| Mathematical Sciences in
the FY 2004 Budget
Samuel M. Rankin III,
Three federal agencies supply the majority of support for mathematical sciences research through seven dedicated programs in the National Science Foundation (NSF), the Department of Defense (DOD), and the Department of Energy (DOE). The 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. The DOD and DOE support research in the mathematical sciences that contributes to the R&D missions of these agencies. Research supported through these programs is primarily carried out in academic institutions.
DOD has five programs supporting mathematical sciences research and related activities: the Directorate of Mathematics and Space Sciences within the Air Force Office of Scientific Research (AFOSR), the Mathematical Sciences Division within the Army Research Office (ARO), the Mathematical, Computer, and Information Sciences Division within the Office of Naval Research (ONR), the Applied and Computational Mathematics Program within the Defense Advanced Research Projects Agency (DARPA), and the Mathematical Sciences Program within the National Security Agency (NSA). The DOE funds mathematics through its Applied Mathematics program within the DOE Mathematical, Computational, and Computer Sciences Research program.
The National Institutes of Health (NIH) also fund mathematical sciences research. Funds are administered through the National Institute of General Medical Sciences (NIGMS) for research in the mathematical sciences that support the NIGMS mission.
Several other agencies have small amounts of funding for mathematics research as it relates to agency missions. These agencies include the National Aeronautics and Space Administration (NASA), the Environmental Protection Agency (EPA), and the National Institute of Standards and Technology (NIST).
TRENDS IN FEDERAL SUPPORT FOR THE MATHEMATICAL SCIENCES
The FY 2004 estimated aggregate spending for mathematical research and related activities would be $342.9 million, a potential increase of 7.7 percent over FY 2003 estimated spending (see Table 1). Most of this increase is a result of the 13.1 percent increase proposed by NSF.
The NSF is continuing to shoulder a significant portion of the federal support for academic research in the mathematical sciences, approximately 68 percent. The mathematical sciences budget within NSF is growing at a much faster rate than the mathematical sciences budgets at other agencies. In fact, budgets for the mathematical sciences in DOD and DOE are barely increasing, if at all. At the same time that growth in the DOD and DOE budgets are stagnating, the fundamental contributions of the mathematical sciences to advances in science and technology continues to increase.
National Science Foundation (NSF): For FY 2004 the mathematical
sciences continue to be an NSF-wide priority area. NSF has requested $89.09
million to carry out the priority area activities in FY 2004, with $67.39
million of this amount in the DMS and the remaining $21.7 million provided
throughout the rest of the Foundation. NSF first designated the mathematical
sciences as a priority area in FY 2002.
Table 1. Federal Funding for the Mathematical Sciences (millions of dollars) #
* This figure is estimated based on language in the FY 2003 omnibus appropriations bill (Public Law 108-7).
** Rough estimate based on conversation with program manager; NIBIB estimates for FY 2003 and FY 2004 were unavailable at press time.
# Budget information from agency documents and conversations with program managers. DOD FY 2003 and FY 2004 figures are estimates.
The DMS is slated to receive a budget of $201.87 million in FY 2004. This would be a $23.42 million increase over the approximately $178.45 million the Division is to receive for FY 2003.
The goal of the mathematical sciences priority area is to advance frontiers in three interlinked areas. For FY 2004 the NSF plans to invest in the following mathematical sciences activities: fundamental mathematics and statistical sciences; interdisciplinary research connecting the mathematical sciences with science and engineering; and mathematical sciences education.
Fundamental mathematical and statistical sciences research includes themes such as dynamical systems and partial differential equations, geometry and topology, stochasticity, number theory, algebraic and quantum structures, the mathematics of computation, Bayesian estimation, and multi-scale and multi-resolution analysis. Support for research in these areas will be provided through focused research groups and individual investigator grants, as well as through institute and postdoctoral training activities.
Three broad interdisciplinary themes have been identified for initial emphasis in the mathematical sciences priority area: mathematical and statistical challenges posed by large data sets, managing and modeling uncertainty, and modeling complex nonlinear systems. Research in these areas will be supported through interdisciplinary focused research groups, interdisciplinary centers, interdisciplinary cross-training programs, and partnership activities with other agencies.
The mathematical sciences education activity will foster closer connections between research and education. Support for undergraduate and graduate education and postdoctoral training, coupled with curriculum reform, is a major part of this activity.
Air Force Office of Scientific Research (AFOSR): The Directorate of Mathematics and Space Sciences provides funds for research and related activities in the mathematical sciences in support of the Air Force mission. Current program emphases include cooperative control, quantum computing, and Maxwell's equations. The AFOSR program includes dynamics and control, physical mathematics and applied analysis, computational mathematics, optimization and discrete mathematics, electromagnetics, and signals communication and surveillance. The AFOSR budget would decline in FY 2004.
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 ARO budget shows a slight increase over FY 2003.
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 four program areas: Integrated Sensing and Processing; Molecular Observation, Spectroscopy and Imaging Using Cantilevers; Optimal Portable Applications Libraries; Quantum Information Science and Technology; and Virtual Electromagnetic and Testrange. The FY 2004 budget for the mathematical sciences would increase by 15.3 percent over FY 2003.
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 MCIS underpins computational science throughout the DOE. For FY 2003 and FY 2004 the budget of the Applied Mathematics program includes $5 million each year for two "thrust" areas: Genomes to Life (computational biology) and Nanoscience. Genomes to Life activity is a partnership with the Office of Biological and Environmental Research; the nanoscience activity is a partnership with the Office of Basic Energy Sciences. The program budget would not increase in FY 2004.
National Institutes of Health (NIH): NIH funds mathematical sciences research through the National Institute of General Medical Sciences (NIGMS) and the National Institute of Biomedical Imaging and Bioengineering (NIBIB). Currently NIGMS is supporting a biomathematics initiative in cooperation with NSF. Mathematical sciences areas of interest are those that support the missions of NIGMS and NIBIB. 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.
National Security Agency (NSA): The NSA has a small grants program which supports fundamental research in the mathematical areas of algebra, number theory, discrete mathematics, and probability and statistics. Other funds are available to support Historically Black Colleges and Universities, Research Experiences for Undergraduates, and a sabbatical leave program for university faculty. As the world's largest employer of mathematicians and constrained to only hire U.S. citizens, the NSA has a special interest in encouraging more U.S. citizens to study mathematics.
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 Navy 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; sequencing and scheduling; and construction of complex system
software. The Division's budget would be level in FY 2004.
Note: Information gathered from agency documents and from agency program officers.