Federal support for the mathematical sciences is slated to grow from an
estimated $390.68 million in FY 2005 to an estimated $397.58 million in
FY 2006, an increase of 1.8 percent. This is the lowest rate of increase
for the mathematical sciences in several years.
The National Science Foundation’s (NSF) Division of Mathematical Sciences
(DMS) would have no increase in FY 2006. The DMS budget for FY 2006 would
remain at $200.38 million.
The aggregate funding for the mathematical sciences in the Department
of Defense agencies (Air Force Office of Scientific Research (AFOSR),
Army Research Office (ARO), Defense Advanced Project Agency (DARPA), National
Security Agency (NSA), and Office of Naval Research (ONR)) would increase
by 4.7 percent. The majority of this increase comes from DARPA, where
the mathematical sciences budget would grow by 13.5 percent.
The Department of Energy (DOE) Applied Mathematics Division would receive
a 9.8 percent increase.
mathematical sciences are funded through the National Science Foundation,
the Department of Defense, the Department of Energy, and the National
Institutes of Health (NIH). As in the past, the majority of federal support
for the mathematical sciences in FY 2006 would come from the NSF, contributing
approximately 50.4 percent of the federal total. The DOD accounts for
around 23.1 percent of the total, with the NIH supplying 19.2 percent,
and the DOE around 7.3 percent. The NSF currently accounts for over 70.0
percent of the federal support for academic research in the mathematical
sciences and is the only agency that supports mathematics research broadly
across all fields. The DOD, DOE, and NIH support research in the mathematical
sciences that contributes to missions of these agencies.
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).
funds mathematics through its Applied Mathematics program within the DOE
Mathematical, Information and Computational Sciences program. NIH funds
mathematical sciences research primarily through the National Institute
of General Medical Sciences (NIGMS) and the National Institute of Biomedical
Imaging and Bioengineering (NIBIB).
other agencies have small amounts of funding for mathematics research
as it relates to agency missions, including 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
FY 2006 estimated spending for mathematical sciences research and related
activities would be $397.58 million, a potential increase of 1.8 percent
over FY 2005 (see Table 1). The NSF Division of Mathematical Sciences
budget would have no increase in FY 2006, greatly impacting the growth
of overall federal support for the mathematical sciences. The increase
at DOE for FY 2006 would be 9.8 percent over the FY 2005 level. DARPA
surprises with a projected 13.5 percent increase. The remaining DOD agencies
would essentially have no growth in FY 2006.
and more, the mathematical sciences are contributing to advances in life
science research, a trend that will grow in the future. Realizing that
the mathematical sciences can be critical to certain areas of biomedical
research, NIH has been actively pairing mathematicians and biomedical
researchers in funded projects over the last several years.
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 underfunded.
According to the Science and Engineering
Indicators, 2004 Edition, only 30.1 percent of full-time academic
doctoral mathematicians receive federal research support. This is much
lower than most other fields of science.
1: Federal Funding for the Mathematical Sciences (millions
of dollars) #
FY 04 FY 05 FY 06 Change Change
Actual Estimate Request 05-06
200.35 200.38 200.38 0.00
13.6 0.0 0.0%
Applied Mathematics 22.6 26.4 29.0 2.6
Institutes of Health
366.95 390.68 397.58 6.9
Estimates based on conversation with program officer.
# Budget information
comes from agency documents and conversations with program managers and
National Science Foundation (NSF): The Division
of Mathematical Sciences (DMS) is housed in the NSF Directorate of the
Mathematical and Physical Sciences (MPS). This directorate also contains
the Divisions of Astronomical Sciences, Chemistry, Materials Research,
Physics, and Multidisciplinary Activities. (For MPS budgets, see Table
II-7; for more on NSF, see Chapter 7.)
mathematical sciences would continue to be an NSF-wide priority area in
FY 2006. The Foundation has budgeted $88.63 million to carry out the priority
area activities, with $70.23 million coming from the Division of Mathematical
Sciences (DMS) and the remaining $18.40 million coming from throughout
the Foundation. The NSF-wide allocation ($18.40 million) 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 currently this designation is to last
through FY 2007. Tentatively, this priority area would receive $88.63
million in FY 2007.
DMS is slated to receive a budget of $200.38 million in FY 2006. The Division
has essentially had the same budget since FY 2004. However, from FY 2003
to FY 2006 the DMS budget will have grown by 12.1 percent, while for the
same period, the MPS budget grows by 4.4 percent. All the growth for the
DMS occurred from FY 2003 to FY 2004.
DMS has essentially two modes of support: research and education grants,
and institutes. Grants include individual-investigator awards, awards
for multidisciplinary groups of researchers, and educational and training
awards aimed at increasing the number of U.S. students choosing careers in the mathematical sciences.
Approximately 72 percent of the DMS funds are available for new awards
and activities. The remaining 28 percent funds awards made in previous
FY 2006, the DMS has the following priorities: maintaining a strong program
of research grants; investing in algorithm development and computational
tools for large-scale problems of scientific importance; broadening participation
in the mathematical sciences; maintaining research training activities
in the mathematical sciences; and continuing support for the Mathematical
Sciences Priority Area.
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. The AFOSR budget would increase
slightly, by 0.3 percent, over FY 2005.
Army Research Office (ARO): The Mathematical Sciences Division manages the following
programs: modeling of complex systems; computational mathematics; discrete
mathematics and computer science; probability and statistics and stochastic
analysis; and cooperative systems. The Mathematical Sciences Division
plays an essential role in the modeling, analysis, and control of complex
phenomena and large-scale systems which are of critical interest to the
Army. The areas of application include wireless communication networks,
image analysis, visualization and synthetic environments, pattern recognition,
test and evaluation of new systems, sensor networks, and autonomous systems.
The division also works closely with the Computer and Information Sciences
Division of ARO to develop mathematical theory for information processing,
information assurance, and data fusion. The FY 2006 budget is the same
as for FY 2005.
Defense Advanced Research Projects Agency
(DARPA): DARPA’s Applied and
Computational Mathematics program is structured around focused
program initiative areas in interdisciplinary and core mathematics. Current
program areas include: Integrated Sensing and Processing; Mathematical
Time-Reversal Methods; Predicting Real Optimized Materials; Quantum Information
Science and Technology; Geospatial Representation and Analysis; Topological
Data Analysis; Stochastic and Perturbation Methods in PDE Systems; Geometric
Langlands; Discovery and Exploitation of Structure in Algorithms; and
Femtosecond Adaptive Spectroscopy Techniques. The FY 2006 budget for the
mathematical sciences would increase by approximately 13 percent
over FY 2005. (For more on DARPA
and other DOD units, see Chapter 6.)
Department of Energy (DOE): Mathematics is funded through the Applied Mathematics
program of the Mathematical, Information, and Computational Sciences Division
(MICS). Research is conducted on the underlying mathematical understanding
of physical, chemical, and biological systems and advanced numerical algorithms
that enable effective description, modeling, and simulation of such systems
on high-end 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 2006 budget also includes $8.5 million
for the Atomic to Macroscopic Mathematics (AMM) effort which provides
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 supports university researchers, partnerships between universities
and national laboratories, and multidisciplinary research teams at national
laboratories. The Applied Mathematics Program FY 2006 budget would increase by 9.8 percent. (For details of DOE funding,
see Table II-11. For more information on DOE,
see Chapter 9).
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). Mathematical
sciences areas of interest are those that support the missions of NIGMS
and NIBIB. Currently, NIGMS is supporting a biomathematics initiative
in cooperation with NSF, and NIBIB is participating in a joint initiative
with NSF and other NIH institutes titled “Collaborative Research in Computational
Neuroscience.” The aggregate budget for the mathematical sciences in NIBIB
and NIGMS would grow only slightly, 0.3 percent, in FY 2006. (For details
of overall NIBIB and NIGMS funding, see Table II-9.
For information on the NIH budget, see Chapter 8.)
National Security Agency (NSA): NSA has a small Grants Program that supports fundamental
research in the mathematical areas of algebra, number theory, discrete
mathematics, probability, and statistics. The Grants Program also accepts
proposals for conferences and workshops in these research areas. Additional
funding (non-grant) is available to support an in-house faculty Sabbatical
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 largest U.S. employer of mathematicians. As such, it has a vested
interest in maintaining a healthy U.S. academic mathematics community. The Grants Program’s
budget would remain unchanged for FY 2006.
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 Mathematical,
Computer, and Information Sciences Division’s budget would
remain unchanged in FY 2006 (see Table
Note: Information gathered from agency
documents and from agency representatives.