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Employment Opportunities for
GRINNELL COLLEGl
LIBRARY
WOMEN
MATHEMATICIANS
and STATISTICIANS
3
33
-
/
WOMEN’S BUREAU BULLETIN No. 262
U. S. DEPARTMENT OF LABOR
James P. Mitchell, Secretary
WOMEN'S BUREAU
Mrs. Alice K. Leopold, Director
rvo-
Grinnell College
LIBRARY
M°o. i
'
Sh
',i. If >I
UNITED STATES DEPARTMENT OF LABOR
James P. Mitchell, Secretary
WOMEN'S BUREAU
Mrs. Alice K. Leopold, Director
Employment Opportunities
for
WOMEN
MATHEMATICIANS
and STATISTICIANS
Women’s Bureau Bulletin No, 262
U. S. GOVERNMENT PRINTING OFFICE
WASHINGTON : 1956
For sale by Superintendent of Documents, U. S. Government Printing Office
\Vashington 25, D. C. Price 25 cents
FOREWORD
This review of the current demand for women in mathematics and
statistics, with its estimate of the future outlook, has been prepared
with the help of many individuals, organizations, colleges, and
employers.
Special thanks are due to Dr. Howard Meyerhoff, Executive
Director, Scientific Manpower Commission, whose interest in the
subject prompted us to undertake to bring up to date our information
in this field and whose cooperation in making data on women available
from the Commission’s surveys made our task easier. In a similar
way we were aided by the cooperation of Dr. Alan Waterman, Director
of the National Science Foundation, and of Dr. Leon W. Cohen, Dr.
Howard F. Foncannon, and Miss Eleanor Rings of his staff, who made
available preliminary tabulations on women from the Foundation’s
1954-55 survey of mathematicians.
The bulletin, which supersedes an earlier Women’s Bureau publica
tion on the same subject, was prepared and written by Shirley Montag
under the supervision of Marguerite W. Zapoleon.
We hope that it will help teachers, counselors, and others who assist
young women—and mature women, too—in their occupational
planning and that it will have an effect on what appears to be a serious
national shortage.
Alice K. Leopold,
Director, Women’s Bureau.
iii
Acknowledgments for Illustrations
For the illustrations, some of which were taken especially for this
bulletin, the Women’s Bureau is indebted to the following:
Anacostia High School, Washington, D. C. (fig. 6);
Bennington College (fig. 1);
Goucher College (cover picture and fig. 3);
International Business Machines Corporation (fig. 1);
National Bureau of Standards (fig. 4);
Radcliffe College (fig. 5);
Royal Neighbors of America (fig. 2);
University of Michigan (fig. 8);
Westinghouse Electric Corporation (fig. 7).
Two mathematics students test some calculations in tn'sonometry on the demonstration
slide rule in their classroom (cover picture).
IV
CONTENTS
Page
Findings
VI
Who are mathematicians and statisticians?
Number of women mathematicians and statisticians_____________________
Characteristics of surveyed groups ______________________
Demand for women mathematiciansand statisticians in 1955_____________
In educational institutions
In government
10
In industry__________________
In other employment__________
Future demand_______________________________________ __________________
For mathematicians,__________________________________________________
For teachers of mathematics__________________________________________
For statisticians
20
Future supply;__________________________________________________________
Preparation needed
24
For mathematicians
24
For teachers of mathematics
25
For statisticians
26
Personal characteristics needed__________________________________
Trying out for the field____ _ _
Obtaining employment___________
Advancement
Earnings
Working conditions__________________ ___,___________________
Organizations
33
. Special groups of women
34
Appendix
35
Definitions^
Sources to which references are made
36
Tables:
1. Education of employed women mathematicians in the National
Register of Scientific and Technical Personnel, 1954—55____
2. Specialties of employed women mathematicians in the National
Register of Scientific and Technical Personnel, 1954-55____
3. Education of 177 women statisticians, 1952 _______________________
4. Employment specialization in 1952 of women graduated with a
bachelor’s degree in mathematics in 1951_________________________
5. Type of employer of women mathematicians in the National Register
of Scientific and Technical Personnel, 1954-55___________________
6. Women mathematicians and statisticians among Federal civilian
employees, by agency, August 31, 1954
7. Women mathematicians employed in private industry, by type of
industry, 1953
8. Earned degrees conferred by higher educational institutions in
mathematics, 1947-48 to 1954-55
9. Median annual salaries paid junior-high-school and high-school
classroom teachers in urban school districts, by population size,
1954-55
2
2
3
5
8
13
16
16
16
19
22
28
29
30
30
31
33
35
4
4
5
7
8
11
14
22
32
v
FINDINGS
On the basis of the analysis of current information on mathemati
cians and statisticians presented in this bulletin, the Women’s Bureau
finds that:
1. More women mathematicians and statisticians are currently
needed, and interesting jobs await those trained at the bach
elor’s degree as well as graduate levels.
2. Young women in high school should be encouraged to try math
ematics and if they have the qualifications for success in math
ematics and statistics should be encouraged to prepare for
these fields; anticipated shortages make the long-run outlook
exceptionally favorable.
3. Young women who combine the qualifications for teaching with
ability in mathematics should be encouraged to teach, at least
part time, since in teaching they can magnify their contribu
tion to the Nation’s progress.
4. Mature college women who have majored in mathematics, pos
sess the personal qualifications for teaching, and have time
available to work, should prepare themselves through refresher
courses in mathematics and education for teaching positions,
if they live in one of the many communities experiencing or
anticipating a shortage of mathematics teachers.
VI
Employment Opportunities for
WOMEN MATHEMATICIANS AND
STATISTICIANS
“Never before in the history of the world have there been such
wonderful opportunities for mathematics and mathematicians.”
This statement was made by a representative of a manufacturer of
electronic calculators at the first conference on training personnel
for the computing-machine field, held in 1954. “In a few years,” he
Figure 1.—A programer whose college major was mathematics operates a magnetic
drum data-processing machine.
said, his company will have “as many opportunities for mathemati
cians with advanced training as the whole country could use a few
years ago” (5).* And a Women’s Bureau comparison of information
from selected industrial firms in 1946-47 and in 1953 indicated that
the number of women employed as mathematicians in industry had
doubled between the two dates.
Evidence presented in this report backs the conclusion that mathe
matics is a flourishing field—and that its growth has made it an
opportunity-filled area for women.
•Numbers in parentheses indicate references listed in the appendix.
(See p. 36.)
1
2
Employment Opportunities for
Who ARE Mathematicians and Statisticians?
**
Professional mathematicians work in higher mathematics. The
pure mathematician works with mathematical laws and principles,
pursuing his “self-motivated progress along dimly discernible paths
of growth toward intellectually satisfying goals” (12). The applied
mathematician directs the results obtained by his colleagues in pure
mathematics to problems in business, government, industry, engi
neering, and the natural and social sciences. The utility of mathe
matics as a tool in other fields of endeavor has given applied mathe
matics new emphasis. This is the area in which opportunities have
developed most rapidly since the Women’s Bureau published its first
report on the Outlook for Women in Mathematics and Statistics
nearly 10 years ago (22). Programers who set up the problems for
the new electronic calculators work in applied mathematics.
Statistics is described as a branch of applied mathematics (6).
Mathematical statisticians who investigate and develop statistical
theory and method are highly trained mathematicians. Other
statisticians use statistics as a tool to further an ever-increasing range
of activity in economics, sociology, finance, public health, the physical
and biological sciences, personnel administration, advertising, opinion
polling, education, and certain manufacturing industries like aircraft.
Especially on higher levels, the same individual may function as both
mathematical and applied statistician.
Formal professional standards are most specific for actuaries.
Members of this rapidly growing profession apply the theory of
probability to keep insurance plans, including employee-benefit and
workmen’s compensation plans, on a financially sound basis.
Assistants to professional mathematicians in these fields are usually
college-trained workers, variously known as mathematical aids or
assistants, statistical technicians, research assistants or clerks, or
statistical machine operators; they are included in this report. Al
though their primary preparation has likewise been in mathematics,
engineers and engineering aids are discussed in a separate bulletin on
engineering (Women’s Bureau Bulletin No. 254).
Teachers of mathematics, at the college and high-school levels,
needed now more than ever to instruct future mathematicians and
scientists, are of course included in this report.
Number of Women Mathematicians and Statisticians
There were about 20,000 mathematicians in the United States in
1955, according to a preliminary estimate of the National Science
Foundation. Possibly 1 out of 8 or 10 were women. This includes
"See appendix for Dictionary of Occupational Titles definitions.
Women Mathematicians and Statisticians
3
mathematical statisticians, but not other statisticians of whom there
were possibly 20,000, including some 7,000 women. The Bureau of
Labor Statistics uses an estimate ranging from 10,000 to 20,000.
Among the 1,600 to 1,800 professional actuaries, there were fewer
than 100 women. The National Science Foundation estimate also
does not include approximately 29,000 high-school teachers who were
instructing in mathematics full time and another 35,000 who were
instructing in mathematics and other subjects as well, according to
estimates of the United States Office of Education. Roughly 1 out of
3 of these, high-school mathematics teachers were women.
ISliSS
(Sill
imam
Figure 2.—A woman actuary in an insurance company discusses calculations with an
assistant actuary and an actuarial assistant.
Characteristics of Surveyed Groups
The characteristics of women mathematicians included in the
National Register of Scientific and Technical Personnel in 1954-55
who reported their employment offer a clue to the specializations
and functions of an experienced group of women mathematicians.
This registered group are more highly trained than many of the
younger women mathematicians who have not had as much opportu
nity to obtain a higher degree, and who are believed to be markedly
underrepresented in the Register, which distributed its questionnaires
for registration through professional societies. The median age of the
404231—57------- 2
Employment Opportunities for
4
women included in the Register was 40 years, and 8 out of 10 had
received either the master’s or the doctoral degree. (See table 1.)
Table 1.—Education of employed women mathematicians in the National Resister of
Scientific and Technical Personnel, 1954-55
Educational level
Number
Total reporting both employment and level of
education. .
Doctor’s decree .. .
Master’s degree__ ______ __
Bachelor’s degree
_
Loss than bachelor’s desrree
_
..
_____
. . .
Percent
449
100. 0
165
197
86
i
36.
43
19
0.
7
9
2
2
Source: National Science Foundation (preliminary unpublished data).
Four out of ten of these women mathematicians reported themselves
as general mathematicians (see table 2), most of whom teach under
graduate college mathematics. Roughly 1 out of 10 women mathema
ticians were in each of the following specialties: analysis; applied
mathematics; statistics, probability, and stochastic processes; and
algebra and number theory, with a somewhat smaller proportion in
geometry and topology. The largest group among the women
employed in private industry who reported their specializations were
those in numerical analysis, classified under applied mathematics in
table 2. This was the only group of specialists among women mathe
maticians in which the employment in industry was higher than it
was in educational institutions. Algebra and numerical analysis
provide important theoretical background for programing in
electronic calculating.
Table 2.—Specialties of employed women mathematicians in the National Register of
Scientific and Technical Personnel, 1954-55
Specialty
Total reporting employment and specialty
General mathematics __________ _
_
Analysis
_ _
_
______ _
Applied mathematics___
_ __________
Statistics, probability, and stochastic processes ___
_
Algebra and number theory.
______ __
_
Geometry and topology .. .
_ ______
Other mathematical specialties. .
_______________
Source: National Science Foundation (preliminary unpublished data).
Number
Percent
471
100. 0
191
48
48
47
46
32
59
40.
10
10.
9.
9.
6.
12.
6
2
2
9
8
8
5
Women Mathematicians and Statisticians
5
The close relationship of mathematicians to physical scientists
and engineers is indicated in an earlier survey in which mathematicians
reported their second interests most often in physics, electronics,
or engineering (19). Secondary-school mathematics teachers, too,
are often expected to add general science to their schedule, with social
studies the next most likely assignment (14)Women statisticians covered in a 1952 survey of social scientists
were similar to the women mathematicians reported in the Register
in age, but different in educational level. Their median age was
about the same, 41 years, but a much lower proportion of the statis
ticians had the doctoral degree and a much higher proportion had the
bachelor’s degree only. (Compare tables 1 and 3.)
Table 3.—Education of 177 women statisticians, 1952
Educational level
Number
Total reporting level of education- ..__ __
Doctor’s degree__
_ _
Master’s degree .
Bachelor’s degree
__ __
Less than bachelor’s degree_______
_
.......
____
_
_
Percent
177
100. 0
17
82
72
6
9.
46.
40.
3.
6
3
7
4
Source: U. S. Department of Labor, Bureau of Labor Statistics, and the U. S. Department of Defense (21)
Specializations of women statisticians were not reported separately
in the study, but among men and women combined, there were almost
no generalists and by far the leading specialty was methodological
techniques, in which almost 60 percent were engaged. Business and
management, economics and economic theory, and sociology and the
social sciences followed, in that order. Only 4 percent worked in the
physical sciences. Since the questionnaire mailing list used in this
survey was compiled from societies in the social sciences and the
humanities, including the American Statistical Association, however,
there is probably a marked underrepresentation of physical scientists.
A survey made in 1948, with a list compiled primarily from American
Men of Science, found biology and psychology the most frequent
second fields of statisticians, after statistics (19). A 1950 estimate
set the number of public health statisticians in the country at 400, or
about 2 percent of all statisticians (1).
Demand for Women Mathematicians and Statisticians in 1955
A woman mathematician employed as a consultant at the United
States Bureau of Standards, and described by her male colleagues as
6
Employment Opportunities for
one of the outstanding workers in her field, is among the many who
report that more than formerly women are finding jobs on all levels
and in all areas of mathematics. This contrasts with the traditional
pattern of most women mathematicians as teachers, most of the
remainder in lowest level positions, and only a few at high levels.
Women mathematicians may not be as much sought as they were
during the war, when every mathematics major had her choice of
many jobs—one woman’s college, for instance, reported a choice of 25
or more jobs in industry and government for each mathematics major
(13). However, the demand exceeds the supply and is growing. The
general impression which might be formed from a superficial survey of
employment literature is that, until recently, many women with the
B. A., or even the M. A., in mathematics did routine work only,
although some had opportunity for varied and interesting assignments.
The advent of the electronic calculators, for which programing is
not routine, has opened a new field for B. A. mathematicians, although
workers with advanced degrees are preferred where available. It is a
fact that many industrial laboratories employ only women for their
computing groups; others employ a high percentage of women. In
one instance, for example, 67 percent of the programing staff are
women—many of them with only a bachelor’s degree (3).
The diversity of job possibilities among which the woman graduated
with a bachelor’s degree in mathematics today may choose is indeed
impressive. Kecent surveys verify the fact that a very high propor
tion of women with mathematics as a major are utilizing their mathe
matics training on their first jobs.
Of the women graduated as mathematics majors by nine eastern
women’s colleges in 1954 or 1955, nearly 5 out of 7 were employed after
graduation in work connected with mathematics. Placement direc
tors report that the others were not employed in mathematics as a
matter of preference rather than lack of opportunity. The largest
number of these 53 employed graduates were teaching mathematics,
or were working as actuarial trainees or as engineering aids. Five
were computers and two were programers. Other positions held
included those of draftsman, technical writer or editor, market re
searcher, research assistant, statistical analyst, utilities technician,
bank trainee, and trainee in biostatistics.
The number of business and teaching positions among these recent
graduates suggests that many of the mathematics majors reported in a
National Science Foundation survey of 1951 college graduates
employed in 1952 in business and commerce and in education were
probably utilizing their mathematics training directly. Table 4
shows that f out of 3 of the women graduated with a bachelor’s degree
in mathematics in 1951 who reported their employment specialization
Women Mathematicians and Statisticians
7
in 1952 were working in mathematics, science, or engineering. Another
1 out of 3 were in educational work and about 1 out of 5 were in busi
ness and commerce.
Table 4.—Employment specialization in 1952 of women graduated with a bachelor's
degree in mathematics in 1951
Employment specialization
Number
Total reporting employment specialization. .
Education _ __
_
..
Mathematics __ _____ _____ __
_
Business and commerce.
_
Natural science, except mathematics.
Engineering
__
_
„___ _
All other fields
. .
_
.
Percent
.
178
100. 0
_ _ . .
_. . _
64
40
37
11
7
19
35.
22.
20.
6.
3.
10.
9
5
8
2
9
7
Source: U. S. National Science Foundation. Education and Employment Specialization in 1952 of June
1951 College Graduates. 1955.
Women mathematicians are usually welcomed to higher level
positions, too, but it is reported that their qualifications must be much
better than those of the available men. The demand is such, however,
that there frequently are no men available. There are even openings
for which there are no women applicants with required qualifications.
In statistics it is said that failure to realize or accept opportunities
awaiting them, rather than discrimination, accounts for the compara
tively small number of women doing professional statistical work (11).
Less than 2 percent of the men and women statisticians covered in a
1952 survey were unemployed (21).
Unlike mathematicians, statisticians find their employment op
portunities most numerous in private industry and government. Only
1 of 5 covered in the 1952 survey was working in an educational
institution (21). And many of those employed by educational insti
tutions were in research rather than in teaching. Among statisticians,
research, operational, and administrative work is more common than
teaching. The largest demand for women mathematicians, as indi
cated by the numbers employed, is still in educational institutions,
although private industry, government, and other avenues of employ
ment are channeling off an increasing number of new graduates each
year, especially at the bachelor's level. Seven out of 10 of the women
mathematicians in the National Register of Scientific and Technical
Personnel in 1954-55 who reported their employment—an experi
enced, highly trained group as noted before—were working in educa
tional institutions, most of them in colleges and universities. (See
table 5.)
8
Employment Opportunities for
Table 5.—Type of employer of women mathematicians in the National Register of
Scientific and Technical Personnel, 1954-55
Type of employer
Number
Percent
Total reporting employment._____
439
100. 0
Colleges and universities
__ _
Other educational institutions .
Private industry __ __ _
Federal Government .
...
State or local government. ...
Nonprofit foundations or organizations
281
31
76
40
1
10
64.
7.
17.
9.
.
2.
0
1
3
1
2
3
Source: National Science Foundation (preliminary unpublished data).
In educational institutions
Teachers of mathematics are needed to instruct not only future
mathematicians but also engineers, scientists, statisticians, and the
many who use mathematics in their daily work. Statistics on mathe
matics teachers from the census of 1950 showed about 5,600 college
professors and instructors of mathematics, including about 1,100
women. This was a smaller number than the 1,700 women estimated
by the Women’s Bureau to be college teachers of mathematics in 1947
(22).
Statistics from these two sources are not exactly comparable, but
evidence of a decline in the proportion of women mathematicians who
are teaching mathematics in colleges is indicated by a comparison of
the numbers in the 1954 -55 and 1951 National Scientific Register.
Although broader coverage was achieved in 1954-55 and the two
groups should not be compared exactly, a considerably smaller pro
portion of the women mathematicians in the National Register of
Scientific and Technical Personnel in 1955 were teaching as compared
with those reached by the National Scientific Register in 1951 (25).
The proportions of all registered mathematicians, men and women, in
college teaching also declined markedly between 1951 and 1954-55, as
demands for their services increased in industry and government.
The need for a higher degree in this type of work is reflected in the
educational level of the registered women mathematicians who were
teaching in 1954-55. Only 5 percent were without a graduate degree; the
others were divided about equally between those with a master’s and
those with a doctor’s degree.
The amount of research being conducted at colleges and universities
has resulted in increasing the number of nonteaching opportunities for
mathematicians on college campuses. In colleges and universities in
Women Mathematicians and Statisticians
9
1954-55, for every six women mathematicians working as teachers
there was one engaged primarily in research. It has also increased
the opportunities for teacher participation part time in large research
projects. In addition, there were widely scattered opportunities for
women in colleges to do technical writing, design, consulting, or ad
ministrative work in mathematics.
Figure 3.—While her mathematics professor supervises, a
college junior majoring in mathematics-chemistry learns
how to save time by using the calculator on a problem
in intermediate calculus.
The demand for high-school teachers of mathematics is large and
growing. Reports from 29 States, the District of Columbia, Hawaii,
and Puerto Rico to the National Education Association Research
Division showed that in 1954-55 only 1,047 persons were graduated
in those areas with qualifications for certificates as high-scliool teachers
of mathematics and that of these roughly one-third did not enter
the teaching profession after graduation. Positions that were filled
September 1955 by new teachers of mathematics in these areas, on the
other hand, numbered 1,919 (id).
10
Mathematicians employed by educational institutions, even at the
college level, tend to be relatively unspecialized within mathematics.
Of women mathematicians employed by colleges and universities, 47
percent consider general mathematics their field of highest compe
tence, with algebra, geometry, analysis, and mathematical statistics
ranking next in order. Although nearly half of the women mathe
matical statisticians included in the 1954—55 Register were in college
and university work, only 19 percent of the men and women statis
ticians included in the 1952 survey, mostly social statisticians, worked
there and less than two-thirds of these were in teaching {21).
In government
By contrast with the mathematical statisticians, these applied
statisticians in the 1952 survey mentioned above were found in
larger numbers in Federal, State, or local governments, where 45
percent of the total were employed {21). In 1954-55, only about
9 percent of the women and 11 percent of the men registered mathe
maticians were in government work, which may, of course, be some
what underrepresented among the registered group. It is also
likely that among statisticians with the doctor’s degree, a higher
percentage are employed in education. Even among this group,
however, a 1948 survey, which reached a relatively greater propor
tion of recipients of higher degrees, found 27 percent of the statis
ticians in government employment witli an additional 4 percent
combining government work with education {19).
Most straight mathematics positions in government are found at
the Federal level. Of the women mathematicians included in the
National Register in 1954-55 who reported their employment, 40
were in Federal work and only one in other government employment.
All States and most of the larger cities have some statistical positions,
as well as some other jobs for those with mathematical training, but
very few of these positions are of the mathematical research type {9).
These have been mainly in connection with unemployment insurance
programs.
On August 31, 1954, the Federal Government employed 1,306
women in mathematical and statistical work. Table 6 lists the
occupational groups and shows the distribution by agency. Only 35
percent of the Federal mathematicians were women, but women
comprised 81 percent of the mathematics aids. The National
Advisory Committee for Aeronautics takes a large segment of both
groups, most of whom are employed outside the Washington, D. C.,
area. Women are only 21 percent of all statisticians, who are con
centrated in the Departments of Defense, Commerce, and Agriculture.
404231 — 57
Tabic 6.—Women mathematicians and statisticians among Federal civilian employees, by agency, Aug. 31, 1954
Executive departments
Total women
employed
Occupational series
Total _ _
_
Statistics____
, _
Mathematics aid
Cryptography------
Number
Percent
women
are of
total
1,306
22. 3
34.
20.
81.
0.
1.
13.
450
416
414
12
7
7
7
9
2
8
4
2
National
Advisory
Commit
tee for
Aeronautics
Com
merce
Health,
Educa
tion, and
Welfare
Veterans
Admin
istration
Agricul
ture
Labor
interior
State
All other
agencies
Army
Navy
Air
Force
370
253
217
104
80
62
52
34
20
16
24
74
110
150
57
46
99
38
79
36
45
17
3
3
37
42
1
59
1
45
6
34
10
5
5
5
21
65
260
1
i
1
8
3
3
3
1
Source: U. S. Civil Service Commission, Occupations of Federal White-Collar Workers, Aug. 31, 1954, 1955; and XJ. S. Department of Labor, Women’s Bureau, Women
White-Collar Employees of the Federal Government: A Study of Their Salaries and Positions in 1954. Processed, 1957.
12
Employment Opportunities for
They form an even smaller percentage of cryptographers and crypt
analysts (code writers and decipherers), about 1 percent in each case.
In both code groups, it is the Army, with 1,936 men and no women in
this work, which accounts for the small proportion of women. The
7 women actuaries comprise about 13 percent of the Federal actuaries.
They deal with problems that involve the setting up or administering
of benefits and payments programs and the appraisal of long-range
expenditures. Especially the Veterans Administration and the Depart
ment of Health, Education, and Welfare in its Old Age and
Survivors Insurance program are interested in such problems.
f! WU
Figure 4.—A mathematician at the National Bureau of Standards checks the work of a
computing machine against the table in her book.
Among women mathematicians employed in government who were
in the National Register of Scientific and Technical Personnel in
1954-55, applied mathematics was the leading specialty, with mathe
matical statistics ranking next.
The influence of the Federal Government in mathematics is greater
than the proportion of workers directly employed by it would indicate.
According to a 1954 report of the National Research Council: “The
Federal Government in 1954 provided $3% million for sponsored
research in mathematics, about $2}i million of which maintained
applied mathematics activities. With negligible exceptions, all work
units in the field receive a substantial fraction of their funds from
Women Mathematicians and Statisticians
13
Government contracts” (12). The impetus given by defense needs
and Government financing has certainly accelerated the rate of
growth of the demand for mathematicians in private industry as well.
Although the Federal Government’s most striking contribution may
be in the applied field, basic research is not neglected. In fiscal year
1954, the National Science Foundation awarded 21 grants totaling
$173,950 to institutions for basic research in mathematics (24). In
each of the years since the inception of the National Science Founda
tion fellowship program in 1952-53, one or two women have been
awarded fellowships for graduate study in mathematics. Summer
institutes for teachers of mathematics have also been financed by the
National Science Foundation. In 1956, such institutes for high-school
and college mathematics teachers were scheduled at 3 institutions,
with stipends for an average of 50 teachers at each institute (26).
State and local governments employ statisticians largely in employ
ment statistics, social insurance, and public health programs. On
January 1,1953, 404 analysts and statisticians were full-time employees
of State and local health departments (16). The public health
statistician defines the health problem of an area in quantitative
terms, develops records and analytical procedures for the administra
tion of programs designed to meet these problems, and measures the
effectiveness of the public health programs. Roughly 700 or more
statisticians working mainly in labor statistics and social insurance
were estimated by the Bureau of Labor Statistics to be employed in
1954 by State and local governments (20). Among them were a few
women who served as senior or chief statisticians in State departments
of industrial relations or of labor or who headed divisions of research and
statistics in such departments. Statisticians are needed, too, in the
administration of social insurance systems set up during the past 20
years.
Actuaries employed by State governments are primarily concerned
with supervising the examination and valuation of insurance companies
doing business in the State, and seeing that they complywith legal
requirements. Some have participated in research in connection with
unemployment insurance programs. In addition to Federal, State,
and local governments, international agencies—like the United
Nations—employ some statisticians. Quotas, however, restrict the
number employed from any one country by these agencies.
In induslry
Although industry is a massive user of mathematics, the number of
mathematicians employed there is relatively small, but increasing
rapidly. Most of the extensive mathematical work required is done
by scientists and by engineers with a knowledge of the theoretical
14
Employment Opportunities for
aspects of their field. Engineers, whose basic professional training
includes higher mathematics, comprise the largest of all professional
groups in private industry. A recent report estimated their number
in a large segment of industry at 409,000 as compared with some
6,400 mathematicians (27). Nevertheless, the demand for mathe
maticians in industry has increased at a tremendous rate. Although
the mathematicians in the National Register of Scientific and Technical
Personnel in 1954-55 cannot be compared exactly with those registered
in 1951, the proportion in private industry was five times that in the
earlier one, indicating a sizable increase. Of the women mathema
ticians in 1954-55, the proportion in private industry was three times
that in 1951.
Forty-two industrial firms interviewed in a Women’s Bureau
survey (22) in 1946—47 had expanded their employment of women
mathematicians from 166 at that time to .135 in 1953. The gain was
102 percent. Moreover, these increases took place during a period when
fewer women were added to the supply from the colleges, as noted later,
and they were not equaled, in other scientific specializations.
By far the largest number of women mathematicians in private
industry are employed by electrical manufacturing firms, with
transportation equipment ranking next. The aircraft industry leads
as an employer within this transportation group. Table 7 shows the
industry distribution of women employed in professional mathematics
Table 7.—Women mathematicians employed in private industry, by type of industry, 1953
Industry
All industries reporting___ ____
Manufacturing.______
_ _
Electrical machinery, equipment, and supplies
Transportation equipment
Chemicals and allied products .
Professional, scientific, and controlling instruments __
Products of petroleum and coal _
Food and kindred products_____
Other manufacturing____
.
Insurance carriers _ _ .
Miscellaneous business services..
Miscellaneous services ..__
Utilities and sanitary services
All other industries.. __ __
Source: Scientific Manpower Commission (unpublished data).
Number
Percent
588
100. 0
493
83. 8
252
135
45
22
20
7
12
48
23
13
6
5
42. 8
23. 0
7. 7
3. 7
3. 4
1. 2
2.0
8. 2
3. 9
2. 2
1.0
. 9
Women Mathematicians and Statisticians
15
work according to a 1953 survey of 991 industrial firms conducted
by the Scientific Manpower Commission. These women comprised
18 percent of all mathematicians employed by these firms.
The women mathematicians in industry in 1955 were engaged
mainly in research and development. Those in consulting, adminis
trative, and inspection work combined were fewer than those in
research. A few were engaged in technical writing or selling or in
production. Numerical analysis was the field of highest competence
claimed by most of the women mathematicians in private industry.
Especially since the war, operations-research teams have called
for mathematicians and statisticians. Operations research is a
relatively new occupational field concerned with providing the mili
tary or industrial executive with analytical studies of the operations
under his control as a basis for more intelligent decisions. In appli
cation, operations research usually involves the use of teams of re
search workers who, depending upon the nature of the problem, may
draw upon such diverse fields as physics, economics, mathematics,
psychology, and statistics. Operations research places heavy reliance
on the use of probability theory and statistics, with increasing
emphasis on the use of high-speed computing machines. Chemical,
petroleum, and food companies are among those who have added
such programs, with scientists and statisticians to administer them,
to their research departments. Private consulting firms specializing
in operations research are beginning to appear, and private research
bureaus which offer these and other services on a fee basis are not new.
Statisticians with background in business administration are also
employed in administrative and business research positions. With
training in corporation finance and accounting, they find jobs with
banks or investment and brokerage firms, where they analyze corpo
ration reports or study the stock and bond market as financial statis
ticians. In department stores, traditionally a good employment
field for women, statisticians set up and use statistical methods of
inventory control; in factories, they devise methods of controlling
the quality of goods manufactured.
Twenty-seven percent of all statisticians included in a 1952 survey
reported employment in private industry (21).
Private industry is the leading employer of actuaries. Most
actuaries work in life insurance companies, with the second largest
group in other types of insurance companies—casualty and fire, for
example (28). Small insurance firms that cannot afford a full-time
actuary hire actuaries in independent practice on a consulting basis.
In recent years, business firms—other than insurance—have employed
16
Employment Opportunities for
actuaries to consult on or administer their pension and retirement
plans, prompting the organization of the Conference of Actuaries in
Public Practice in 1950.
Prospective actuaries employed by an insurance company very
early in their experience learn to derive formulas and compute premi
ums and values for life insurance and annuity policies. They make
computations in connection with changes in existing policies. Their
duties may involve computations of requested settlement options
not printed in the policy and of amortized bond values. In a mutual
company they may compute dividends. They usually prepare
replies to requests which require computations. Advancement to
actuarial assistant may come fairly early. There is a tendency for
some of those who start training as actuaries to move to other spheres
of activity in insurance offices, to investment, administrative, ac
counting, and high executive positions. There are occasionaf calls
from Latin America and other foreign countries for actuaries trained
in the United States.
Among women members of the Society of Actuaries in 1956, two
are chief executive officer and actuary, respectively, of a large fraternal
organization; one is a consulting actuary; five are associate actuaries
of medium-sized insurance companies or consulting firms; seven arc
assistant actuaries of very large companies or of a consulting firm;
one is a mathematician and two are assistant mathematicians in very
large companies. Another is a university instructor in actuarial
mathematics.
In olher employment
The few mathematicians and statisticians not employed by educa
tional institutions, by government, or in private industry are in
nonprofit organizations. In 1954-55, less than 4 percent of both the
registered women and men mathematicians were employed by non
profit foundations or organizations. Six percent of the statisticians
reported in the 1952 study were employed by nonprofit organizations
{21). Many labor and trade organizations hire statisticians for their
research departments. Directors of research and statistics in such
organizations generally have graduate training in the social sciences,
especially economics.
Future Demand
For mathematicians
“The computer era represents a second industrial revolution” (5).
“The effect of efectronic equipment on our economic life is of the
same magnitude as the effect of the H-bomb on our military strategy”
Women Mathematicians and Statisticians
17
(15). “Any estimate of the number of people required to meet future
needs in the computer field is almost sure to be an underestimate” (5).
These predictions are most enthusiastic, but they are substantiated
by facts. Even the most guarded appraisal indicates an extremely
promising outlook. While the advent of the high-speed computer
is only one contributory factor to the current burst of interest in
applied mathematics, it is the most recent and probably the most
dramatic.
Figure 5.—In a computation laboratory, a college senior learns how the automatic
computer MARK IV operates.
The first computer was developed during World War II to solve
ordinary differential equations of ballistics. Since then, they have
been used by the Federal Government for problems in weather predic
tion, explosion theory, and many others in the physical sciences as
well as for problems connected with the census of population. Some
characteristics of digital computers now in operation may be useful
in indicating the role of the mathematicians who operate them:
1. The computers will perform multiplication at speeds as fast as
30 millionths of a second.
18
Employment Opportunities for
2. They have “memories” of many thousands of words (either
numbers or instructions).
3. They arc able to follow instructions in succession and set up
automatically the proper connections between machine parts.
4. If at any point in the calculation there are two or more alterna
tive courses for the subsequent operation, they will select and
perform the correct one according to specified conditions
contained in their instructions (15).
It should be evident from this description that computing machines
are not giant brains. The mathematician must decide exactly what
operations are to be done to yield an answer, then break down the
problem to elementary operations of which the machine is capable.
This is the function of the coder and programer. The operator
puts the problem on the computer through “input” devices, causes it
to commence operation through a signal to the control unit, and
receives the result from the “output” devices.
Due largely to electronic computing, the demand for mathemati
cians has been multiplying very rapidly—in mathematical termin
ology, “growing exponentially”—for the past 7 years. Although
one expert predicts that the rate of increase will level off after 5 or 6
years, due to the availability of standard codes, others advise those
interested in the training of personnel to count on an even more
rapid rate of increase in the next decade (5). The Division of
Applied Mathematics at the National Bureau of Standards concerned,
among other things, with these machines and ways in which they can
be used, was set up in 1947. There are now 66 mathematicians in
the Division, including 24 women.
Although business is rapidly adopting operations-research tech
niques, the Federal Government is still the vital factor behind applied
mathematics. Inasmuch as the reasons which originally gave rise
to the Federal subsidies have neither weakened nor shown signs of
doing so, this source of strength appears to be assured for the fore
seeable future. The growing interest of private industry will likewise
further the continued expansion of mathematics in the applied field.
Although the emphasis on future demand here—and in most
currently published material—is on applied mathematics, and in
spite of the comment in a popularly written career guide that “pure
mathematics offers few job opportunities, save to a relatively few
wizards” (2), pure mathematics is also an active field. Although
each selects more courses in the area of his special interest, the
basic mathematical training of the pure mathematician, the applied
mathematician, and the statistician may be the same. Those workingin applied mathematics require a knowledge of the field to which the
mathematics is applied. Developments in pure mathematics are
Women Mathematicians and Statisticians
19
still basic to advance in the applied field, as recognized by the National
Science Foundation in its program of grants and fellowships for work
in this field. Shortages are greatest, however, in the applied field.
For teachers of mathematics
Among the most serious problems besetting the conduct of applied
mathematics programs, according to the National Research Council,
is the difficulty of finding applied mathematicians qualified and
interested to accept faculty appointments. The program director
for mathematical sciences at the National Science Foundation suggests
that the most critical shortage is in the teaching of mathematics.
Tf industry took only 5,000 mathematicians now from college teaching,
where the 1950 census found only 5,600, the future supply would be
cut off at its source. It has been suggested that mathematicians
from industrial and government projects be invited to teach at uni
versities and take part in their research activities on a temporary
basis {12). This program would accomplish the double purpose of
alleviating the teacher scarcity and of giving mathematicians the
opportunity to combine academic work with their industrial or
government duties. It would also enable them to contribute to a
supply upon which their own work depends.
Women, even more than men, have seen the range of jobs outside
teaching widening greatly in recent years, encouraging the trend
from teaching to industry {10). Nevertheless, many find certain
advantages in teaching. Not the least of these is the fact that it
is possible to go back to teaching, at least below the university level,
after leaving it for a time without the loss of status incurred by
periods of inactivity in many other professions. It offers good pos
sibilities not only for full-time work, but also for part-time and
substitute teaching. Successful teachers, of course, emphasize the
satisfactions of working with young people and watching them mature
mathematically. The need for mathematics teachers in high schools
is already severe, as noted earlier, and, as enrollments in the lower
schools make their resulting impact on the colleges a few years hence,
the additional faculty needed will make the current demand at the
college level seem slight. There will be a growing demand for
mathematics teachers for the next decade on the basis of population
increases and enrollments alone.
It is also possible that the proportion of all students who will enroll
in mathematics may increase as a result of efforts stemming from cur
rent dissatisfaction with the so-called recent neglect of mathematics
in high school, in the face of growing needs for natural scientists and
engineers.
In 1954, according to the United States Office of Education, one-
20
Employment Opportunities for
third of the public high schools did not offer trigonometry, solid
geometry, or advanced algebra. These schools have about one-tenth
of the students enrolled in the last two grades of high school where
these subjects are normally offered. One-tenth of the high schools in
the country did not offer elementary algebra, but only a small fraction
of the ninth-grade students are enrolled in these schools. Enrollments
in elementary algebra equal about two-thirds of the students enrolled
in the ninth grade. About one-fourth of the high schools do not offer
plane geometry; these high schools have about 7 percent of the pupils
who would be in the grade where they would normally take the subject.
Actual enrollments in plane geometry amount to about one-third of
these students. The chairman of the Physical Sciences Council at
Brown University reported that about 80 percent of the applicants
in 1955 for enrollment in the undergraduate applied mathematics
division failed to meet admission requirements, because they had not
taken the necessary high-school courses in mathematics and the
sciences or had scored poorly in these subjects in the College Board
tests. Engineering schools make similar observations. As more
opportunities for scholarships in engineering, science, and mathemat
ics arc made available to qualified students, the need for high-school
courses to prepare them for college work in mathematics will be even
more keenly felt.
For statisticians
Although the first system of statistical quality-control methods was
initiated about 25 years ago, statistics, like applied mathematics,
proved its value on a larger scale than ever before in World War II.
For instance, statistical studies were made of merchant ship losses as
a function of convoy size and of aircraft losses as a function of time
since overhaul. Techniques for inventory control were developed to
estimate tires and other supplies. In 1951, there were 1,458 statis
ticians in civil-service positions in Washington, D. C.; in 1931, there
were only 79 (20). In private industry, the organization of economic
research departments in large corporations indicates the growing
emphasis on statistical studies and research. Of 42 such departments
on which date of establishment was available in a recent study, more
than half were organized during the 1940’s. These departments
ordinarily hire not only economists but also statisticians with second
specialties in economics. They do market research and conduct
commercial sample and other surveys. A slow but steady increase
in opportunities over the long run is predicted.
Some other fields accounting for an increasing utilization of statis
tical methods are the biological and medical sciences, psychological
testing, education, and public health. For instance, when the major
Women Mathematicians and Statisticians
21
problems of public health departments concerned acute diseases of
high incidence or prevalence, the statistician’s job was limited to
computing relatively crude health indices based on records collected
routinely, such as death certificates and physicians’ reports of com
municable diseases. With the conquest of major communicable
diseases and the transfer of attention to chronic-disease control,
hospitalization, and medical care, the need arose for more complicated
statistical studies. In Federal agencies which have substantial health
activities, e. g., Public Health Service, Children’s Bureau, Defense
Department, the demand for specially trained statisticians exceeds
the supply (1). The limited facilities for training in the past decade
have built up a backlog of demand by existing units that alone would
last for the next several years. The Federal Government’s need for
sampling experts is particularly acute.
Tn view of the demand for statisticians and the currently limited
supply, there are also very good employment prospects in teaching.
Rising demand in business administration, engineering, and the
natural sciences, as well as in the social sciences, in which statistics
is becoming increasingly applied, has already resulted in an increase
in the number of institutions offering courses in statistics, and further
expansion is likely. Although there were only about 750 professors
and instructors of statistics reported in the 1950 census, including
less than 70 women, the demand for specialists in this faculty area is
bound to grow. Mathematical statistics has received a great deal of
attention in this country during the past 25 years, and according to
an authority at the American Statistical Association, mathematical
statisticians are “always in demand.”
Many more actuaries are needed, with no prospect of the actuarial
profession becoming overcrowded for many years. Life insurance,
health insurance, and insurance pension and retirement plans are
expected to continue to expand, as are casualty and fire insurance
(28) (4). rIhe new demand for actuaries in the consulting field has
already been noted and is expected to continue as smaller companies
set up pension, retirement, and other insurance plans.
Although the actuarial profession has not been closed to women,
it is apparent that most jobs are filled by men. Standards set by the
professional organization are very high and require years to complete,
so that only women of persistence as well as of outstanding ability can
succeed in meeting them. In 1955, the Society of Actuaries had only
21 women among its 890 fellows and 19 women among its 684 associ
ates. The greatest limitation on opportunities arises from the reluc
tance of most life insurance companies to assign women to executive
duties and to positions requiring frequent contacts outside their own
department or company (9). Nevertheless, the unusual demand
Employment Opportunities for
22
favors opportunities for tire well-prepared woman actuary. The fact
that the number of women in this field has been increasing in recent
years in all probability indicates a continuing trend, at least so far as
employment is concerned.
Future Supply
Meanwhile, as the demand for women mathematicians has been
growing, the supply has fallen behind. Table 8 shows the number of
degrees conferred in mathematics from 1947-48 to 1954-55. The
Table 8.—Earned degrees conferred by higher educational institutions in mathematics,
1947-48 to 1954-55
Bachelor’s and first pro
fessional
Year
1947-48__
1948-49__
1949-50__
1950-51...
1951 52__
1952-53-_
1953-54-.1954-55-..
4,
5,
6,
5,
4,
4,
4,
4,
266
040
392
753
721
396
090
034
Women
1,
1,
1,
1,
1,
1,
1,
1,
647
527
446
442
332
274
368
310
women
Total
39 711
30 893
23 974
25 1, 109
28 802
29 677
33 706
32 761
Doctor’s
Number
Number
Number
Total
Master’s and second pro
fessional
Women
148
181
190
180
139
112
127
148
Percent
women
21
20
20
16
17
17
18
19
Total
128
126
160
184
206
241
227
250
Source: Department of Health, Education, and Welfare. Office of Education.
ferred by Higher Educational Institutions, published annually.
Women
10
10
9
9
11
14
14
11
Percent
women
8
8
6
5
5
6
6
4
Earned Degrees Con
decrease since 1950-51 may be attributed to the lower birthrate in
the 1930’s, the results of which are now being felt at the college level.
The increase in the number of women in 1953-54 reversed the down
ward trend, but the gain did not continue the following year.
New graduates, men and women, prepared to teach high-school
mathematics have also been declining in number, although 1956 saw
the first reversal of the alarming downward trend. In 1955-56, 2,600
were graduated, 44 percent below the 1950 number but 21 percent
above the number graduated the preceding year (14). The fact that
mathematics had been adversely affected bv additional factors as well
as by the low birthrate of the 1930’s is indicated by the lesser decline
of 34 percent in the number of all college graduates prepared to teach
in high schools during the same 6-year period. However, mathe
matics appears to have recovered more quickly from the decline since
the rate of increase of all graduates prepared to teach high school
was only 15 percent, from 1955 to 1956.
Women Mathematicians and Statisticians
23
illlfi!
Figure 6.—A high-school mathematics teacher explains the intricacies of
solid geometry to two students and encourages their interest in the field
of mathematics.
These figures on new graduates are larger than the numbers which
become available for employment from this source. Losses occur,
among men, for military service and other employment; among the
women, for full-time homemaking and other employment. The
National Education Association found that only seventy-seven per
cent of the women and seventy-four percent of the men who had pre
pared for mathematics teaching in the academic year 1954 55 were
either teaching, seeking teaching jobs, or continuing formal study (14).
Although a few mathematicians come from related fields, not many
can be expected from these sources. More than 9 out of 10 of the
mathematicians registered in 1951 had received their highest degree in
mathematics (25). The largest group derived from other specializa
tions came from the physical sciences and engineering, fields which are
also facing shortages and are unlikely to provide many additional
mathematicians.
College enrollments are now increasing, so the future potential
supply is more encouraging than it has been for some years. However,
unless a much larger proportion of high-school students prepare
themselves to study college mathematics, and unless a much larger
proportion of college students specialize in mathematics, we shall have
not only a continuing shortage in this key group but also a bottleneck
effect on engineering, the physical sciences, statistics, and many other
fields dependent on mathematics instruction. The scarcity of
24
Employment Opportunities for
students is less felt in pure mathematics, however, than in applied
fields. In 1953, the great centers of pure mathematics reported a
gratifying number of really gifted students, while some of the out
standing schools of applied mathematics already had difficulty in
filling their funded graduate-student positions with qualified candi
dates {12).
Preparation Needed
For mathematicians
There are employment opportunities at all levels of education in
mathematics although they become greater at the high levels. In
programing work, the problems encountered vary from those which
can be handled by high-school students unusually proficient in mathe
matics to those requiring a doctorate level of education in mathe
matics. Only slightly exaggerated was the statement made at a 1954
conference on training personnel for the computing machine field,
where the programer’s qualifications were noted by one of the par
ticipants “as anything from those of an 8-year-old up to a finished
Ph. D. in mathematics” (5). The variations in the uses to which
electronic computers are put result in a demand for programers at
the bachelor’s and master’s levels as well as at the Ph. D. level.
As background for the 6 to 12 weeks of on-the-job training given
for programing preparation, most employers presently seem to look
for a “good, solid classical background in mathematics.” While
suggesting that course work include numerical analysis, most authori
ties stress that it is more important than ever that college courses
avoid excessive development of specialized techniques and aim rather
at breadth of mathematical background. One electronics manufac
turer explained that emphasis in university courses on programing
preparation is not so crucial, inasmuch as a capable person with good
mathematical background has no difficulty in learning this on the job.
Nevertheless, in 1954, training with respect to electronic computers
existed as regular courses in some 30 universities scattered over most
of the United States. More of these were in electrical engineering
than in mathematics departments (5). Among these computing
centers are those at Columbia, Purdue, New York, Wayne Universi
ties and the Universities of Illinois and Michigan, and Georgia Insti
tute of Technology.
In one 4-year curriculum leading to a bachelor of science in applied
mathematics, students take 8 semester courses in mathematics, 4 in
applied mathematics, and 8 in engineering, physics, and chemistry (an
economics option may be added soon). This type of program offers the
kind of background needed by young women seeking work in industry
who may or may not use electronic calculators, but who will assist
Women Mathematicians and Statisticians
25
research chemists, physicists, engineers, and others in the mathe
matical phases of their work. Since the graduate with a mathe
matics major who enters industry usually operates a calculating
machine and has occasion to use a slide rule, it is desirable for her to
pick up those skills in school. For work in research departments of
all large industrial concerns, a college background in physics and
drafting is helpful. As was common during World War II, a few
large industries are hiring promising young women with mathematics
and science backgrounds whom they send on for further schooling
while working.
For a beginning professional position as a mathematician in the
Federal Civil Service, college graduates without experience must
have not only their bachelor’s degree but courses in mathematics
totaling at least 24 semester hours. For some type's of positions,
additional courses in the physical sciences or engineering may be
required up to 12 semester hours.
The emphasis on courses outside mathematics—for instance, in the
physical sciences—is a trend everywhere being promoted for applied
mathematicians. Some type of formal study in physics, chemistry,
engineering, biology, psychology, statistics, or economics is usually
necessary to make the mathematician effective in applied work.
A committee of the Social Science Research Council warns that until
more mathematicians and mathematical statisticians select a minor
in social sciences, as many now do in physics, their communication
with social scientists will continue to be handicapped.
For teachers of mathematics
To teach mathematics in college, it is usually necessary to have a
Ph. D. degree or bo working toward one. Professorships almost in
variably indicate advanced graduate training and the equivalent of
post-Ph. D. research experience. For college instructors of applied
mathematics, it is desirable to have had first-hand experience with
computing machines. Formal requirements for secondary-school
teachers vary widely according to State certification standards and
in times of severe shortage are sacrificed frequently for the sake of
filling positions.
A study published in 1950 polled 263 liigh-school mathematics
teachers, 107 heads of college mathematics departments, and 83 heads
of college education departments in the Middle West to determine
college courses desirable in training secondary-school teachers. The
first 10 subjects were college algebra, trigonometry, methods in highschool mathematics, solid geometry, educational psychology, super
vised teaching, analytical geometry, general high-school methods,
college geometry, and advanced college algebra. High-school mathe
26
Employment Opportunities for
matics teachers favored professional courses in education to a greater
extent than did college education department heads. Another survey
produced evidence to support the following courses and experiences
in training secondary-school mathematics teachers: statistics, applied
mathematics, mathematics of finance, history of mathematics, field
work in mathematics, audiovisual aids, and social problems (7). The
Mathematical Association of America considers calculus and differ
ential equations essential, and wotdd include as much work as possible
in the sciences (9).
To an increasing extent, high schools provide, beside the traditional
college preparatory courses, such mathematics courses as general
mathematics, shop mathematics, consumer mathematics, business
arithmetic. High-school teachers should be prepared to give both
types of instruction.
For statisticians
Mathematical statisticians almost invariably have a doctorate in
their specialty. Very few universities give, adequate training in
mathematical statistics at the present time (9). Among those that
do are Columbia, Princeton, and Stanford Universities, the Universi
ties of California, Chicago, and North Carolina, and Iowa State
College. A high-school background for statisticians should include
as much mathematics as possible and the natural and social sciences,
and should develop the ability to write clear, concise English. In
college, algebra, plane trigonometry, analytical geometry, differential
and integral calculus, plus courses in statistical method, are essential
{20). Original work in statistics demands an understanding of matrix
algebra, n-dimensional Euclidean geometry, the theory of measure
and integration, the Fourier integral, and the theory of complex
variables (6).
Students intending to be applied statisticians often take degrees in
fields where they intend to apply their statistical training. A study
made in 1950 of members of the American Statistical Association
showed that 27 percent had taken their highest degrees in economics;
20 percent in statistics; and 12 percent in mathematics. Other major
subjects were business, psychology, and sociology (8). A 1952 survey
which reached statisticians through organizations in the social sciences
and humanities, found that more than 40 percent had majored in
mathematics or statistics {21). Almost half of those found in business
and management in the 1952 survey had only the bachelor’s degree
{21). To qualify for a beginning position with the Federal Govern
ment as a professional statistician, the candidate must take the
Federal Service Entrance Examination, which is open to all graduates
of a 4-year college course leading to the bachelor’s degree. For cer-
Women Mathematicians and Statisticians
27
tain openings in statistics, a minimum number of academic credits in
a related area of study may be required of those who have no profes
sional experience.
(i
hi
i■
mm
Figure 7.—A high-school senior, finalist in the 1956 Science
Talent Search, displays her statistical study of what has
happened for both high-average and low-average students
of her school, since their graduation.
For statistical quality-control work, the use of sampling to inspect
materials or products, it is desirable to have one or two courses in
engineering statistics and to be a graduate of a chemical, electrical, or
mechanical engineering curriculum. For the prospective public health
statistician, professional study should include substantial courses in
anatomy, physiology, and pathology, along with epidemiology, public
health administration, microbiology, and environmental hygiene. In
dustrial hygiene, medical care, and hospital administration are desir
able. Graduate study in a school of public health accredited by the
American Public Health Association is a prerequisite for career
advancement. There were, in 1950, 11 such schools (I).
For actuaries, the generally recognized mark of professional status
is successful completion of a series of examinations given by the Society
28
Employment Opportunities for
of Actuaries, in the life insurance field; or by the Casualty Actuarial
Society, in the casualty insurance field. There are eight examinations
in each series. A candidate becomes an associate member after pass
ing five examinations given by the Society of Actuaries or fourgiven by the Casualty Actuarial Society. After passing all eight,
which requires between 5 and 10 years on the average, the actuary is
a fellow or full member. However, associates as well as fellows are
regarded as having professional status as actuaries.
In the Society of Actuaries series, it is desirable to take the first
three examinations while still in college. These test language apti
tude, general mathematics, and special mathematics (on finite differ
ences and probability and statistics). The Casualty Actuarial Society,
in the first three examinations, tests statistics, probability, elementary
life-insurance mathematics, general principles of insurance, insurance
law, and f social insurance. The remaining examinations require
practical experience and home study and are taken while employed in
actuarial work at a lower level than that of the actuary.
Basic requirements for a beginning actuarial position in the Federal
Civil Service specify the completion of a 4-year college course leading
to a bachelor’s degree. A minimum of 24 semester hours of mathe
matics must be included in the study of those candidates who have no
professional experience, although 6 hours of statistical theory and
method may be substituted for 6 of the mathematics credits. As of
1955, five universities in the United States offered specialization in
actuarial science. Besides the required mathematics, a college pro
gram preparing for actuarial work might include English composition,
speech, economics, banking and finance, accounting, business adminis
tration, and business law.
Personal Characteristics Needed
Mathematicians in the electronics computing field have been de
scribed as bright people, with mathematical aptitude and interests,
plus perseverance and motivation. These qualities are characteristic
of professional workers in mathematics and statistics generally.
Success in the programing and coding field requires in addition,
according to two women mathematicians at the National Bureau of
Standards, a special aptitude—like that for music. Seeking a pre
professional indication of this talent, it was noted that most of the
Bureau programers and coders like puzzles.
Fundamental qualities in a statistician are a liking for numbers,
strict mathematical accuracy, ability to manipulate figures and power
to draw general conclusions from them; a logical mind, a certain
amount of imagination, and patience to check and recheck are likewise
indicated {11).
Women Mathematicians and Statisticians
29
The actuary has been described as more of a businessman than a
mathematician. He must have administrative and executive ability,
the ability to work well with many types of people, good command of
the English language, and good health to permit 5 to 10 years of com
bined study and employment.
Trying Out for the Field
After a certain level of education has been reached, the student
mathematician may be able to obtain short periods of employment
where he can apply his training on the lower levels while observing
professional workers. In the Federal Civil Service there are positions
for student trainees in mathematics. Some of these positions may
provide summer employment for college students majoring in mathe
matics and others may provide scheduled periods of employment for
students in college cooperative courses. A written test is required,
consisting of a scientific aptitude test which includes spatial visualiza
tion, mathematical formulation, table reading, and form perception.
Salary levels increase as students acquire more education. Junior
students taking the examination may qualify for the highest salary
level available to students by taking an additional test in mathematics.
The Mathematics Student Journal, published for high-school students
by the National Council of Mathematics Teachers with the cooperation
of the Mathematical Association of America, will help to test interest
in mathematics as well as to supply information. Students interested
in statistical work may work as statistical clerks or student assistants
on research projects using statistical techniques. Preliminary actu
arial examinations taken while still in college may indicate the likeli
hood of future success in actuarial work, and advance the opportunity
for employment.
Figure 8.—College students are given practical experience in statistical and actuarial
procedures in this actuarial science laboratory.
30
Employment Opportunities for
Obtaining Employment
College teaching positions arc mainly found through professors and
chairmen of mathematics departments. Many assistant or instructor
positions are filled by outstanding present or former graduate students,
and most higher positions, by promotion. Both graduate and under
graduate schools should be chosen carefully toward this end if such em
ployment is anticipated.
Joining professional organizations and attending meetings is often
fruitful of leads to openings. Some bulletins of professional organiza
tions list employment opportunities, in statistics, the bimonthly news
bulletin of the American Statistical Association and the American
Statistician carry such information.
High -school teaching positions are obtained through college and
teacher placement bureaus or often by direct application to school
systems. Examinations are sometimes required of nonresidents.
In the Federal Government, mathematical and statistical positions
are covered by civil-service examinations. The requirements for be
ginning positions have been noted previously. Examinations for sci
entific personnel for higher positions are “unassembled,” i. e., based
on review of the candidate’s experience, education, and tfaining. In
State insurance departments, the top actuarial official is often ap
pointed by the governor. For staff actuarial positions, application is
made to the commissioner in charge of the insurance program. These
and State statistical positions are filled either by examination or ap
pointment, depending on the State.
To find positions in private industry, professors and departmental
chairmen and college placement bureaus are helpful, as are the public
employment offices operated by State Employment Services. Answer
ing advertisements in professional journals, large metropolitan daily
newspapers, and financial journals may be rewarding.
Advancement
In colleges and universities, advancement from the intermediate
levels to full professorship is often dependent on length of service and
other factors, such as contributions through publications, since all
candidates for advancement have presumably reached the Ph. D. level.
In public school systems, automatic salary increases are usually given
periodically according to a schedule, and sometimes depend on com
pleting additional courses. The head of a department in a high school
may receive an additional salary increment. Promotion beyond that
is to assistant principal or other administrative work. In the Federal
Government, advancement is through civil-service ratings. Although
Women Mathematicians and Statisticians
31
there are automatic, periodic salary increases within a grade, ad
ministrative action is required to proceed from one grade to another.
Advancement in industry to supervisory or administrative positions
brings an obvious change of rank, often without further education, but
this is based more on administrative than on mathematical ability.
There are positions, programing, for example, where the title may
not change from the B. A. through the Ph. D. level. The level of
programing done may vary, of course. Some young women math
ematicians after assisting engineers have completed enough experi
ence and training to become junior engineers.
The advancement of actuaries is generally regulated by the exami
nations they must pass. Exceptions arise in small insurance compa
nies, small consulting firms, and State insurance agencies. Usually
an actuary who has passed all the examinations, however, is promoted
to officer status when a vacancy as an actuary is available.
Earnings
In 1954 -55, the median annual earnings of mathematicians without
the Ph. D. who were registered with the National Register of Scientific
and Technical Personnel were $5,927; for registered Ph. D. mathema
ticians, the median was $6,325. Undoubtedly the medians were lower
for women mathematicians than for men, although thev were not com
puted in time to be published here. A recent report showed that men
graduated at the bachelor’s level with a mathematics major in 1951
arid employed in 1952 had a median salary of $3,400. The median
forewomen was $2,800 (23). However, the median reported for women
receiving bachelor’s degrees in 1955, followed up by the Women’s
Bureau and the National Vocational Guidance Association in early
1956, was $3,848 for those employed as mathematicians or statisticians.
Obviously, beginning salaries have been increasing.
Professional incomes of mathematicians are generally lowest in
educational institutions, intermediate in government, and highest in
private industry (25). The salaries offered in industry create extra
ordinary employment problems for the Government, while in educa
tion they are offset somewhat by the longer summer vacations and
holiday periods, and the less rigidly scheduled nature of academic
work. The Federal Government starts mathematicians, like engi
neers and physical scientists, at a higher salary rate than it does be
ginners in the same grade in other professional fields. Salaries in
colleges and universities vary greatly by institution. Beginning
salary of an instructor in mathematics may be as low as $3,000; the
maximum salary of a full professor may reach $15,000 or more.
Salaries for instructors in mathematical statistics are generally higher.
32
Employment Opportunities for
Professorships in mathematical statistics may pay as high as $18,000
to $20,000 per year (9).
High-school teaching is less well paid than work in industry, al
though long summer vacations, here, toe, offer an offsetting attraction.
Mathematics teachers, of course, are on the same salary scale as other
high-school teachers, and women teachers in most communities are
on the same salary scale as men. Women college graduates of the
class of 1955 who early in 1956 reported employment in high-school
teaching averaged $3,061, according to a survey conducted by the
National Vocational Guidance Association in cooperation with the
Women’s Bureau. Average (median) salaries in 1954-55 for higlischool teachers, many of whom have had long years of teaching
experience, are given in table 9.
Table 9.— Median annual salaries paid junior high-school and high-school classroom
teachers in urban school districts, by population size, 1954-55
Population size of urban district
Junior high school
Over 500,000______ „ _ _
100,000 to 500,000_______
30,000 to 100,000
10,000 to 30,000 ___________________ ______ ______
5,000 to 10,000
2,500 to 5,000
$4,
4,
4,
4,
3,
3,
931
311
382
103
751
579
High school
$5,
4,
4,
4,
4,
3,
864
650
686
385
021
848
Source: National Education Association. Salaries and Salary Schedules of Urban School Employees,
1954-55. Research Bulletin 33, No. 2, April 1955.
The latest comprehensive data on salaries of statisticians are for
1952, when the median salary of women statisticians reporting was
$5,600 compared with a median of $7,000 for men. The entire group
of statisticians was found to have the highest median salary of all
groups studied, although it was the youngest of a number of groups in
the social sciences and the humanities surveyed through the coopera
tion of the American Council of Learned Societies. The median
annual salary for all statisticians was $6,800; for those with the Ph. D.,
$7,500. These 1952 salaries exceed those of mathematicians in
1955. The high proportion of statisticians in nonacademic work may
explain this in part, since the median salary for statisticians employed
by colleges and universities was lower than in government and private
industry {21).
A 1950 study of statisticians in the American Statistical Association
found that the median income of statisticians with independent prac
tice as their primary source of income was $13,300, but the median
for salaried employees, excluding teachers, was $7,000 (8). Statis
Women Mathematicians and Statisticians
33
ticians reporting income from second sources mention most often
teaching outside of regular duties. Other common sources of addi
tional income are consulting, royalties, and lectures {21).
The salary of a beginning actuary is likely to range between $4,200
and $5,000 per year. In 5 years, it may increase to perhaps $7,500.
A number of actuaries in the country make over $30,000, while it is
possible for those who head firms to earn $50,000 or more. Separate
statistics are not available on the relatively few women in this field.
Working Conditions
The office environment in which much of the work of the mathe
matician and statistician is done is likely to be modern and well
equipped with cafeteria and other employee services. The mathema
tician usually has regular hours. The applied mathematician or
statistician, however, may be required to work after regular office
hours on rush projects. Actuaries are seldom required to work over
time except for a short period at the end of the year, and hours in
many insurance companies are limited to 35. Depending partly on
the work habits of the individual, mathematicians or statisticians in
administrative positions may put in extra time in the office or on
homework much more than subordinates. In the lower levels, while
the hours are regular, the work is often tedious, and the necessary
close concentration may be tiring to the eyes and nervous system.
As compared with work in some of the sciences, mathematics is
usually free of physical hazards encountered in handling dangerous
equipment or materials.
Organizations
Some of the professional organizations now existing in mathe
matics were founded more than a hundred years ago, but the
number has risen at an ever-increasing rate since the 1930’s. The
most recent are the small but fast-growing splinter societies
in applied mathematics. The organizations publish journals,
transmitting new developments in the field, and subscription to these
publications is usually included in the membership fee. Yearbooks,
booklets, pamphlets, and reprints describing various aspects of the
field are likewise distributed. Frequently the societies obtain reduced
prices for their members on pertinent books of other publishers. The
organization’s offices generally act as a central source of professional
information, convening conventions for direct interchange among
members, who are reached through publications and special services
at all other times.
34
Employment Opportunities for
The American Mathematical Society concentrates on research in
mathematics, while the Mathematical Association of America spe
cializes in collegiate mathematics. The National Council of Teachers
of Mathematics is open to anyone interested in the teaching of mathe
matics. Springing up beside these long-established groups are socie
ties representing the newer branches of mathematics: the Society for
Industrial and Applied Mathematics, the Industrial Mathematics
Society, the Association for Computing Machinery, the Operations
Research Society of America, and the Institute of Management
Sciences. {12).
The American Statistical Association and the Institute of Mathe
matical Statistics are the overall societies in statistics. Among spe
cialized groups are the Econometric Society and the Psychometric
Society founded in the early 1930’s for advancement of the theory
and application of statistical methods to economics and psychology.
The Biometric Society, organized in 1947, is devoted to the mathe
matical and statistical aspects of biology, and the American Society
for Quality Control, interested in the use of statistics in assessing the
quality of production in industry, was organized in 1946. Actuarial
societies include the Casualty Actuarial Society and the Society of
Actuaries, previously mentioned, and the recently founded Confer
ence of Actuaries in Public Practice.
Special Groups of Women
No qualifications other than ability to do the required mathematics
and statistics were noted in the review of literature and announce
ments for positions, or in interviews with employers in the course of
this study. The tremendous demand has largely removed barriers
that may have existed previously to the employment of women or
special groups of women in this field of work. Married women are
hired when available, as are older women with the required training.
In view of the fact that the content of mathematics has advanced so
rapidly in the past years, however, it is unlikely that older women
would be prepared to take most positions without additional training.
Teaching mathematics at the lower levels is an exception. Most
orthopedic or hearing disabilities would not be handicapping in this
work, but defective vision, unless corrected, would be a handicap.
Women Mathematicians and Statisticians
35
Appendix
DEFINITIONS
Mathematician as defined in the Dictionary of Occupational Titles (18):
MATHEMATICIAN (profess. & kin.) 0-35.76. Solves and directs the
solution of problems in higher mathematics incidental to investigative, develop
mental, and research work in scientific fields, such as engineering, physics, and
astronomy: Determines mathematical principles involved and most efficient
methodology for solution of problems. Acts as an adviser or consultant on
application of mathematical analysis to scientific problems. May perform
research to discover new or improved methods for application of mathematical
theory or analysis to new or unexplored areas of scientific investigation.
Statistician as defined in the Dictionary of Occupational Titles (18):
STATISTICIAN (profess. & kin.) II. 0-35.75. statistician, physical-science.
Discovers facts and solves quantitative problems in the field of physical science
by application of statistical methods to a mass of individual observations:
Observes scientific phenomena and devises techniques for their tabulation and
analysis, varying methods according to nature of subject matter. May specialize
in statistical analysis in a specific scientific field, such as physics, chemistry, or
biology.
STATISTICIAN (profess. & kin.) I. 0-36.51. statistician, social-sciences.
Discovers general facts and interprets quantitative information by application
of statistical methods to a mass of related individual observations in the field
of social sciences, such as economics, sociology, or psychology: Obtains and
devises methods for obtaining basic data, determining character and volume of
information necessary for solution of a statistical problem. Reduces and deter
mines most effective techniques for reduction of data according to nature of
available information and type of problem under study. . . . Usually has
broad training in mathematics. . . .
Actuary as defined in the Dictionary of Occupational Titles (18):
ACTUARY (profess. & kin.) 0-36.55. insurance actuary. Deals with statis
tical, mathematical, and financial calculations involving probability of future
payments or contingencies in pension and insurance plans, such as insurance
against losses arising from death, disability, sickness, and unemployment:
Evaluates risks, calculates premium rates, and constructs tables of probability
for such contingencies as mortality, disability, sickness, and accidents. Develops
contract provisions of insurance and pension plans. Determines proper basis
and methods for valuing liabilities of insurance and pension organizations.
Determines equitable bases for distributing surplus earnings under participating
insurance and annuity contracts. Is generally concerned with maintaining
permanent financial stability of insurance and pension plans.
36
Employment Opportunities (or
SOURCES TO WHICH REFERENCES ARE MADE
(1) American Public Health Association, Committee on Professional Education.
Proposed report on educational qualifications of public health statisticians.
American Journal of Public Health and the Nation’s Health 40: 857-863,
July 1950.
(2) Benge, Eugene J. The right career for you. New York, N. Y., Funk and
Wagnalls Co., 1950. 150 pp.
(3) Bryn Mawr College. Conference on the role of women’s colleges in the
physical sciences, held at Bryn Mawr College, Bryn Mawr, Penn., on June
17-18, 1954. Bryn Mawr, Penn., the College, June 1954. 16 pp.
(4) Cowie, D. J. Duties of actuaries. Weekly Underwriter 164: 1269-1272,
May 19, 1951.
(5) Jacobson, Arvid W., Ed. Proceedings of the first conference on training
personnel for the computing machine field, held at Wayne University,
Detroit, Mich., June 22 and 23, 1954. Detroit, Mich., Wayne University
Press, 1955. 104 pp.
(6) Jones, Howard L. and Roberts, Harry V. Statistics as a career. The
American Statistician 6: 6-10, October 1952.
(7) Kinney, Lucien B., Edwin Eagle, and Charles Purdy. The teaching of
mathematics in high school and college. Review of Educational Research
21: 305-316, October 1951.
(8) Malinowski, Zenon S. Economic status of statisticians associated with the
American Statistical Association in 1950. Chicago, 111., unpublished doctoral
dissertation, July 1955. Mss.
(9) Mathematical Association of America. Professional opportunities in mathe
matics. Buffalo 14, N. Y., the Arnold Buffum Chace Fund, 1954. 24 pp.
(10) Maul, Ray C. Fewer teachers to meet greater demand. Mathematics
Teacher 46:305-306, May 1953.
(11) McGinness, Josephine. Statistics. Peapack, N. J., Personnel Services,
Inc., 1949. 6 pp.
(12) National Academy of Science—National Research Council. Final report on
a survey of training and research in applied mathematics in the United States.
Washington, D. C., the Council, 1954. 60 pp. Mimeo.
(13) National Council of Teachers of Mathematics. Guidance pamphlet in
mathematics for high school students. Washington 6, D. C., the Council,
1953. 40 pp.
(14) National Education Association, Research Division. A brief summary of
the 1956 teacher supply and demand report. Washington 6, D. C., the
Association. 26 pp. Reprint from the Journal of Teacher Education,
March 1956.
(15) Rees, Mina. Digital computers. American Mathematics Monthly 62:414
424, June, July 1955.
Women Mathematicians and Statisticians
37
(16) U. S. Department of Health, Education, and Welfare, Office of Education.
Education for the professions. Washington 25, D. C., U. S. Government
Printing Office, 1955. 317 pp.
(17) ----------------- National summary of offerings and enrollments in high school
subjects, 1948-49. Washington 25, D. C., the Office, May 1951. 4 pp.
(Circular No. 294).
(18) U. S. Department of Labor, Bureau of Employment Security. Dictionary
of occupational titles. Vol. I, definitions of titles. Second edition. Wash
ington 25, D. C., U. S. Government Printing Office, 1949.
(19) ----------------- Bureau of Labor Statistics in cooperation with the U. S. De
partment of Defense. Employment, education, and earnings of American
men of science. Washington 25, D. C., U. S. Government Printing Office,
1951. Bull. 1027. 48 pp.
(20) ---------------------------------- in cooperation with Veterans Administration. Em
ployment outlook in the social sciences. Washington 25, D. C., U. S. Gov
ernment Printing Office, 1954. Bull. 1167. 66 pp.
(21) -----------------------------------in cooperation with the U. S. Department of De
fense. Personnel resources in the social sciences and humanities. Wash
ington 25, D. C., U. S. Government Printing Office, 1954. Bull. 1169. 140
pp.
(22) -----------------Women’s Bureau. The outlook for women in mathematics and
statistics. Washington 25, D. C., U. S. Government Printing Office, 1947.
Bull. 223-4. 21 pp.
(23) (U. S.) National Science Foundation. Education and employment speciali
zation in 1952 of June 1951 college graduates. Washington 25, D. C., U. S.
Government Printing Office, 1955. 78 pp.
(24) ----------------- Fourth annual report for the fiscal year ending June 30, 1954.
Washington, D. C., U. S. Government Printing Office, Nov. 1, 1954. 138 pp.
(25) ----------------- Manpower resources in mathematics. Washington 25, D. C.,
U. S. Government Printing Office, 1954. 22 pp.
(26) ----------------- National Science Foundation awards grants for summer insti
tutes for teachers of science and mathematics. Washington 25, D. C., the
Foundation, Jan. 30, 1956. 5 p. release.
(27) ----------------- Science and engineering in American industry. Preliminary
report on a survey of research and development costs and personnel in 1953
54. Washington 25, D. C., U. S. Government Printing Office, 1955. 41 pp.
(28) U. S. Veterans Administration, Department of Veteran Benefits, in coopera
tion with the U. S. Department of Labor, Bureau of Labor Statistics. Edu
cational requirements for employment of actuaries. Washington 25, D. C.,
U. S. Government Printing Office, December 1955. 14 pp.
(29) -------------------------------------------------------Educational requirements for employ
ment of statisticians. Washington 25, D. C., U. S. Government Printing
Office, December 1955. 8 pp.
U. 5- GOVERNMENT PRINTING OFFICE: 19§7
@FedFRASER