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al Introduction and Historical Perspective
Mathematics has become essential and pervasive in the U.S. workplace, arid pro
jections indicate that its use will expand, as will the need for more workers with a
knowledge of collegelevel mathematics. However, socioeconomic and demographic
projections as well as circumstances within the college and university mathematical
sciences system suggest that an adequate supply of appropriately educated workers is
not forthcoming. Development of mathematical talent will be impeded by the low
general interest in mathematics as a college major; the relatively small numbers of
minorities and women studying and practicing mathematics; a shortage of qualified
faculty to deal with huge enrollments in lowlevel courses and students with widely
varying levels of preparation; and the difficulty of maintaining the vitality of the mathe
matical sciences faculty.
The MS 2000 Project and the Scope of This Report
Because a healthy flow of mathematical talent is
important for the nation's welfare, the National Research
Council initiated in 1986 the project Mathematical Sci
ences in the Year 2000 (MS 2000) to assess the status of
college and university mathematical scier~ces and to design
a plan for revitalization and renewal. This report describes
the circumstances and issues surrounding the people in
volved in the mathematical sciences, principally students
and teachers. The description is not complete because
comprehensive data are not available, but most data that
are relevant and available are included and are adequate to
describe the circumstances in the mathematical sciences.
Two additional descriptive reports~ne on curriculum
and the other on resourcesare forthcoming,. Together
these three reports will form the basis for the the MS 2000
Committee's final report, which will contain recommen
dations for actions to achieve revitalization and renewal of
the college and university mathematical sciences enter
pr~se.
This report is concerned with all students of collegiate
mathematics. However, mathematics majors have a spe
cial role to play because they are the source of the new
faculty members necessary to renew and sustain the sys
tem. And increases in the need for mathematics in the
workplace in turn fuel a need for more academically skilled
workers. A dramatic demonstration of this need is the
'For the purposes of this report the discipline referred to as the "mathematical sciences'' includes mathematics, applied mathematics. and statistics.
A broader definition is generally used in the taxonomy of scientific disciplines. For a discussion of the mathematical sciences research community
see Reneu ing U.S. Mathematics s: Critical Resou' ~ e fo' the Future (National Academy Press. Washington. D.C.. 1984). pp. 7785. Computer science
is not a branch of the mathematical sciences. but its close ties with mathematics. both intellectually and administratively, have significantly affected
college and university mathematical sciences over the past two decades. This report does not attempt to describe circumstances in computer science,
but references tO computer science are necessary because of these ties and their effects.
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A Challenge of Numbers
doubling of the number of scientists and engineers in a
single decade (Figure 1.1~.
Understanding students and teachers in the mathe
matical sciences who they are, what they learn and teach,
and how they use what they learnrequires understanding
the vast and diverse system in which they work. The
mathematical sciences programs in U.S. colleges and
universities account for nearly logo of all collegiate teach
ing in the United States and nearly 3097c of all collegiate
teaching in the natural sciences and engineering. Eac
term, approximately 3 million students are taught by more
than 40,000 fulltime and parttime faculty members and
8,000 graduate teaching assistants in 2,500 institutions. To
better understand this system and how current circum
stances evolved, a review of events of the past 30 years is
helpful.
Three Roller Coaster Decades
For centuries, mathematics has been recognized as
interesting,, challenging,, and essential for the support of
science and engineering. Within this century, mathematics
has become much more broadly applicable and important.
Giant strides toward reco;,nition of its significance were
made during World War II. After World War II, U.S.
mathematicians branched out, studyin;, and developing
(in thousands)
4000 · .
3 000 r
2000
1000
1 976

11~ Engineers
· Scientists
1986
FIGURE 1.1 Total number of scientists and engineers.
SOURCE: National Science Board (NSB, 19871.
2
new areas in many directions very successfully. This
period of innovation and the concurrent expansion of
college and university mathematics programs positioned
mathematics as a key participant in the nation's emphasis
on science spurred on by the 1957 launch of Sputnik. Thus
began three decades of extraordinary changea decade of
expansion, followed by a decade of adjustment and depres
sion, followed by a decade of partial recovery.
The decade following Sputnik's launch was one of
expansion for U.S. mathematics. Statistics became more
widely recognized as a distinct discipline and began to
flourish. Then as now, to a slightly lesser extent most
of the research in mathematics and statistics was per
formed in universities. College enrollments increased,
faculties expanded, and positions were plentiful. The
number of bachelor's degrees in mathematics awarded
annually tripled, and the number of graduate degrees
increased fivefold in this decade. Support for specialized
research programs, which was available from federal
agencies for individuals, was ideally suited to the mathe
matical research mode.
In the late 1 960s, immediately following the dramatic
expansion of science and mathematics programs, the na
tion's interest and attention shifted to social issues. Al
though more students continued to enter colle ,e as access
to higher education expanded significantly, many came
without adequate preparation for college mathematics and
with questions about the relevance of learning any. Over
the 20year period from 1965 to 1985, college enrollments
doubled, and mathematical sciences enrollments more
than kept pace. However, most of the increase in mathe
matics enrollments was at the lower levels, with remedial
enrollments in high school mathematics taught in college
leading the way.
The surge in the numbers of decrees awarded in the
mathematical sciences in the late 1960s and early 1970s
and the lack of establi shed employment markets for mathe
maticians outside of academe created more degree holders
than there were jobs, especially at the doctoral level; in
addition, part of the response to increased enrollments in
mathematics courses was to let studentfaculty ratios in
crease. A depressed employment market resulted that
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Introduction and Historical Perspective
fasted nearly a decade, into the early 1980s. To some extent
this depression was spread across all science and engineer
ing fields. Statistics was an exception, with some modest White Males
increases in degrees granted and a better nonacademic 74%
employment market.
College and university mathematical sciences facul
ties were changing. Increasing responsibilities for teach
ing precalculus and highschoollevel courses, the predic
tion that college enrollments would soon decline, and the
perception that mathematics Ph.D.s were plentiful changed
employment practices on college faculties. The changes
included the creation of positions with heavy teaching
loads for fulltime faculty and the use of more parttime and
temporary teachers. Many faculty members had little time
and motivation for personal scholarship; some lapsed into
inactivity. Teaching introductory algebra and calculus to
students majoring, in other areas became more widespread
and restricted the independent growth of mathematics and
mathematicians. Some faculty members did not teach
what they thought about their research and also had
little enthusiasm or latitude to think about what they taught.
These forces reduced the attention to curriculum develop
ment and redo. In response to nationally articulated
goals in the mid1960s, the fraction of Ph.D.s on mathe
matical sciences faculties had increased significantly to
nearly 80% in fouryear institutions, but a seeming mis
match between training and duties prompted a reversal of
this effort. In particular, new doctoral degree holders,
educated for research, were mismatched with the teaching
positions available. Consequently, both teaching and
research suffered.
In research universities, graduate students, plentiful in
the 1960s, assumed a large share of the teaching responsi
bilities. Inflation on a weak mathematics employment
market and better opportunities in other areas such as
computer science spread quickly among U.S. students, and
the numbers choosing mathematics as a major area of study
began to decline. This decline was partially offset at the
graduate level by increases in the number of nonU.S.
students that, combined with the significant decline in the
number of U.S. students enrolled in mathematics, changed
/ _
~
_ ~
 _ ~
White Females
19%
NonWhite Males
5%
NonWhite Females
1%
FIGURE 1.2 Ph.D. degrees in mathematics, 19861987.
SOURCE: American Mathematical Society (AMS, 1987~.
to nearly one of two in 1988. This trend, coupled with the
heavy teaching burden carried by graduate students, cre
ated teaching problems across the country.
Factors other than the poor employment market also
reduced the number of mathematical sciences majors. One
factor was the predominance of white middleclass males
in the study and practice of mathematics. Relatively few
women and minorities were choosing mathematically based
careers and curricula, although more women, more blacks,
and more Hispanics were entering college. The fraction of
bachelor's degrees earned by women did increasefrom
about onethird of the total in the mid 1 960s to almost one
half by 1 98~but the increase was smaller at the master's
level and smaller still at the doctoral level (Figure 1.21.
That comparatively few blacks and Hispanics choose
mathematically based careers has continued to be the case.
The number of Native Americans choosing such careers is
small but does reflect approximately this aroup's share of
the total U.S. population, while AsianAmericans continue
to show a preference for these careers.
In the 1960s and 1970s, little attention was given to
creating employment opportunities for mathematical sci
entists in the nonacademic workplace. Academic employ
ment in a research environment was the dominant destina
tion for degree holders in mathematics, and these opportu
nities had diminished. Thus, not only were there rough
transitions to the workplace for those with bachelor's and
master's degrees, but Ph.D.s, too, were not suitably matched
the nonU.S. representation from about one of five in 1970 with the teaching jobs that were available in colleges.
3
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A Challenge of Numbers
Mathematical sciences enrollments in introductory
and remedial courses continued to increase in the 1970s,
fueled by added mathematics requirements in the curricula
of fields such as business and by shifts to majors that
required more mathematics. This development reflected
an increasing need for mathematics in the workplace, both
for professionals in other areas and for mathematical
scientists. Mathematics was emerging as more important
in professional education, achieving a new prominence
that complemented its centurieslong role in human intel
lectual development. Problemsolvina ability and adapta
bility dominated the requirements of new jobs. Said
another way, liberal arts education especially mathemat
ics education was becoming closer to professional edu
cation. However, the nonacademic employment market
for mathematical scientists continued to be poorly under
stood and was invisible to many.
Departments across the country met the increased
enrollments of the 1 970s with a variety of types of faculty
members and the same traditional courses, mostly because
they were busy and lacked resources (Figure 1.31. Many
temporary and parttime teachers were hired on an ad hoc
basis tenn after term. Thus began a dismantling of the
buildup to a high fraction of faculty with Ph.D.s that had
just been achieved. The responsibilities of departments
became more diverse and more difficult to carry out
(thousands)
2.000
1.500
1 .000
Advanced
_., ~:~ I, I: ,. ~ , ,: :' ''lo .... :'::': ::'
O:. ~ ~ ~ . ~ . ~ .: ~ :: :. I . ~ . ~ ..~ .: ... , ~, : ~. ::. I.: :, ~ I. ~ : ~.. ~: ..~. .,
' 'a 1 1 111 111 :1
965
1970 1975 1980 1985
FIGURE 1.3 Left: Total undergraduate enrollments in mathematical sciences departments. Right: Mathematical sciences
faculty at colleges and universities. SOURCE: Conference Board of the Mathematical Sciences (CBMS, 1987).
because of heavier involvement in coordinating activities,
fewer experienced and involved teachers, large remedial
and placement problems' and fewer mathematics majors.
No other collegiate discipline teaches as many students
with such widely differing levels of preparation as does
mathematics, and most of the students are expected to use
the mathematics in subsequent courses. An overwhelming
combination of problems of collegiate teachingunmoti
vated and underprepared students, unenthusiastic teachers,
language problems in the classroom, outdated and irrele
vant curricula and courses, large classes, heavy teaching
loads, too few resources, and little use of modern technol
ogycame together in the 1 970s and resonated in mathe
matics classrooms across the United States.
By the early 1980s, the number of degrees awarded
annually in the mathematical sciences had fallen by nearly
50% at all three levels (Figure 1.41. Occurring simultane
ously with the decline in the numbers of degrees awarded
were increases in enrollments and in reliance on parttime
faculty. Belatedly, institutions decided that the high mathe
matical sciences enrollments would persist, and they began
to employ regular faculty members. By this time there
were too few U.S. citizens among the new doctoral degree
holders to meet the demand; indeed, there were overall
shortages of candidates. There were (and are) no surplus
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ . . Hi. ~ .
pUU1b U1 Illa~l~rnaucal sciences tn.~.s no large number
40,000
30.000
20.000
1 0~000
o
1970
1980 1985
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Introduction and Historical Perspective
BOX 1.1 Computer Science
Computer science has developed since World War I} from roots in mathematics and electrical engineering.
It has become a separate academic discipline within the past two decades and has developed its own sources of
students and federal fundin;, for research. (See the 1984 David Report (NRC, 1984) for a fuller analysis.)
Computer science is not considered to be a part of the mathematical sciences, and that is the position taken
throu Shout this report. However, older reports on the mathematical sciences may include computer science data,
and computer science and mathematics continue to be administered by the same unit in most colleges and
universities (see Box 3.3~. Because of these historical, administrative, and intellectual ties, the emergence and
rapid growth of the discipline of computer science have had a significant effect on the mathematical sciences. At
points in this report some of these effects are conjectured, but only the effects of computer science on the
mathematical sciences are considered. No attempt is made to describe the conditions in computer science.
Nevertheless, the grouping of computer science with the mathematical sciences in many college and university
departments and the dual teaching roles of many faculty members are facts.
The 1985 CBMS Survey (Box 3.3) concluded that in fouryear colleges and universities, half (49%) of all
computer science course sections were taught in departments with mathematics and the other half (51 Tic) in com
puter science departments. (This breakdown did not include courses in computing, taught by many units in busi
ness and engineering, for example.) Thus approximately 270,000 students enrolled in computer science courses
were taught in mathematics departments in fall 1985. This compares to estimated enrollments of 1,827,000 in
mathematics and statistics courses in these departments in fall ~ 985. Thus approximately 13% of the teaching, in
these departments was in computer science (the 1985 Annual AMS Survey results give an estimate of 10% rather
than Who, but the 1984 Annual AMS Survey yielded 12% see Box 3.2~.
In twoyear colleges in 1985, approximately 10% of the 1 million students enrolled per term were enrolled
in computing and data processing.
The 1985 CBMS Survey listed 27,500 bachelor's degrees awarded by departments of 'mathematics" and 400
awarded by departments of statistics in the period July 1984 to June 1985. Of these 27,500 degrees, 40% were
awarded in computer science (8,700) or jointly with computer science (2,5003.
The 1985 CBMS Survey reported that of the 3,750 Ph.D.s on the nation's fulltime computer science faculty,
41 % had their doctorates in mathematics. Of the 2,200 Ph.D.s on the parttime computer science faculty, 61 % had
their doctorates in mathematics. Of the total fulltime computer science faculty, 35% had their highest decrees in
mathematics, and of the total parttime computer science faculty, 42% had their highest degree in mathematics.
Of the 5,650 members of the fulltime computer science faculty, 2,O50 were employed by 'mathematics'
departments. Of the 5,350 members of the parttime computer science faculty, 3350 were employed by
'mathematics" departments. This translated to 3,150 fulltime equivalents (FTE) offaculty members teaching one
half of the computer science sections in "mathematics" departments and 4,250 FTE of faculty members teaching
the other half in computer science departments. It is noted that computer science departments are concentrated
in the universities where teaching loads are lower.
s
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A Challenge of Numbers
of postdoctoral positions and no candidates from other
disciplines who fit the faculty needs. Ad hoc hiring
practices continued, partly because of a lack of suitable
candidates for regular faculty positions.
From another perspective, by 1970 a large infrastruc
ture of mathematical sciences graduate study and research
had been established across the country and was spread
through more than lSO universities. Success in research
was clearly the principal criterion for respect within this
community, and the research environment was clearly the
best in the world. However, federal support formathemati
cal sciences research became less available, as did other
governmental and institutional support (NRC, 1984), and
the employment market was very depressed. There were
many discouraged faculty members and persons seeking
faculty positions. Many defected to other areas. By 1980,
the mathematical sciences infrastructure was clearly weak
ening.
During the 1970s and continuing until the present,
many departments' programs, especially at fouryear col
leges, contained a mixture of mathematics, statistics, and
computer science. Planning, was confounded further by
conflicting trends within these three disciplines. Computer
science was booming, statistics was growing steadily, and
mathematics was struggling to adjust to a depressed em
00000
0000
000 ~
he..
1~^
00
1950 1956 1962 1968 1974 1980 1986
o
Coo ~
Too 00
° 04C.°0°
c, ~ .e
,~ ,G, ~
Bachelor's
Master's
FIGURE 1.4 Mathematical sciences degrees awarded
SOURCE: National Center for Education Statistics (NCES,
198Sa).
ployment market, fewer majors, and huge enrollments in
introductory courses.
Computer science was emerging as a separate aca
demic discipline. Many computer science programs had
been formed within mathematical sciences departments,
and the number of majors and the course enrollments were
rising rapidly. Since there were far too few people with
academic degrees in computer science to fill the available
faculty positions and because of computer science's close
connections to mathematics, many mathematics faculty
members were able to cross over to computer science. And
students who once might have been mathematics majors
began to choose computer science as a major. By 1988
separate computer science departments had been estab
lished in most large universities, but in smaller institutions
the hybrid department was still the rule. Approximately
half of all computer science enrollments continue to be in
these combined departments, thus competing for faculty
time and energy and the interest of the students (see BOX
1.1~.
While much of the ferment over the past two decades
also affected other academic disciplines, especially the
sciences and engineering, the impact on the mathematical
sciences was more extreme. The declines in the numbers
of mathematics degrees awarded were relatively larger,
and the declines in the numbers of majors in other science
and engineering disciplines turned around much more
quickly in the early 1980s. Mathematics has been the
slowest field to recover although there has been some
recoveryone reason being the close ties between mathe
matics and academe. No other science or engineering
discipline depends as heavily on academic employment for
its graduates, especially those with doctorates, as does
Doctorate mathematics. Consequently the health of the mathemati
cal sciences enterprise is very closely tied to the health of
education, especially higher education.
By 1982 a number of serious problems posing a risk to
the general health of mathematics had become apparent.
The numbers of degrees awarded were near the lowest;
course enrollments were the highest, with the heaviest
concentration at the lower levels; teaching loads had in
creased dramatically; federal support for research was at a
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Introduction and Historical Perspective
BOX 1.2 Sources of Data
Several sources of data were used to compile this report. The main sources include:
· American Mathematical Society (AMS);
· Conference Board of the Mathematical Sciences (CBMS);
· National Center for Education Statistics (NCES) of the Department of Education;
· National Research Council (NRC); and
· National Science Foundation (NSF).
In general, the mathematical professional societies' (AMS and CI3MS) data relate only to the field of mathe
matical sciences and do not allow any comparisons across fields. When field comparisons are made, the sources
of data are usually the NRC, NSF, or NCES. Inconsistencies do arise, partly because of different survey
populations. For instance, some data on mathematical sciences include data on computer science. Where possible
in this report, mathematical sciences data have been separated from computer science data. It is not feasible to
reconcile or explain all the differences Analysis of data in detail reveals differences that cannot be reconciled,
but the implications of these differences appear to be minor. Nevertheless, the different sources have beers found
to be consistent enough to depict the general circumstances in the mathematical sciences enterprise.
The tables in the text are numbered consecutively within each chapter, as are the figures (mostly graphs).
Tables giving the data used to construct the figures presented in this report are included in the report's appendix
and are numbered to correspond to the relevant text chapter rather than to a particular text figure or table. For
example, Table A4.3 is the third table in Appendix Tables that contains data for Chapter4, while Table 4.3 is simply
the third table in the text of Chapter 4. The sources of the information shown in the tables and figures are given
according, to the standard referencing system used throughout the report.
very low point, especially in core areas of mathematics;
and faculty morale was frequently low. Responding to the
expansion of the previous two decades and the associated
problems had talcen most of the faculty time and energy.
During that period, whole new areas of mathematical
sciences had developed, including operations research,
discrete mathematics, mathematical biology, statistical
design and analysis, and nonlinear dynamical systems. In
fact, the term "mathematical sciences" itself had become a
part of the taxonomy of science. In spite of these new
developments in the mathematical sciences, new applica
tions, and new opportunities for using technological ad
vancements, the teaching of mathematics had essentially
not changed. Both the curricular content and its delivery
had remained static. Mathematical sciences departments
were not able to simultaneously cope with enoImous
instructional loads, maintain excellence in faculty scholar
ship, and allocate resources to innovations or even known
improvements. The forces at work were too diverse and
too disparate.
National Efforts Toward Renewal
In 1982 the mathematical sciences community began
to address these problems on a national level. In 1984 the
National Research Council (NRC) published Renewing
U.S. Mathematics: Critical Resource for the Future (re
ferred to as the David Report; NRC, 1984), documenting
7
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A Challenge of Numbers
the weakening of federal support for research in the mathe
matical sciences. That report was the first of a series of
efforts within the NRC and in professional societies to
assess the health of the mathematical sciences and to
design a plan for renewal. The NRC project Mathematical
Sciences in the Year 2000 (MS 2000), of which this report
BOX 1.3 Statistics
The discipline of statistics is included in this
report as a part of the mathematical sciences, pnnci
pally because statistics has an intellectual base in
mathematics, mathematics students are the principal
source of statistics graduate students, and significant
federal funding for academic research that develops
fundamental statistical concepts and methods comes
from the "mathematical sciences" units of federal
agencies (NRC, 1984~.
Degree programs in statistics are mostly gradu
ate degree programs. The number of students en
rolled in statistics and the number of undergraduate
statistics majors are much smaller than the analo
gous numbers for mathematics. In major universi
ties, statistics usually constitutes a separate aca
demic department, but in other institutions statistics
is likely to be taught in the same unit as mathematics
(see Box 3.3~. In addition, statistics courses are
taught in a variety of administrative units, including
business, engineering, medical sciences, and social
sciences.
Partly because of the close administrative and
intellectual ties between statistics and mathematics,
much of the data on statistics in colleges and univer
sities in this report is a;,gre~,ated with analogous data
on mathematics. Some disag~regation is possible
and has been done when possible in this report.
However, in general, the data are dominated by those
for mathematics, and caution must be used in draw
ing conclusions about statistics from the aggregated
data.
8
is a part, was initiated in 1986. MS 2000 is an effort to
assess the state of college and university mathematical
sciences and to design a national agenda for revitalization
and renewal. The events of the past three decades, detailed
here, lend urgency to this effort. A major step in broaden
ing the audience for this message and including all of
mathematics education was taken by the NRC in publishing
Everybody Counts early in 1989 (NRC, 1989~. The issues
and implications identified in this report and the two
additional descriptive reports on curriculum and resources
will assist the MS 2000 Committee in presentin;, an a ,enda
that will ensure a healthy flow of mathematical talent into
the next century.
Contents of This Report
Fundamentally this report concerns students and teach
ers. The events and forces described above indicate the
complexity of this simplesounding enterprise and how the
current predicaments have developed. Box 1.2 describes
the sources of the data used to compile this report and
explains the relationship between the text tables and fi ,
ures and the additional data presented in the report's
Appendix Tables. Box 1.3 details characteristics of the
statistics component of college and university mathemati
cal sciences and describes the the context in which infor
mation in that area is provided. Chapter 2 describes in
broad strokes the larger communities of the U.S. labor
force and higher education, which both encompass the
mathematical sciences enterprise. Chapter 3 describes the
major components of, trends in, and utilization of college
and university mathematical sciences. Chapter 4 focuses
on mathematical sciences majors, both undergraduate and
graduate. Chapter 5 describes mathematical scientists in
the workplace; colleges and universities are a principal
topic, since academe is still the dominant employer of
mathematical scientists. That situation, however, is chang
in=. The increased use in various professions of the mathe
matical sciences adds to their traditionally important uses
in everyday life, civic activities, and our rich intellectual
culture.