division is divided into the following programs: applied analysis; computational mathematics; discrete mathematics and computer science; probability and statistics and stochastic analysis; and mathematical modeling and simulation. The Mathematical Sciences Division plays an essential role in the modeling, analysis, and control of complex phenomena and systems which are of critical interest to the Army. The areas of application include ad hoc and wireless networks, image and scene analysis, and the test and evaluation of new systems. The FY 2005 budget would increase by 5.3 percent over FY 2004.
Defense Advanced Research Projects Agency (DARPA): DARPA's Applied and Computational Mathematics program activities are structured around two interrelated central themes: development of well-conditioned fast algorithms and strategies for the exploitation of high-dimensional data and mathematical modeling to enable virtual design. These themes are addressed through the six program areas: Integrated Sensing and Processing; Time-Reversal Methods; Predicting Real Optimized Materials; Quantum Information Science and Technology; Geospatial Representation and Analysis; and Virtual Electromagnetic and Testrange. Additionally, DARPA has core mathematics activities supporting work in Geometric Langlands and Stochastic Partial Differential Equations. The FY 2005 budget for the mathematical sciences would increase by 7 percent over FY 2004.
Department of Energy (DOE): Mathematics is funded through the Applied Mathematics program of the Mathematical, Information, and Computational Sciences Division (MICS) of DOE. Research is conducted on the underlying mathematical understanding of physical, chemical, and biological systems and advanced numerical algorithms that enable effective description and prediction of such systems on terascale computing systems. Research in applied mathematics supported by MICS underpins computational science throughout the DOE. The FY 2005 budget for the Applied Mathematics Program continues the Computational Sciences Fellowship program at its current level of $3.5 million. The FY 2005 budget also includes $8.5 million for the new "Atomic to Macroscopic Mathematics" (AMM) research effort to provide the research support in applied mathematics needed for understanding complex physical processes that occur on a wide range of interacting length-and time-scales. Current state-of-the-art theory and modeling of complex physical systems requires that the physical phenomena being modeled either occur at a single scale, or widely separated scales with little or no interaction. The AMM effort will support university researchers, partnerships between universities and national laboratories, and multidisciplinary research teams at national laboratories. The Applied Mathematics Program FY 2005 budget would increase by $6.7 million over FY 2004.
National Institutes of Health (NIH): The NIH funds mathematical sciences research through the National Institute of General Medical Sciences (NIGMS) and the National Institute of Biomedical Imaging and Bioengineering (NIBIB), in support of these institutes' missions. These mission areas include population biology, system biology, macro-molecular structures, and bioinformatics for NIGMS and computational science, model development, and bioinformatics for NIBIB. Computational science includes development and application of theoretical methods, mathematical modeling and computational simulation techniques in the study of biological systems. Bioinformatics includes research, development, and applications of informatics tools and approaches for expanding the use of biological, medical, behavioral or health data, including those to acquire, store, organize, archive, analyze or visualize data. Also, NIGMS is currently supporting a biomathematics initiative in cooperation with NSF. The FY 2005 NIH budget supporting the mathematical sciences would grow slightly over FY 2004.
National Security Agency (NSA): The NSA has a small grant program that supports fundamental research in the mathematical areas of algebra, number theory, discrete mathematics, probability, and statistics. The grant program also accepts proposals for miscellaneous conferences and workshops in these research areas. Additional funding is available to support Historically Black Colleges and Universities, Research Experiences for Undergraduates, and a faculty sabbatical leave program. The program administrators are especially interested in funding initiatives that encourage the participation of underrepresented groups in mathematics (such as women, African-Americans, and other minorities). NSA is the world's largest employer of mathematicians and is constrained to hire only U.S. citizens. As a result, the NSA has a special interest in encouraging more U.S. citizens to study mathematics. The FY 2005 NSA budget would increase by 16.7 percent over FY 2004.
Office of Naval Research (ONR): The ONR Mathematical, Computer,
and Information Sciences Division's scientific objective is to establish
rigorous mathematical foundations and analytical and computational methods
that enhance understanding of complex phenomena, and enable prediction
and control for Naval applications in the future. Basic research in the
mathematical sciences is focused on analysis and computation for multi-phase,
multi-material, multi-physics problems; predictability of models for nonlinear
dynamics; electromagnetic and acoustic wave propagation; signal and imaging
processing; modeling pathological behaviors of large, dynamic complex
networks and exploiting hybrid control to achieve reliability and security;
optimization; and formal methods for verifiably correct software construction.
The Division's budget would decrease in FY 2005.
Note: Information gathered from agency documents and from agency program officers.