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2 Response to the 1984 National Plan
FEDERAL RESPONSE
The responses of science-intensive federal agencies to the recommen-
dations of the 1984 Report have been highly variable, ranging from
bold and sustained action in some cases to moral support with virtu-
ally no action in others. The two major agencies most directly in-
volved are the NSF, which accounts for 55% of the total federal sup-
port for the mathematical sciences and more than 90% of the support
for pure mathematics, and the DOD, which provides nearly 40% of the
total federal support for the mathematical sciences and 65% of the
support for applied mathematics and statistics.
Nearly two years before its 1984 Report was published, the Ad Hoc
Committee on Resources for the Mathematical Sciences had gathered
comprehensive data comparing federal support of mathematical sci-
ences research with support for related fields. These data were used
as part of the research briefing on mathematics given in October 1982
to George A. Keyworth, director of the Office of Science and Technol-
ogy Policy (OSTP), by a panel of the Committee on Science, Engineer-
ing, and Public Policy (COSEPUP) of the National Academy of Sci-
ences. The data had been developed under the aegis of the government's
Interagency Committee for Extramural Mathematics Programs
(ICEMAP) and were used extensively throughout the years 1982 to
1986 in staff presentations within several of the agencies, particularly
NSF. The early response to these data by OSTP and NSF was swift,
resulting in a 20% increase in the budget of NSF's Division of Mathe-
matical Sciences from FY 1983 to FY 1984.
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RENEWING U.S. MATHEMATICS
Total federal agency academic support for the mathematical sciences
over the five years since the 1984 Report's appearance is profiled in
constant dollars in Table 2.1. (Some federal agencies also support
significant internal research in the mathematical sciences, which is not
included in Table 2.1.)
National Science Foundation
By the start of the 1980s, the Division of Mathematical Sciences at the
NSF had already begun an effort to better support the mathematical
sciences research infrastructure as well as research per se. A new
postdoctoral program was initiated after discussions in the National
Science Board, led by G. D. Mostow and others. Intensive debate over
proposed "research institutes" led eventually to the funding of the
Mathematical Sciences Research Institute (MSRI) at the University of
California-Berkeley and the Institute for Mathematics and its Applica-
tions (IMA) at the UniversitY of Minnesota, both now regarded as
highly successful
~ ,. ~ . .
cow
The debate also led to emphasis on '/alternative
modes,', WhiCh encompassed several other programs, notably an ex-
panded postdoctoral program.
Following the June 1984 publication of the National Plan in the 1984
Report, a strong NSF response was sustained. In November 1984, the
National Science Board, the governing body of the NSF, passed a
resolution calling on all federal science agencies to join with NSF in
remedying the marked imbalance in support that the report had pointed
out. Strong leadership by Erich Bloch, NSF director, his predecessor
Edward Knapp, and Richard Nicholson, associate director for the
Directorate for Mathematical and Physical Sciences, resulted in con-
tinued high priority for mathematics in the allocation of its funds. As
a result, NSF support of mathematical sciences research nearly doubled
(almost 50% real growth compared to 29% for total NSF R&D) over the
six years from FY 1983 to FY 1989. Equally important was the way
these funds were used. With strong backing from their advisory panels,
three successive directors of the Division of Mathematical Sciences, E.
F. Infante, John Polking, and Judith Sunley, led an effort to restructure
the support patterns of NSF mathematics programs, balancing sup-
port for the research infrastructure (as represented by graduate stu-
dents, postdoctoral researchers, computing facilities, and so on) with
research support for principal investigators.
22
This ordering of priorities continues to be recommended by the NSF's
Mathematical Sciences Advisory Panel. Thus virtually all of the real

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RESPONSE TO THE 1984 NATIONAL Pi
TABLE 2.1 Federal Agency Academic Support for the Mathematical
Sciences, Constant 1984 Dollars (Millions)
Percent
Increase,
FY 1984 to
Agency PY 1984 FY 1986 FY 1988 PY 1989 FY 1989
Department of Defense
APOSR 10.20 11.94 11.81 13.04 28
ARO 6.80 7.54 8.76 9.11 34
ONR 11.90 11.50 9.50 9.53 -20
DARPA 4.94 9.91 7.13 N.A.
NSA 1.60 2.04 N.A.
Total DOD 28.90 35.92 41.58 40.85 41
Department of Energy 2.90 3.54 5.48 5.43 87
Other agencies. 2.00 1.80 0.83 0.79 -61
Total non-NSF 33.80 41.26 47.89 47.07 39
NSF
DMS 41.20 46.45 52.67 52.20 27
Other 4.00 4.94 4.54 6.34 59
Total NSF 45.20 51.39 57.21 58.54 30
TOTAL FEDERAL
ACADEMIC SUPPORT 79.00 92.65 105.10 105.61 34
~Estimate, including the National Aeronautics and Space Administration, the Na-
tional Institutes of Health, and the National Institute of Standards and Technology.
Also includes NSA prior to FY 1988.
Acronym key: AFOSR = Air Force Office of Scientific Research, ARO = Army
Research Office, 0NR = Office of Naval Research, DARPA = Defense Advanced Re-
search Projects Agency, NSA = National Security Agency, NSF = National Science Foun-
dation, DMS = Division of Mathematical Sciences.
N.A. = Not appropriate.
SOURCE: FY 1990 Joint Policy Board for Mathematics submission to the American
Association for the Advancement of Science (AAAS). Higher Education Price Index
used as dollar deflator.
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RENEWING U.S. MATHEMATICS
growth in the division's budget over the last six years has gone into
infrastructure support.
These priorities, consistent with the thrust of the 1984 National Plan,
have had a significant impact on the Ph.D. pipeline. An undesired
side effect is that, because of funding limitations, no progress has
been made on another important part of the plan: increasing the number
of principal investigators supported. It should also be noted that,
although the profile of grants in the Division of Mathematical Sciences
has changed for the better because of the consistent application of
these priorities, balance within the grants to the extent recommended
by the 1984 National Plan has not yet been attained. Thus future
priorities will need to emphasize both principal investigators and the
infrastructure for support.
Department of Defense
The percentage growth of total DOD support for the mathematical
sciences has been nearly the same as that at NSF, 94% over the six-year
period from FY 1983 to FY 1989 (about 46~o real growth compared to a
23% increase in the total DOD R&D budget). The form of the growth
has been quite different, however.
The three service agencies the Air Force Office of Scientific Research
(AFOSR), the Army Research Office (ARO), and the Office of Naval
Research (ONR) have been in a period of flat funding and have not
evolved comprehensive plans for strengthening their support of the
mathematical sciences. However, when the DOD,s University Re-
search Initiative program was launched in 1986, high priority was
assigned to mathematics by the directors of the service agencies and
the civilian R&D management of DOO, notably Undersecretary Rich-
ard DeLauer and Deputy Undersecretary Ronald Kerber. Still, there
has been no net increase in funding except in support of computa-
tional facilities.
Support at DOD has grown principally because two new mathematical
sciences research programs were created, one at the Defense Advanced
Research Projects Agency (DARPA) and the other at the National
Security Agency (NSA).
The new DARPA program in Applied and Computational Mathemat-
ics, currently funded at the $9 million level (7% of total federal sup-
24

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RESPONSE TO THE 1984 NATIONAL PLAN
port), was initiated by Craig Fields, now DARPA's director. It has
emphasized relatively large ($500,000 to $2 million) project grants to
groups of mathematicians working on broad problems in areas identi-
fied by DARPA staff as (1) important to the DOD and/or DARPA
mission; and (2) particularly promising scientifically. Originally, the
principal areas were dynamical systems, turbulent flow, computational
algorithms, data/image compression, and harmonic analysis/cluster-
ing algorithms. The contracts have greatly strengthened the research
efforts in those areas and have provided exciting models of problem-
focused group (or team) research. This program has generated. in-
creased appreciation of the importance of mathematics to the DOD
mission well beyond the boundaries of DARPA. At the same time the
DARPA program has caused some concern within the mathematical
community for two reasons: (1) the program has tended to provide
more support for a few mathematicians who were already well sup-
ported, and therefore has done little to increase the number of people
supported in the field; and (2) initially the program has remained
independent of the broader mathematical community.
With 600 mathematicians on its staff, the NSA is one of the largest
employers of mathematicians in the country. Though still producing
large amounts of classified research, mathematicians at NSA—backed
by successive directors W.E. Odom and W.O. Studeman and Chief
Scientist Kermith Speierman—have broadened their interaction with
the larger mathematical sciences community. The extramural Mathe-
matical Sciences Program at the NSA has had a positive impact on
federal support for the field far greater than its size ($2.5 million, or
2% of total federal support) might indicate. It has established a pro-
gram of "small science" research grants that support some 80 mathe-
maticians, most of whom work in areas traditionally labeled as pure
mathematics. Awards are made subject to a peer review system or-
ganized by the NRC's Board on Mathematical Sciences (BMS). The
program has helped to increase somewhat the number of principal
investigators supported in the field. The building of both formal and
informal bonds with the mathematical sciences community is also a
significant benefit.
Department of Energy
The Department of Energy (DOE) doubled its support for the mathe-
matical sciences over the period from FY 1984 to FY 1988, focusing
primarily on computational sciences and applied mathematics but also
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RENEWING U.S. MATHEMATICS
on geometry and mathematical physics. Its budget for supercom-
puting quadrupled over the same period. A postdoctoral fellowship
program begun in 1989 supports 14 computational mathematicians at
national laboratories; this program promises to strengthen ties be-
tween academic mathematicians and the DOE laboratories.
Mathematics of Computation Initiative
The 1984 Report's recommendation for a special mathematics of com-
putation initiative resonating with the recommendations of earlier
reports, such as the "Lax Report"2—was implemented to a large de-
gree. This initiative was meant to encourage mathematics graduate
students and new faculty to develop the new mathematics that will be
needed to effectively use the many supercomputers now in use or
planned. An NSF summary of federal funding for computational
mathematics research shows an increase from $4 million to $12 million
over the period from 1982 to 1987.3 In particular, the NSF created a
new program in computational mathematics with FY 1987 expendi-
tures of nearly $3 million to focus attention on this goal. The AFOSR
and DOE doubled their budgets in this area, while the ARO increased
its effort by 50%. DARPA's new program, which did not exist in 1982,
supported $1 million worth of computational mathematics in FY 1987.
In addition, the NSF supercomputing centers are major resources for
this endeavor. Clearly, a good infrastructure for support of this initia-
tive has been established.
Federal Progress Toward Achieving Quantitative Goals
of the 1984 National Plan
The goals for federal support set forth in the 1984 Report are the
quantitative elements of its National Plan for renewal. These esti-
mates of what it would take to restore balance between support for
mathematical sciences research and support for related fields were
derived from an analysis of the needs of the inner core of the research
enterprise in the mathematical sciences. This core was determined to
consist of 2600 senior investigators5 and a renewal pipeline of 1000
graduate students, 200 postdoctorals, ancl~400 young investigators.
Section IV.B of Appendix A adds details to these goals. The annual
cost of support in 1989 was estimated to total $225 million.6
Table 2.2 summarizes gains made in four key categories over the five
years since the 1984 Report was published. Several comments are in
26

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RESPONSE TO THE 1984 NATIONAL PLAN
TABLE 2.2 Federal Support of Mathematical Sciences Research-
Progress Over Five Years, 1984 to 1989
1984 Percent Percent of 1984
National Change, National Plan
Plan 1984 1989 1984 to Goal Reached
Category of Support Goal Level Level 1989 by 1989
Number of researchers
supported
Senior investigators 2600 1800 1900 +6 73
Postdoctoral researchers 400g 132 1886 +42 47
Graduate research
assistants
Total dollars (millions)
1000 411 661b +61 66
225C 99.6d 133 +34 59
aThe 1984 National Plan calls for awarding 200 two-year postdoctorals annually,
resulting in a population of 400 at any given time.
bMost recent counts comparable to the 1984 numbers, from fall 1988. (NSF Division
of Science Resources Studies, personal communication.)
C1984 National Plan goal adjusted for inflation using Higher Education Price Index;
revised National Plan goal is $250 million.
din 1989 dollars, using Higher Education Price Index.
Order about increases in total support for the field. In actual dollars,
total federal support has climbed from $79 million in 1984 to $133
million in 1989, an increase of 68% over the five years. As described
above, support by the two major funders, NSF and DOD, increased by
roughly the same percentage but through different mechanisms at
NSF through consistent increases in the budget of its Division of
Mathematical Sciences and at DOD principally through the creation of
two new programs, one at DARPA and the other at NSA.
As Table 2.2 shows, the actual dollar increase of 68% translates into
real growth of about 34%, most of which has gone into support for
graduate students and postdoctorals,7 in accordance with priorities
set in 1984. Nevertheless, we are still far from the goals of annually
funding 2600 senior investigators, 200 new postdoctoral researchers,
1000 graduate research assistants, and 400 young investigators. Fur-
thermore, the balance called for in the 1984 National Plan between
support for senior investigators, on the one hand, and emerging schol-
ars, on the other, has not yet been achieved.
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RENEWING U.S. MATHEMATICS
Actual dollar increases of 68% in five years (95% over the six years
from 1983 to 1989) represent bona ficle gains for the mathematical
sciences (34% and 46%, respectively, in real dollars). This occurred in
a period when funding for the sciences was less than robust. How-
ever, apparently significant incremental increases can be misleading
when the base level is very small. Table 2.2 shows vividly that there is
still a long way to go. For example, total support for the field in 1984
stood at 44% of the goal recommended in the 1984 Report, and in 1989
it stood at 59% of that goal, after adjusting for inflation.
Table 2.3 updates Figure 1.2 and Table 1.1 and covers a longer period
than does Table 2.2. These counts omit summer postdoctoral posi-
tions and other grants that do not reflect the spirit of the 1984 Na-
tional Plan's recommendations. The absolute numbers of federally
supported graduate research assistants and postdoctorate in the mathe-
TABLE 2.3 Selected Ph.D. Pipeline Comparisons for 1980 and 1988
Mathematical
Point of Comparison
Chemistry Physics Sciences
Graduate research assistants
federally supported
1 980 3733 2976 421
1988 4673* 3591* 661
Annual Ph.D. production
1 980 1 538 862 744
1988 2018 1172 749
Postdoctoral researchers
federally supported
1980
1 988
Ratio of federally
supported graduate
research assistants
to Ph.D. degrees
produced (1988)
Ratio of federally
supported postdoctoral
researchers to Ph.D. degrees
produced (1988)
2255 1210 57
2587 1280 188
2.32 3.06 0.88
1.28 1.09 0.25
41986 figures; later data not yet available.
SOURCE: National Science Foundation, Division of Science Resources Studies.
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RESPONSE TO THE 1984 NATIONAL PLAN
TABLE 2.4 Type of Support for Full-Time Graduate Students in
Doctorate-Granting Institutions, 1987
Number Number Number Fraction
of with with with
Graduate Teaching Research Research
Students Assistantships Support. Support
Biological sciences 37,734 8,210 22,114 0.586
Physics 11,075 4,089 5,660 0.511
Chemistry 15,664 7,005 7,630 0.487
Engineering 61,194 11,005 27,550 0.450
Social sciences 48,699 9,745 13,644 0.280
Computer sciences 13,578 3,258 3,612 0.266
Mathematical sciences 12,354 7,089 2~231 0.181
Includes research assistantships, fellowships, and traineeships.
SOURCE: National Science Foundation, Division of Science Resources Studies
(personal communication).
matical sciences shown in Table 2.3 remain only small fractions of the
figures for comparable groups in chemistry and physics. The ratios
presented in Table 2.3 more pointedly illustrate how the supported
research time during the training years falls short in the mathematical
sciences. Table 2.4 shows that in 1987 only 18% of full-time mathe-
matical sciences graduate students received research-related support,
compared to the 45 to 50% of graduate students in the physical sci-
ences and engineering who had such support. Clearly, researchers in
training in the mathematical sciences still have a difficult time gaining
the depth and breadth of experience common among researchers in
other sciences.
The number of federally supported individual investigators in mathe-
matics, estimated as under 1800 in 1984,8 stood at about 1900 in 1989
(Table 2.5~. The 1984 Report discussed at some length (pp. 61-64) its
conservative estimates that there are at least 2600 highly productive
researchers in the mathematical sciences and that the field needs a
cadre of about 2600 fully active, federally funded researchers in order
to be balanced with other fields that use mathematics. Supporting an
additional 700 investigators not only would increase their individual
productivity, but would also encourage a larger fraction of mathema-
ticians to stay highly productive, thereby increasing the field s overall
productivity.
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RENEWING U.S. MATHEMATICS
TABLE 2.5 Number of Mathematical Sciences Research
Investigators Supported by Federal Grants and Contracts
in FY 1988
Agency
Research Investigators Supported
Department of Energy
Department of Defense
ONR
NSA
ARO
DARPA
AFOSR
Total non-NSF research
National Science Foundation
Total NSF research
Total federal agency count
Less duplicates
TOTAL INDIVIDUAL
INVESTIGATORS SUPPORTED
918
223
41
213
112
342
1 022b
1364C
2386
—480d
1906
Since the field's renewal efforts most critically depend on university
departments, 94 DOE laboratory investigators are omitted from this number.
iAll non-NSF investigator counts listed are 95% of agency figures
because those agencies advise that at least 5% of their grants are non-
research.
CThe NSF Division of Mathematical Sciences also supports 56 investiga-
tors for non-research activities such as conferences and other special
projects, who are omitted from the total shown.
abased on discussions with cognizant federal program officers, this
Committee conservatively estimates that at least 480 investigators appear on
more than one federal grant.
Acronym key: AFOSR = Air Force Office of Scientific Research, ARO =
Army Research Office, 0NR = Office of Naval Research, DARPA = Defense
Advanced Research Projects Agency, NSA = National Security Agency, NSF =
National Science Foundation.
SOURCE: Program officers' counts, personal communication.
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RESPONSE TO THE 1984 NATIONAL PLAN
The infrastructure of the mathematical sciences is composed primarily
of people, with funded investigators constituting the supporting struc-
ture for the field. Federal support for this core is the major infrastruc-
ture requirement of the discipline. However, other elements gradu-
ate research assistants, postdoctoral researchers, funds for travel, and
support for collaborative research are becoming increasingly impor-
tant now as the field unifies internally and expands externally, be-
cause those trends require greater breadth on the part of researchers.
Funding for computer time and for hardware fixed costs is a rapidly
growing requirement. The evolving needs of the infrastructure are
addressed by the second thrust of the 1984 National Plan as summa-
rized in Chapter 1.
Apropos of balance with other fields of science, the fraction of scien-
tists engaged in R&D in educational institutions who receive federal
support remains significantly lower in the mathematical sciences than
in chemistry or physics and astronomy. According to the 1987 NRC
survey of doctoral recipients,9 37% of the mathematical scientists in
educational institutions who identified R&D as their primary or sec-
ondary activity had federal support. Comparable figures for chemists
and for physicists and astronomers were 56% and 75%, respectively.
RESPONSE OF THE UNIVERSITIES
Few, if any, universities responded to the recommendations in the
1984 Report by conducting comprehensive reviews of the circumstances
of their mathematics departments and formulating plans for improv-
ing those circumstances as part of strengthening the health of the
discipline. It is difficult to say whether this was due to a lack of
strong initiative by individual departments, to inertia of university
administrations, or both. It is safe to say, however, that the general
pattern of reaction does not seem to reflect awareness of the serious
problems that must be overcome to achieve the renewal of the U.S.
mathematical sciences enterprise.
University administrations were also urged in the 1984 Report to act
as proponents of mathematical sciences research, interceding with
government agencies and seeking new government and industry ini-
tiatives that could benefit their mathematical sciences departments.
Again, very few universities appear to have responded.
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RENEWING U.S. MATHEMATICS
The universities that did respond were principally those where deans,
provosts, and presidents were made aware of the key issues by their
mathematical sciences department chairs, often acting in tandem with
a federal agency or with professional society representatives. This
committee's canvassing of departments indicated that such a response
was not the norm, however. Actions taken by university administra-
tions have included support for departmental computer hardware,
some start-up grants for new hires, and increased salary offers to
allow the departments to compete for top-quality faculty. These
measures have alleviated some of the strains on these departments.
University associations have taken no action in response to the recom-
mendations in the 1984 Report. The report, with its stark descriptions
of the circumstances of mathematics departments, was brought to the
attention of leaders in university associations but did not find its way
onto their active agendas.
RESPONSE OF THE MATHEMATICAL
SCIENCES COMMUNITY
The group that has done the most and yet still has the most to do is the
U.S. mathematical sciences community. It is useful to look at its
response to the 1984 Report at two levels, the response of its leader-
ship and the response of individual members of the community.
Response of Leadership
The mathematics community is engaged in a multistage, multiyear
critical examination of its roles in research, education, and public
policy. This ambitious undertaking, which will take several major
steps forward in 1990, began in 1980 when leading mathematicians
became alarmed over markedly decreased flows of talent and resources
into their field, and into science and technology more broadly. They
stimulated the development of a postdoctoral program and two new
research institutes supported by NSF funding. They mobilized the
professional societies in mathematics and enlisted the aid of the NRC
in analyzing the forces undermining the infrastructures of mathemat-
ics research and education, for the purpose of developing national
plans to reverse the trends of declining Ph.D. production, erosion of
federal support, deterioration within mathematics departments, in-
creasing student and public apathy toward mathematics, and growing
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RESPONSE TO THE 1984 NATIONAL PLAN
complacency within the field itself about some of its responsibilities.
The focus for the analyses was not the past, however; it was the
opportunities that mathematics provides for the future well-being of
science and technology, the nation, and its individual citizens.
The comprehensive assessment that these actions set in motion will
continue throughout the l990s and is generating in successive steps
the plans and organizational mechanisms needed at the national level
to renew and continuously maintain the vitality of this country's broader
mathematical sciences enterprise. In 1990 the mathematical sciences
community will have before it for widespread discussion organiza-
tional plans for its many future roles—in research, in precollege edu-
cation, in college and university education, and in relating its work to
various other communities. These discussions will be important ele-
ments of what is being called within the community the Year of Na-
tional Dialogue.
Highlights of the major steps taken by the mathematical sciences
community since 1980 to bring the dialogue to its present stage are as
follows:
1980 New postdoctoral fellowship program The NSF launches its
Mathematical Sciences Postdoctoral Research Fellowships pro-
gram to increase postdoctoral opportunities in mathematics.
1981 Research institutes The Mathematical Sciences Research Insti-
tute at the University of California-Berkeley and the Institute
for Mathematics and Its Applications at the University of Min-
nesota are created with NSF backing, further expanding the
NSF's emphasis on the infrastructure for mathematical research.
1981 The David Committee The NRC, the principal operating agency
of the National Academy of Sciences (NAS) and the National
Academy of Engineering, establishes a prestigious committee
of scientists and engineers, chaired by Edward E. David, Ir., to
review the health and support of research in the mathematical
sciences in the United States.
1982 The Browder briefing pane! At the request of the White House,
the NAS's Committee on Science, Engineering, and Public Pol-
icy (COSEPUP) establishes panels to brief the Science Advisor
to the President on research opportunities in six fields. First to
report is the Mathematics Panel, chaired by William Browder,
which points out that mathematics is flourishing intellectually
but that its research infrastructure is eroding rapidly.
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RENEWING U.S. MATHEMATICS
1983 The loins Policy Board for Mathematics The American Mathe-
matical Society (AMS), the Mathematical Association of Amer-
ica (MAA), and the Society for Industrial and Applied Mathe-
matics (SIAM) create a nine-member joint executive action arm,
the Joint Policy Board for Mathematics (JPBM), to begin imple-
menting the recommendations of the David Committee. The
JPBM emphasizes unity across the discipline, one of the five
basic recommendations to the mathematics community later
made by the David Committee.
Renewing U.S. Mathematics: Critical Resource for the Future The
1984 "David Report" highlights the flowering of mathematics
and its uses since World War II and calls attention to serious
signs of trouble: (1) the impending shortage of U.S. mathema-
ticians and (2) a marked imbalance between federal support of
mathematics research and support for related fields of science
and engineering. Based on a careful analysis, it calls for more
than a doubling of the FY 1984 federal support level and lays
out a ten-year implementation plan, with specific roles for
government, universities, and the mathematical sciences com-
munity.
1984 The Board on Mathematical Sciences In December 1984 the NRC
establishes the Board on Mathematical Sciences (BMS) to pro-
vide a focus of active concern at the NRC for issues affecting
the mathematical sciences, to provide objective advice to fed-
eral agencies, and to identify promising areas of mathematics
research along with suggested mechanisms for pursuing them.
The BMS has become an important mechanism for drawing to-
gether representatives of all the mathematical sciences.
1985 The Mathematical Sciences Education Board At the urging of the
mathematical sciences community, the NRC establishes in
October 1985 the Mathematical Sciences Education Board (MSEB)
to provide "a continuing national assessment capability for
mathematics education" from kindergarten through college. A
34-member board is appointed that is a unique working coali-
tion of classroom teachers, college and university mathemati-
cians, mathematics supervisors and administrators, members
of school boards and parent organizations, and representatives
of business and industry. This step reflects another of the
basic recommendations of the David Committee: strong in-
volvement of all sectors of the mathematics community in is-
sues of precollege education.
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RESPONSE TO THE 1984 NATIONAL PLAN
1985 Board on Mathematical Sciences' department chairs' colloquium—
An annual series of colloquia for chairs of mathematical sci-
ences departments, begun by the Science Policy Committee of
the AMS, is taken over and extended by the BMS. These suc-
cessful meetings enable department chairs to pool their ideas
and experience, focusing the ensemble into a valuable action
group for addressing problems common to many mathematical
sciences departments.
1986 TheJoint Policy Board on Mathematics, Washington, D.C., office—
The JPBM's Washington, D.C.J activities come to embrace
enhanced congressional contact and a vigorous public infor-
mation effort. An office of governmental and public affairs is
opened and it helps launch National Mathematics Awareness
Week, which is to become an annual April event. Contact with
the media and resultant coverage of mathematics are increased,
thus starting the long-term coordinated effort, recommended
by the David Committee, to increase public information and
understanding.
1986 Board on Mathematical Sciences' Science and Technology Week Sym-
posium This symposium, which is held annually at the NAS's
Washington, D.C., facility, highlights the role of research mathe-
matics in the sciences and engineering for an audience of scien-
tists and policymakers.
1987 Department of Defense advisory panels—The BMS advisory panel
to the AFOSR releases a report assessing the AFOSR mathe-
matical sciences program. The BMS Panel on Applied Mathe-
matics Research Alternatives for the Navy (PAMRAN) pro-
duces a report for ONR on selected research opportunities
relative to the Navy's mission.~° The BMS advisory panel to
the Mathematical Sciences Program of the NSA is formed.
1987 Project MS 2000 At the urging of IPBM, and under the super-
vision of the BMS and MSEB, the NRC launches a comprehen-
sive review of the college and university mathematics enter-
prise through the Mathematical Sciences in the Year 2000 (MS
2000) project. This is analogous to the David Committee's
review of the health and support of mathematics research na-
tionally.
1988 100 Years of American Mathematics The occasion of the centen-
nial of the AMS is used to develop a year-long series of related
events promoting discussion within the mathematical sciences
community of major issues it faces in research and education.
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RENEWING U.S. MATHEMATICS
1988 Office of Scientific and Public Affairs The American Statistical
Association's (ASA) public information office is established to
provide an interface between statisticians, the public, and the
federal government.
1989 Challenges for the 'posit The ASA report outlining significant
application areas ant! societal problems for statisticians to
explore in the l990s is released.
1989 Everybody Counts'2—The first BMS-MSEB-MS 2000 "report to
the nation" on the state of mathematics education in the United
States, kindergarten through college, based on the MSEB's
precollege work and on preliminary work of the MS 2000 proj-
ect. It emphasizes the potential of a modified mathematics
education for contributing to the national welfare and outlines
a national strategy for bringing about needed change in the
l990s.
1990 Renewing U.S. Mathematics: A Plan for the l990s This report,
which is a five-year update of the 1984 Report. It describes
emerging research opportunities and new challenges for gov-
ernment, universities, and the mathematical sciences commu-
nity to continue the program to renew U.S. mathematics.
1990 Second report to the nation The final report of the MS 2000
project, to appear near the end of 1990, will lay out a national
plan for revitalizing mathematics education in U.S. colleges
and universities.
Response of Individuals in the Research Community
The many mathematicians and statisticians who have peopled the
advisory committees to federal agencies over the last six years have,
by and large, exhibited the same bold imagination and concern with
critical examination of their field that are reflected in the decade of
initiatives just listed. They have continued to emphasize most strongly
the support of graduate student and postdoctoral researchers. This
strategy may be working: Ph.D. production appears to be turning
upward after many years of decline.
r
Not surprisingly, the beneficial effects of the strategy to improve the
research infrastructure are not experienced by many mathematicians.
What is seen in university mathematical sciences departments is that
the percentage of high-quality mathematicians with federal support is
lower than the corresponding percentage in other fields of science and
that the number of principal investigators supported has remained
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RESPONSE TO THE 1984 NATIONAL PLAN
inadequate over the last six years. Hardly surprising, therefore, is the
bona fide concern over the strategy to be followed in the next five or
six years. This concern is most prevalent among investigators doing
research in pure mathematics, the group for which the largest gap
exists between the number of highly qualified researchers and the
number with federal support.
NOTES
tWhat is now the Division of Mathematical Sciences at the NSF grew out of the
former Division of Mathematical and Computer Sciences, which was divided in 1983.
2Report of the Panel on Large-Scale Computing in Science and Engineering, P. D. Lax,
chair (National Science Foundation, Washington, D.C., 1982).
3NSF Division of Mathematical Sciences, personal communication. Amounts quoted
are in actual dollars and have not been adjusted for inflation.
Renewing U.S. Mathematics: Critical Resource for the Future, National Research Council
(National Academy Press, Washington, D.C., 1984), pp. 57-65.
5There are some 10,000 mathematicians and statisticians in the mathematical sci-
ences research community, of whom one-half are productive and about one-quarter
highly productive, according to criteria spelled out in the 1984 Report.
6This figure results from updating the 1984 estimated budget of $180 million with
the Higher Education Price Index published in Statistical Abstract of the U.S., 1990,
Bureau of the Census, U.S. Dept. of Commerce, Washington/ D.C.
Support has also been given to the mathematics of computation initiative, which is
not itemized in Table 2.1. The number of postdoctorate in 1984 was already double the
counts given in the 1984 Report (dating from 1980 and 1981) because of initiatives begun
concurrent with that report's preparation.
Renewing U.S. Mathematics: Critical Resource for the Future, 1984, p. 95.
9Survey of Doctorate Recipients project, National Research Council (personal com-
munication).
HA second PAMRAN opportunities report is scheduled for release in 1990.
Challenges for the '90s (American Statistical Association, Washington, D.C., 1989).
,2Everybody Counts: A Report to the Nation on the Future of Mathematics Education,
National Research Council (National Academy Press, Washington, D.C., 1989).
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