| Introduction Research in the mathematical sciences
is funded primarily through the National Science Foundation (NSF), the Department
of Defense (DOD, including the National Security Agency), the Department of Energy
(DOE), and the National Institutes of Health (NIH). As in previous years, the
majority of federal support for the mathematical sciences in FY 2008 would come
from NSF, contributing approximately 49.2 percent of the federal total. DOD accounts
for around 20.7 percent of the total, with the NIH supplying 17.7 percent, and
the DOE around 12.4 percent. NSF currently accounts for almost 80.0 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.
DOD, DOE, and NIH support research in the mathematical sciences that contributes
to the missions of these agencies. DOD supports mathematical sciences
research and related activities in several programs: the Directorates of Mathematics,
Information, and Life Sciences and Physics and Electronics, within the AFOSR;
the Mathematical and Information Sciences Division within the ARO; the Mathematics,
Computers, and Information Sciences Research division within the ONR; the Defense
Sciences Program and the Microsystems Technology Office within DARPA; and the
Mathematical Sciences Program within the NSA. DOE funds mathematics through its
Applied Mathematics program within the DOE Mathematical, Information and Computational
Sciences subprogram. NIH funds mathematical sciences research primarily through
the National Institute of General Medical Sciences (NIGMS) and through the National
Institute of Biomedical Imaging and Bioengineering (NIBIB). Trends in Federal Support for the Mathematical Sciences FY 2008 estimated aggregate spending
for mathematical sciences research and related activities would be $454.2 million,
a potential increase of 9.2 percent over FY 2007 estimated spending. The NSF Division
of Mathematical Sciences budget would increase by 8.6 percent in FY 2008, while
the DOD agencies would increase by 10.0 percent for FY 2008. DARPA increases its
mathematical sciences spending by 50.0 percent while ARO mathematics budget decreases
by 14.3 percent. The remaining DOD agencies would essentially have little or no
growth in FY 2008. The DOE mathematical sciences budget increases by 15.9 percent
while NIH funding increases by 5.7 percent. The mathematical sciences make major
contributions to the country’s intellectual capacity and the need for results
from the mathematical sciences in scientific discovery and technological innovation
is on an accelerating pace. Many disciplines depend on discoveries in the mathematical
sciences to open up new frontiers. Even so, many mathematical scientists who are
performing excellent research and who submit grant proposals deemed of very high
quality, are consistently either not funded or are under funded. According to
the Science and Engineering Indicators, 2006 Edition, in FY 2003 only
31.0 percent of full-time mathematical sciences faculty with doctoral degrees
received federal research support. This is much lower than most other fields of
science. Table
1: Federal Funding for the Mathematical Sciences (millions
of dollars) # 
FY 06 FY 07 FY 08 Change Change
Actual Estimate
Request 07-08
07-08
Amount Percent National
Science Foundation DMS
199.5 205.7
223.5 17.7
8.6% Department
of Defense AFOSR
32.1 36.0
37.6 1.6
2.8% ARO
14.0 14.0
12.0 -2.0
-14.3% DARPA
16.0 18.0
27.0 9.0
50.0% NSA*
4.0 4.0
4.0 0.0
0.0% ONR
*
13.6 13.6 13.6 0.0 0.0% Total
DOD
79.7 85.6
94.2 8.6
10.0% Department
of Energy Applied Mathematics 32.0 29.5 36.9 7.4
25.1% SciDAC **
2.7 10.0
10.0 0.0
0.0% SAPs **
1.0 7.6
7.9 0.3
3.9% OSG **
0.8 1.3 1.3 0.0 0.0% Total
DOE
36.5 48.4
56.1 7.7
15.9% National
Institutes of Health NIGMS
38.0 38.0
42.0 4.0
10.5% NIBIB
38.7 38.1 38.4 0.3 0.8% Total
NIH
76.7 76.1
80.4 4.3
5.7%
____ ____
____ Total
All Agencies
392.4 415.8
454.2 38.3
9.2% *
Estimates based on previous budgets. #
Budget information is derived from agency documents and conversations with agency
program managers and representatives. **
Scientific Discovery through Advanced Computing (SciDAC); Scientific Applications
Partnerships (SAPs); Open Science Grid (OSG) 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. The DMS supports advances
in the intellectual frontiers of the mathematical sciences, activities contributing
to advancing knowledge in other scientific and engineering fields, and research
that is critical to national competitiveness. The 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. The DMS provides core support for five mathematical
sciences research institutes, as well as major support for three other institutes.
These institutes, funded on a competitive basis, serve to develop new ideas and
directions in the mathematical sciences, as well as to promote interaction with
other disciplines. The DMS is slated to receive a budget of $223.5
million in FY 2008, an increase of $17.7 million or 8.6 percent over the FY 2007
budget. The $17.7 million is broken down as follows: $7.3 million for core programs;
$5.2 million for Cyber-enabled Discovery and Innovation (CDI), an NSF-wide initiative;
$1.5 million for Science Beyond Moore’s Law, an MPS initiative; $1.0 million for
discovery-based undergraduate experiences; and $2.7 million for mathematical sciences
institutes and networks. The mathematical sciences designation as an NSF
priority area ended in the FY 2007 budget. The FY 2008 MPS budget reflects spending
of $6.6 million for continuing priority-area awards made in prior years. Other
components of the priority area investment will return to core programs for continued
support. For FY 2008, the DMS has several priorities. Core
support for the mathematical sciences includes individual investigator awards,
support for graduate and postdoctoral students within individual awards, and investments
in formal interdisciplinary partnerships. The objective of CDI is to broaden the nation’s
capability for innovation through the development of a new generation of computationally
based discovery concepts and tools that can deal with complex, data-rich systems.
Areas of emphasis for the mathematical sciences include algorithm development
and computational tools for large-scale problems of scientific importance, modeling
of phenomena that occur over a large range of spatial and temporal scales, and
finding patterns in the structure of large data sets. Going beyond Moore’s law will require algorithms
that increase the speed of basic computations exponentially in concert with hardware
improvements. Emphasis will include algorithm design, analysis, and implementation;
scalability in space and time; quantification of errors and uncertainty in visualization
of large data sets. Broadening participation in the mathematical sciences will
support interactions and research networks among a diverse population, including
students and researchers at a wide array of institutions. Education and training
activities include research experiences and mentoring activities aimed at increasing
the number of U.S. students choosing careers
in the mathematical sciences. Air Force Office of Scientific Research
(AFOSR): Funding for the mathematical sciences at AFOSR is found
in the Directorates of Mathematics, Information, and Life Sciences and Physics
and Electronics. The
AFOSR mathematics program includes specific portfolios in dynamics and control,
physical mathematics and applied analysis, computational mathematics, optimization
and discrete mathematics, electromagnetics, and signals communication and surveillance.
Current areas of interest include cooperative/collaborative control of a team
of unmanned aerial vehicles conducting operations; improved mathematical methods
and algorithms that exploit advanced computational capabilities in support of
Air Force computing interest; the development of accurate models of physical phenomena
that enhance the fidelity of simulation; and the development of resilient algorithms
for data representation in fewer bits, image reconstruction/enhancement, and spectral/frequency
estimation in the presence of external corrupting factors. The AFOSR FY 2008 budget
for the mathematical sciences would increase 2.8 percent over FY 2007. Army Research
Office (ARO): The Mathematics Program, housed
in the Mathematical and Information 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, network science, robotics,
and autonomous systems. The division also works closely with the Computer and
Information Sciences Division of ARO to develop mathematical theory for systems
control, information processing, information assurance, and data fusion. The FY
2008 budget for the Mathematical Sciences Division is $12 million. The ARO budget
would decrease by 14.3 percent from FY 2007. Defense Advanced Research Projects Agency
(DARPA): The Defense Sciences Office
(DSO) inside DARPA has a mathematics program encompassing both Applied and Computational
Mathematics and Fundamental Mathematics. The
thrusts of DSO’s programs are structured around focused initiative areas in interdisciplinary
and core mathematics. Current program areas include: Discovery and Exploitation
of Structure in Algorithms, Femtosecond Adaptive Spectroscopy Techniques for Remote
Agent Detection, Geospatial Representation and Analysis, Integrated Sensing and
Processing, Mathematical Time Reversal, Predicting Real Optimized Materials, Protein
Design Processes, Robust Uncertainty Management, Stochastic and Perturbation Methods
in PDE Systems, and Waveforms for Active Sensing as well as Focus Areas in Theoretical
Mathematics, Fundamental Laws of Biology, Sensor Topology and Minimal Planning,
and Topological Data Analysis. The Microsystems Technology Office has several
programs where mathematical algorithms play a central role in the optimization,
control, and exploitation of microelectronic and optical systems. These
include the following programs: Analog-to-Information, Cognitively Augmented Design
for Quantum Technology, Multiple Optical Non-redundant Aperture Generalized Sensors,
Non-Linear Mixed Signal Microsystems, and Space-Time Adaptive Processing. The
DARPA mathematics budget would increase by 50.0 percent over FY 2007. Department of Energy (DOE): Mathematics at DOE is funded through the Advanced Scientific
Computing Research (ASCR) program under its sub-program, Mathematical, Information,
and Computational Sciences (MICS) Division. Funding
for the mathematical sciences is found in the Applied Mathematics activity, the
Scientific Discovery through Advanced Computing (SciDAC) activity, the Scientific
Applications Partnerships activity, and the Open Science Grid. The Applied Mathematics
activity supports research 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. Applied Mathematics supports work in a wide variety
of areas of mathematics, including: ordinary and partial differential equations,
numerical linear algebra, fluid dynamics, optimization, mathematical physics,
control theory, accurate treatment of shock waves, mixed elliptic-hyperbolic systems,
and dynamical systems. The FY 2008 Applied Mathematics activity budget includes
increased support for mathematical research issues relevant to petascale science
(up $2 million), research in optimization control and risk analysis in complex
systems (up $1.9 million), support for multiscale mathematics (up $2.5 million),
and funding for the Computational Science Graduate Fellowship Program (up $1.0
million). Support for multiscale mathematics is $11 million in FY 2008. Around
eight percent of ASCR’s budget goes to university based research. The DOE FY 2008
budget for the mathematical sciences will increase by 15.9 percent over FY 2007.
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 at around $12 million a year in
cooperation with NSF, and NIBIB is participating in a joint initiative with NSF
and other NIH institutes, “Collaborative Research in Computational Neuroscience.”
The aggregate budget for the mathematical sciences in NIBIB and NIGMS would increase
by 5.7 percent in FY 2008. National Security Agency (NSA): The Mathematical Sciences Program of the NSA administers a
Grants Program that supports fundamental research in the areas of algebra, number
theory, discrete mathematics, probability, and statistics. The Grants Program
also accepts proposals for conferences and workshops in these research areas.
In addition to grants, the Mathematical Sciences Program supports 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 employer of mathematicians in the United States. As such, it has a vested interest in maintaining a healthy
academic mathematics community in the United States. The
NSA mathematics budget would remain unchanged for FY 2008. Office of Naval Research (ONR): The ONR Mathematics, Computers, and Information Research
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 2008. Note: Information gathered from agency
documents and from agency representatives. | 
