| Highlights -
Federal support for the mathematical
sciences is slated to grow from an estimated $384.00 million in FY 2006 to an
estimated $396.34 million in FY 2007, an increase of 3.2 percent. -
The National Science Foundation’s (NSF) Division of Mathematical Sciences (DMS)
would increase by 3.2 percent to $205.74 million. -
The aggregate funding for the mathematical sciences in the Department of Defense
(DOD) 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 8.5 percent. The
majority of this increase comes from two agencies, AFOSR (15.6 percent) and DARPA
(9.1 percent). Introduction Research
in the mathematical sciences is funded through the National Science Foundation,
the Department of Defense (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 2007 would
come from the NSF, contributing approximately 51.9 percent of the federal total.
The DOD accounts for around 20.9 percent of the total, with the NIH supplying
19.8 percent, and the DOE around 7.4 percent. NSF currently accounts for almost
80 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 Directorate of Mathematics and Information Sciences within the AFOSR; the
Mathematical Sciences Division within the ARO; the Mathematical, Computer, and
Information Sciences Division within the ONR; the Defense Sciences Program and
the Microsystems Technology Office within DARPA; and the Mathematical Sciences
Program within the NSA. The
DOE funds mathematics through its Applied Mathematics program within the DOE Mathematical,
Information and Computational Sciences program. The National Institutes of Health
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). 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 2007 estimated aggregate spending for mathematical sciences research and related
activities would be $396.34 million, a potential increase of 3.2 percent over
FY 2006 estimated spending. The NSF Division of Mathematical Sciences budget would
increase by 3.2 percent in FY 2007, while the DOD agencies would increase by 8.5
percent for FY 2007. AFOSR surprises with a 15.6 percent increase, while DARPA
increases by 9.1 percent. The remaining DOD agencies would essentially have no
growth in FY 2007. All other agencies would remain level or decrease slightly. The
mathematical sciences are making major contributions to the country’s intellectual
capacity and the need for results from the mathematical sciences in scientific
discovery and technological innovation is accelerating. Many disciplines depend
on discoveries in the mathematical sciences to open up new frontiers. Mathematical
sciences research supports new results in the life and social sciences as well
as more traditional fields, such as the physical sciences, computer science, geosciences,
and engineering. Yet,
even with this increasing need for mathematics, 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, having 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 05 FY 06 FY 07 Change Change
Actual Estimate Request 06-07
06-07
Amount Percent National
Science Foundation
DMS
200.24 199.30 205.74 6.44
3.2% Department
of Defense
AFOSR
30.3 32.1
37.1 5.0
15.6%
ARO
10.0 10.0
10.0 0.0
0.0%
DARPA
19.2 16.5
18.0 1.5
9.0%
NSA
3.5 4.0
4.0 0.0
0.0%
ONR
13.6 13.6 13.6 0.0 0.0% Total
DOD
76.6 76.2
82.7 6.5
8.5% Department
of Energy
Applied Mathematics 29.6 29.4 29.5 0.1
0.3% National
Institutes of Health
NIGMS
35.0 38.0*
38.0* 0.0
0.0%
NIBIB
38.2 41.1 40.4 -0.7 -1.7% Total
NIH
73.2 79.1
78.4 -0.7
-0.9%
____ ____
____ Total
All Agencies 379.64 384.00 396.34 12.34
3.2% *Estimates
based on conversation with program officer.
# Budget
information comes from agency documents and conversations with program managers
and representatives. 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
mathematical sciences would continue to be an NSF-wide priority area in FY 2007,
the last year of this five-year designation. The Foundation has budgeted $78.45
million to carry out the priority area activities in FY 2007, with $69.26 million
of this amount coming from the DMS and the remaining $9.19 million coming from
throughout the Foundation. The NSF-wide allocation ($9.19 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 2003. In 2003, the Mathematical Sciences Priority Area was projected
to receive $109.50 in the FY 2007 budget. The current budget environment has severely
curtailed this Priority Area. The
DMS is slated to receive a budget of $205.74 million in FY 2007. This 3.2 percent
increase is the first increase in the DMS budget since FY 2004. The DMS budget
has increased $26.95 million since FY 2003, the first year the mathematical sciences
was designated a priority area, and when the DMS budget was $178.79 million. The
DMS budget increased $21.56 million or 12.1 percent from FY 2003 to FY 2004 with
the last increase of $5.39 million to come in the FY 2007 budget. The FY 2007
MPS budget is slated for a 6.0 percent increase over FY 2006. 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. For
FY 2006, the DMS has the following priorities: -
Maintaining a strong program of research grants, both single investigator and
small group 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; -
Continuing support for the Mathematical Sciences Priority Area, while initiating
the mainstreaming of its activities in the DMS portfolio. Air Force Office of Scientific Research
(AFOSR): The
Directorate of Mathematics and Information Sciences provides funds for research
in the mathematical sciences in support of the Air Force mission. 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; innovative methods and algorithms that improve
modeling and simulation capabilities that will enable understanding, prediction,
and control of complex physical phenomena crucial to the Air Force; 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 budget would increase 15.6 percent over
FY 2006. Army Research Office (ARO): The Mathematics Program, housed
in the Mathematical Sciences 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, 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
2007 budget for the Mathematical Sciences Division remains at the FY 2006 level. 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, Quantum Information Science and Technology, 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, 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 Analog-to-Information program, the Multiple Optical Non-redundant
Aperture Generalized Sensors program and the Non-Linear Mixed Signal Microsystems
program. The DARPA mathematics budget would increase by 9.1 percent over FY 2006. 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, 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 Applied Mathematics program 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 2007 budget for the Applied Mathematics Program increases the Computational
Sciences Fellowship program by $ 500,000 to $4 million. The FY 2007 budget also
includes $8.5 million, the same as for FY 2006, 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. The AMM effort supports university researchers,
partnerships between universities and national laboratories, and multidisciplinary
research teams at national laboratories. The FY 2007 Applied Mathematics budget
would increase by 0.3 percent over FY 2006. 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 the National
Science Foundation and NIBIB is participating in a joint initiative with the NSF
and other NIH institutes, “Collaborative Research in Computational Neuroscience.”
The aggregate budget for the mathematical sciences in NIBIB and NIGMS would decline
by 0.9 percent, in FY 2007. 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 2007. Office of Naval Research (ONR): The ONR Mathematical, Computer, 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 2007.
Note: Information gathered from agency
documents and from agency representatives.
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