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STATE COLLEGE LIERARt
THE OUTLOOK
FOR WOMEN
Amy
MATHEMATICS AND
STATISTICS
Bulletin No. 223-4
U. S. DEPARTMENT OF LABOR
WOMEN’S BUREAU
UNITED STATES DEPARTMENT OF LABOR
L. B. SCHWELLENBACH, SECRETARY
WOMEN’S BUREAU
FRIEDA S. MILLER, DIRECTOR
The Outlook for Women
in
Mathematics and
Statistics
Bulletin of the Women’s Bureau No. 223—4
U. S. GOVERNMENT PRINTING OEFICE
WASHINGTON : 1948
For sale by the Superintendent of Documents, U. S. Government
Printing Office, Washington 25, D. C.
Price 10 cents
This bulletin is No. 223-4 in the following series on
THE OUTLOOK FOR WOMEN IN SCIENCE
No.
No.
No.
No.
No.
No.
No.
223-1
223-2
223-3
223-4
223-5
223-6
223-7
No. 223-8
The Outlook for Women in Science
The Outlook for Women in Chemistry
The Outlook for Women in the Biological Sciences
The Outlook for Women in Mathematics and Statistics
The Outlook for Women in Architecture and Engineering
The Outlook for Women in Physics and Astronomy
The Outlook for Women in Geology, Geography, and
Meteorology
The Outlook for Women in Occupations Related to Science
Note on Pagination.—Throughout the series, page numbers show both the vol
ume number and the page number in that volume. For example, page 24 in
volume 3 is shown as 3-24 ; in volume 6, as 6-24.
LETTER OF TRANSMITTAL
United States Department of Labor,
Women’s Bureau,
Washing ton, December 22, 19J/7.
Sir: I have the honor of transmitting a description of the outlook
for women in mathematics and statistics which has been prepared as a
part of a study on the outlook for women in science. The extra
ordinary demand for women with scientific training during World
War II and the resulting questions which came to the Women’s Bureau
prompted us to undertake this study. The paucity of published in
formation on women in science and the encouragement of the scientists
and educators who were consulted in the course of this study con
firmed the need for the information here assembled and synthesized.
The study was planned and directed by Marguerite Wykoff Zapoleon
and completed with the assistance of Elsie Katcher Goodman and
Mary H. Brilla of the Employment Opportunities Section of the
Bureau’s Research Division. Other members of the Bureau staff
who helped to broaden the coverage of this study through interviews
in the field were regional representatives Margaret Kay Anderson,
Martha J. Ziegler, Rebecca G. Smaltz, and another member of the
research staff. Jennie Mohr. Corinne LaBarre, research assistant, of
the Western Personnel Institute, Pasadena, Calif., furnished the in
formation obtained from western colleges.
The part of the study here transmitted was written by Mary H.
Brilla.
Respectfully submitted.
Frieda S. Miller,
Hon. L. B.
Schwellenbach
Secretary of Labor.
Director.
• ■ '■ ■ "
’ ■ ■ 1^
FOREWORD
Much has been written about science and scientists, but little has been
told about the work women trained in science have done and can do in
the future.
Although these women are few in number when compared to men in
science or to women in such occupations as teaching and nursing, their
contribution to the national welfare, so strikingly demonstrated in
World War II, goes forward daily in the laboratories, classrooms,
offices, and plants in which they work.
The every-day story of where these women work, of what kind of
work they are doing, and of what other young women who join their
ranks in the future may do has been the subject of this report on the
outlook for women in science. Unlike the usual monograph which
describes an occupation in detail at a particular point in time, this
study, like the Women’s Bureau series on occupations in the medical
and health services which preceded it, is concerned primarily with
changes and trends.
Although more than 800 books, articles, or pamphlets were culled
for background information, the principal raw material for the entire
study of which this bulletin is a part came from such primary sources
as scientific organizations, employers and trainers of women scientists,
and men and women scientists themselves. Principal sources were as
follows:
Scientific organizations: The National Research Council supplied
useful directories of scientific laboratories and organizations.
Helpful criticism and direction to other authorities were ob
tained from its Office of Scientific Personnel. Sixty separate
organizations of scientists supplied information on their women
members, by interview or correspondence.
Federal agencies: Unpublished information on personnel in sci
entific fields was supplied by:
The United States Bureau of Labor Statistics,
The National Roster of Scientific and Specialized Personnel,
The United States Office of Education,
The United States Civil Service Commission, and
The United States Public Health Service.
In addition, 52 separate bureaus, offices, or other operating units
of the Federal Government known to employ scientists were
solicited for information regarding the number of women em
ployed on jobs requiring scientific training and the type of work
4-V
4-VI
FOREWORD
they were doing. Detailed statistics over a period of years were
available from some agencies, while only fragmentary data wTere
obtained from others. The women’s military services likewise
supplied information on the wartime use of women trained in
science in the WAC, WAVES, and the Marine Corps.
Private industry: One hundred industrial firms were visited in
-1945 and 1946 to obtain information, usually by interview with
the director of research or the personnel director, on the women
employed by any part of the organization in any capacity re
quiring scientific training of college level. Prewar, wartime,
and postwar statistics were obtained where available, as well as
suggestions and comments. In many instances, some of the
women in scientific work were interviewed on the job. The
firms visited included:
Seventy-eight firms listed in the National Research
Council’s 1946 directory of 2,443 firms having research
laboratories. The firms visited are listed in the directory
as employing 24,816 persons as scientific or technical per
sonnel in their laboratories. This number represented
28 percent of the total personnel of this type estimated as
employed in all the laboratories listed. In addition to this
numerical coverage, an attempt was made to include among
the 78 firms visited small as well as large firms, plants in
all parts of the United States, and a variety of industries.
However, the intricate industrial organization, interrela
tionships, and variety of research revealed in the directory,
added to the fact that some firms did not report personnel
statistics and none reported women separately, made the
selection of a true sample complicated beyond its value for
this purpose. The firms visited were chosen rather as a
clue to industrial firms most likely to be engaged in the
type of -work in which women trained in science are used. In
all firms, information was requested for the entire organ
ization rather than for the research laboratory only.
Eighteen commercial testing laboratories which offer test
ing services to industry and individuals and which
employed women were also visited. Seven others contacted
did not employ women. These 25 laboratories represented
10 percent of the 244 commercial testing laboratories listed
in the National Bureau of Standard’s 1942 Directory of
Commercial Testing and College Research Laboratories.
Since personnel is not reported in the directory, there is
no clue to the coverage of workers.
FOREWORD
4—VII
Three large additional industrial firms which employed
women in laboratory work but were not listed as having re
search laboratories were visited, as was one biological sup
ply house.
Research institutions: Eight research institutions or centers,
some of them identified with a particular college or university,
also supplied information on women members of the scientific
staff.
Colleges and universities: Statistical information on the number
of women graduated with degrees in science, mathematics, and
engineering over a period of years from 1939^0 to 1946 was
obtained from 30 colleges and universities and from 9 engineer
ing schools. Again an attempt was made to obtain wide
geographical coverage and to cover different types of institu
tions, such as women’s colleges, State universities, and small
liberal arts colleges. The information available from these
sources, too, varied. Placement bureaus and heads of science
departments as well as deans of women at these institutions and
at six other colleges contributed reports on the demand for
women trained in the sciences. The Western Personnel Insti
tute made possible the inclusion of data which it collected for
the Bureau from its affiliated colleges and universities in the
far West.
Since no recent data were available on the number of women
teaching science in the colleges, a count was made in 1947 of
the women identifiable by name who were listed on science
faculties in the catalogs of 330 institutions of higher learning
which were then available in the United States Office of Edu
cation Library. These institutions were selected because they
are believed by the United States Office of Education to be
representative in their enrollments of the 1,749 institutions of
higher education in the United States and, therefore, are likely
to have faculties equally representative.
Other sources: In addition, 97 individuals not included in the
afore-mentioned sources, most of them women scientists, con
tributed information, suggestions, or helpful criticisms of
the preliminary manuscripts circulated before revision for
publication.
While every effort has been made to obtain wide coverage, there
remain some dark corners still unexplored because of the range and
variety of these fields and the difficulty of obtaining information from
widely scattered sources. Perhaps this beginning will result in
further additions to our so-little knowledge.
772328°—48------ 2
Courtesy National Bureau of Standards
Figure 1.—A mathematician at the National Bureau of Standards works
on a sampling problem as part of a research program conducted by
the Statistical Engineering Laboratory at the Bureau.
4—VIII
CONTENTS
Page
Letter of transmittal------------------------------------------------------------------------Foreword
Prewar distribution--------------------------------------------------------------------------Annual addition to the supply------------------Wartime changes --------------------------------------------------------------------------Earnings and advancement---------------------------------------------------------------Organizations
4-9
The outlook------------------------------------------------------------------------------------Appendix:
Minimum education and experience requirements for beginning Federal
civil-service positions as:
Mathematician 4-18
Statistician------- ---------------------------------------------------------------------Sources to which reference is made in the text-------------------------
4-m
4-v
4-2
4-3
4-3
4-7
4-9
4-19
4-20
Illustrations:
1. A mathematician works on a sampling problem------------------------------- 4-vm
2. A mathematical statistician in the U. S. Department of Labor----------- 4-15
4-1X
Mathematician as Defined in the Dictionary of Occupational
Titles (13)
A term applied to a worker who has attained eminence in some field
of mathematics and is a recognized authority in that field.
Mathematical Statistician as Defined by the National Research
Council’s Committee on Applied Mathematical Statistics (10)
“The mathematical statistician is a mathematical expert who con
cerns himself primarily with critical mathematical investigations of
statistical problems which arise in * * * various fields, and with
the development of methodology for dealing routinely with them.”
Statistician and Actuary as Defined in the Dictionary of
Occupational Titles (13)
“Statistician (profess, and kin.) 0-28-10. Plans procedure and
technique for solution of statistical problems and devises formulas for
induction of data; must possess a thorough knowledge of mathematics;
analyzes quantitative statistical data, such as money, labor problems,
marketing, and agricultural problems; adjusts standard methods of
mathematical analyses to type of data used; devises or develops new
methods of analysis; selects methods of presenting information, such
as charts, diagrams, graphs; searches out and corrects inconsistent
data. May write reports and summaries presenting the findings.”
“Statistician, actuarial; actuary (insurance). A statistician (pro
fess. and kin.) who calculates the rates to be charged for different types
of insurance (annuity, life, fire), basing his calculations on scientific
investigations and analyses of natural laws affecting human life, theft
hazards, and other conditions which affect insurance.”
4-X
THE OUTLOOK FOR WOMEN IN MATHEMATICS
AND STATISTICS
The term “mathematician” is usually reserved for those who have
a Ph. D. or its equivalent in mathematics and are engaged almost
exclusively in research or in college teaching.1 Engineers and those
engaged in the physical sciences also need preparation in higher
mathematics, which they apply to specific problems within their fields.
This discussion, however, is confined to the mathematician, the mathe
matical and applied statistician, and others whose principal prepara
tion for their occupation is college-level training in mathematics or
statistics. Among them are actuaries, teachers of high-school mathe
matics, statistical clerks, computers, mathematical aids and assistants.
Engineering aids and engineering draftsmen, similar in their re
quirement and use of mathematics, are discussed in the bulletin on
engineering. (See Bull. 223-5.)
Although the exact number of mathematicians and of others
engaged in mathematical occupations is unknown, some idea of the size
of the total group may be gained from the maximum number registered
with the National Roster of Scientific and Specialized Personnel dur
ing the wTar, in April 1944: those in the field of mathematics num
bered 17,357; in statistics, 3,737; and in actuarial science, 839. Only
3 percent of the latter were women, while 12 percent of those in mathe
matics and 14 percent of those in statistics were women (IS). Since
registration with the Roster is voluntary, there is no way of knowing
how complete or how representative these figures are. But these
percentages of women members correspond to those in the principal
mathematical societies. About 15 percent of the members of the
Mathematical Association of America and about 13 percent of those
of the American Mathematical Society are women. Approximately
10 percent of the members of the American Statistical Association are
women, and 3 percent of the fellows and associates of the two actuarial
societies are women (5). However, among high-school teachers of
mathematics, estimated at some 40,000 in 1947, women are in the
majority, and they predominate in the National Council of Teachers
of Mathematics. Many of these are trained principally in education,
rather than in mathematics, and they are probably not among those
on the National Roster list.
1 In civil service and very occasionally in industry, however, the term is used also for
the beginning professional level which requires the bachelor’s degree with a major in
mathematics.
4-1
4-2
WOMEN IN MATHEMATICS AND STATISTICS
Prewar Distribution
In 1940, according to an American Council on Education study,
there were 695 living recipients of Ph. D. degrees in mathematics con
ferred in the preceding decade. Of the 647 who reported their occu
pation, 85 percent were teaching, and an additional 4 percent combined
teaching and research. Less than 6 percent were engaged solely in
research, and no other single type of work claimed as much as 2 percent
of the group (6).
The exact number of mathematics teachers before the war is not
known. But the first Roster count in December 1942 revealed that
there were 3,483 mathematics teachers in institutions of higher learn
ing; and 686, nearly one-fifth, of these were women {14). Mathe
matics was taught in some 28,000 high schools in the country (7). In
many of these, there was only one mathematics teacher, who also
taught one or more other subjects; in others, there wei’e several full
time mathematics teachers on the faculty, sometimes as many as 25
or even more.
The relatively small number of mathematicians in industrial re
search before the war is indicated by Thornton C. Fry’s estimate that
in 1940 there were about 150 mathematicians doing consultative work
on mathematical problems in industry {4). The largest prewar de
mand for women trained in mathematics was reported consistently
by college placement bureaus to be in teaching or as statistical clerks
in insurance or other business firms. Mathematics majors with special
training in mathematical statistics or such applied courses as mathe
matics of finance, for example, were especially in demand. A few
women, however, were employed even before the war in calculating
or computing jobs with firms manufacturing such products as instru
ments and electrical equipment.
Some of this work was only arithmetical, and some women saw little
difference, except in location, between their work as computers in an
engineering department and that of cost clerks or calculating machine
operators in the office. Several employers reported that they hired
college mathematics majors not because of the need for higher mathe
matics on the job but because such training indicated accuracy and a
liking for computing. However, even before the war, there were some
exceptional women who were doing responsible mathematical work
in industry. For example, one woman with a Ph. D. in mathematics
from a large women’s college has been engaged in research in the mathe
matical research department of a utility company for about 15 years.
Although such cases are unusual, they indicate that opportunities
do exist for the woman with ability.
WOMEN IN MATHEMATICS AND STATISTICS
4-3
In 1038, only 85 women mathematicians and statisticians were em
ployed by the Federal Government {16). The Civil Service Com
mission reported that the demand for women mathematicians before
the war was never great.
Annual Addition to the Supply
A small but steadily increasing number of persons took doctorates
in mathematics before the war, and in 1940, 103 persons obtained Pli.
D.’s in mathematics, the largest number in any one year up to that
time {6). In the relatively new field of mathematical statistics, only
5 or 6 doctor’s degrees were awarded annually before the war, accord
ing to recent estimates {10).
No figures are available on the number of persons receiving first
degrees in mathematics in 1940. But the United States Office of Edu
cation reports the combined number of graduates with majors in
mathematics and in physical science in 1941-42 as 3,053, of whom onethird were women {19). In the same year, almost 1,000 people pre
pared to teach mathematics were graduated from colleges and univer
sities, and about 45 percent of these graduates were women {19).
For the most part, their degrees were from schools of education.
Wartime Changes
During the war there was a tremendous increase in the demand for
women trained in mathematics in industry, in Government, and in re
search institutions working on Government projects. One women’s
college reported that every mathematics major had her choice of 25
jobs in industry or Government, and that the demand was overwhelm
ing in research work. A coeducational university, which before the
war had few outlets for mathematics majors except in routine cal
culating jobs, found many attractive jobs available to mathematics
majors during the war, mostly in Government-sponsored research.
ThiM same story was repeated in a number of college placement bureaus
throughout the country. There was a definite shift from the usual
type of employment for mathematics majors in teaching and in clerical
jobs in business firms to computing work in industry and on Govern
ment war projects.
Of 81 industrial firms visited by Bureau representatives near the end
of the war or after its close, only 15, less than one-fiftli, had employed
college women in mathematical occupations during the war either in
the research laboratory or in the plant, usually in the engineering
department. Among them were gas and electric power companies, and
manufacturers of transportation equipment, communications and
4-4
WOMEN IN MATHEMATICS AND STATISTICS
other electrical equipment, instruments, metal and metal products.
The foods, paper products, and chemical industries were also repre
sented, but the principal employment of women mathematical aids or
assistants, computers, and calculators (as they were variously called),
like that of engineering aids, was found in the industries in which
engineering and physical problems rather than chemical problems
were paramount. None were found in the 18 commercial laboratories
visited.
Since their work consisted primarily of assisting engineers or
research personnel with calculations or of performing inspecting or
checking operations involving computations, their duties varied from
purely routine arithmetical work to the solution of difficult problems
requiring the use of calculus and other forms of higher mathematics.
Graph and chart making was sometimes involved. In an aircraft
plant, for example, beginning “computers” read blueprints and made
weight calculations on simple parts, using slide rules and calculating
machines. More experienced computers employed in the same plant
were working under the supervision of test engineers and assisted them
by working out solutions of differential and integral equations, by
plotting test data, and by preparing data sheets and charts. The only
industrial establishment visited in which women were called mathe
maticians was another aircraft plant. The requisite training was 2
years of advanced college mathematics, or, for “senior” mathemati
cians, 4 years of training and experience. More routine work was done
by technical computers, who were required to have at least 1 year of
college mathematics.
On Government-sponsored projects farmed out to university and
other private research laboratories during the war, like those carried on
at the Radiation Laboratory at Massachusetts Institute of Technology
and the Manhattan project work at the University of Chicago, women
mathematicians, especially those who combined physics with their
mathematical training, were employed in relatively small numbers,
along with a larger number of computers with only the bachelor’s
degree. Because such demand was virtually nonexistent before the
war, it made a sizable impression. Some women transferred from
college teaching to this type of work during the war period.
The women’s military services, especially the WAVES, in the early
expanding phase of their programs, were particularly eager to recruit
college graduates with training in mathematics and science. Approxi
mately 1,500 college graduates, most of them with mathematics or
science majors, became WAVES officers who were trained for technical
work in communications, air navigation, and aerology, often by other
WAVES, whose earlier scientific training and teaching experience had
resulted in their selection for such work.
WOMEN IN MATHEMATICS AND STATISTICS
4-5
A large group of the women became aerological officers and were
engaged in meteorological work. (See Bull. 223-7, on Meteorology.)
Others were assigned to such jobs as instruction in air navigation and
work in ordnance. One woman supervised naval personnel assigned
to a ballistics laboratory; another worked on computations of ballistic
range tables and bomb tables, making computations from penetration
charts and of various problems of exterior ballistics. A few others
were assigned to survey work in radio, radar, and electronics, checking
specifications and obtaining information from radio companies for
complete identification of radio parts.
Mathematician, computer, geodetic computer, and cryptographer
were among the job titles of a small group of WAC personnel who had
the needed mathematical background for such work. Those who had
some statistical training worked as statistical clerks, financial clerks,
and financial technical clerks (28).
In the Federal Civil Service, women trained in mathematics were
sought for many jobs, beginning at the junior professional level,
which required only the bachelor’s degree with a major in mathe
matics. They were employed not only in the War Department
(Ordnance, Signal Corps, Engineer Corps) and in the Navy De
partment, including the Naval Research Laboratory, but also in the
National Advisory Committee for Aeronautics, the Bureau of Recla
mation, the Federal Bureau of Investigation (as cryptographers), the
National Bureau of Standards, and the Coast and Geodetic Survey.
Special courses in mathematics were given in the Engineer Corps,
Ordnance, and the Signal Corps, all in the War Department, to train
needed personnel (22).
In Government, as in industry, the work varied from simple cal
culations to more complex assignments. Much of it was routine,
but, as one research man long in Government service puts it, most
mathematical work, no matter the degree of difficulty, involves rou
tine. However, the difference between the mathematician and the
routine computer, according to a well-known woman mathematician,
“is precisely in handling the nonroutine aspects of the problem
* * *. The distinctive contribution of the mathematician is either
in clarifying the structure of a problem which has confused the
engineer or physical scientist, and formulating it in mathematical
language; or in creating a new mathematical theory, or extending
a branch of an old one.”
The increased Government and industrial demand, plus the drafting
of men into military service, resulted in shortages of qualified teach
ers. Early in the war, on the basis of reports from 1,060 colleges and
universities in the fall of 1942, the United States Office of Education
stated that mathematics was one of the subject fields in which there
772328°—48------3
4-6
WOMEN IN MATHEMATICS AND STATISTICS
was a great number of vacancies, 57, on these college and university
faculties {17).
The demand for statisticians and statistical clerks increased tre
mendously during the war. In 1944, the American Statistical Asso
ciation had requests for more statisticians than it could supply, at
salaries of $2,000 to $6,000 annually {12). College placement bu
reaus reported that women mathematics majors had their choice of
a wide variety of jobs as statistical clerks or computers. The War
and Navy Departments, medical centers, public health departments
and agencies and other medical groups, as well as insurance com
panies, and at least one Federal Reserve bank were among the em
ployers of recently trained statisticians.
A study of the employment of the members of the American Statis
tical Association in 1945 showed that the largest proportion of them,
nearly two-fifths, were in Government, most of them in the Federal
Government. Almost one-fifth were in colleges and universities, and
another one-fifth were in manufacturing industries and financial
institutions. About half of the members lived in two areas, the
Washington, D. C., area and New York State, chiefly New York City.
There was an approximately equal number in each of these areas {8).
In the Institute of Mathematical Statistics the proportion of members
in academic positions was much higher; more than one-half of them
were so employed {10).
The lack of teaching personnel made it necessary for some schools
to curtail their course offerings in mathematics. This was especially
serious for those who wanted to go on with advanced training, but
who found that only standard mathematics courses were being offered
{3).
The number of doctorates awarded in mathematics, never large,
declined sharply during the war as prospective students were with
drawn into military service. More than 100 were earned in 1940; only
41 in 1944 (5). The number of persons receiving first degrees in
mathematics and science also declined from 3,053 in 1941-42 to 2,709
in 1943—44. The number of women in the group, however, increased
from 1,012 to 1,141 {19).
Under the special Engineering, Science, and Management War
Training programs, a number of women were given special training
in mathematics to equip them for war jobs in industry and Govern
ment, according to the United States Office of Education. Among
these courses were: engineering mathematics and calculus, as well as
such specialized applied courses as mathematics for aircraft workers,
for high-school teachers, for engineering aids {18). In addition, ap
proximately 3,500 production and inspection engineers and other in
dustrial personnel, from over 800 of the larger industrial corpora-
WOMEN IN MATHEMATICS AND STATISTICS
4-7
tions, were trained in the use of some of the simpler statistical methods
of quality control, in short intensive courses given throughout the
country (10).
The wartime emphasis on sciences, particularly the physical sciences
and mathematics, stimulated enrollments in regular college mathe
matics classes. Prof. G. B. Price, in a study of enrollments in mathe
matics courses for the Mathematical Association of America, found
substantial increases in enrollments between 1941-42 and 1942-43.
The increase was usually 30 percent for men’s colleges and ranged
from 25 to 40 percent in eastern women’s colleges (3). But coeduca
tional schools, with few exceptions, reported little or no increase in
the number of students taking mathematics. Despite the higher en
rollment of women in mathematics courses, the number of women ma
joring in this field remained very small. Reports from 24 colleges and
universities on women graduating with majors in mathematics indi
cated no abnormal fluctuation in the number of such graduates during
the war period.
Earnings and Advancement
The earnings of a college graduate with a degree in mathematics
depend upon the type of work that she does. They are low in the
largest field, that of teaching, although they have been increasing
recently. According to scattered college placement bureau reports,
most of the beginning jobs in teaching and in business pay less than
$2,000 per year; during the war, many beginning jobs in industry
paid $2,000 or more per year, and this was the beginning rate for
mathematicians in Government. In 1947 the entrance salary in the
Federal Civil Service for mathematicians and statisticians was $2,644
per year.
"Teachers’ salaries vary considerably, not only in different sections
of the country but also in cities of different size. In 1940-41, the
median salary of $2,768 paid to high-school teachers in cities having
a population over 100,000 was nearly twice as large as the $1,428
received by those in cities of 2,500 to 5,000 population. By 1946—17,
the median salary of teachers in the largest cities had increased to
$3,593. For those who taught in cities whose population was 2,500 to
5,000, the median salary in that year was $2,274. Although the differ
ence between the earnings of teachers in the largest cities and those in
the smallest cities was less in 1946-47 than in 1940-41, nevertheless it
remained a substantial one (9). According to the United States
Office of Education: “The median salaries of professors in different
types of publicly controlled institutions ranged in 1939-40 from
$2,900 to $5,000, and in different types of privately controlled insti-
4-8
WOMEN IN MATHEMATICS AND STATISTICS
tutions, from $1,800 to $5,000. Associate and assistant professors,
and instructors, on an average, received less” (W).
Statisticians, at the PIi. D. level, are paid somewhat higher salaries
than are mathematicians. This is partly a result of their scarcity.
Only about 50 Ph. D.’s in mathematical statistics have been awarded
so far, according to a recent estimate (10). It is also due in part to
a difference in type of employment. Most persons who have the Ph. D.
in mathematics teach in colleges and universities, where salaries
are relatively low. On the other hand, professional statisticians are
more likely to be employed in industry or in Government, often at
higher salaries. This is particularly true of actuaries. At the bache
lor’s level, salaries are more nearly equal to those in mathematics, al
though the opportunities are broader for the graduate trained in
mathematical and applied statistics.
Women mathematics majors with the bachelor’s degree sometimes
become statistical clerks, whose jobs usually pay about the same as
those of computers. Although salaries for statistical clerks with
college background were as low as $1,000 per year before the war, in
1946 placement bureaus reported that mathematics majors were being
hired as statistical clerks by State agencies and private industry at
$140 and $150 per month, or about $1,680 to $1,800 per year.
Except for Ph. D.’s, women trained in mathematics tend to be em
ployed at the assistant level. In the industrial establishments and
in the Government agencies visited in connection with this study, only
a few women mathematicians were found in high-level jobs, and they
usually had also specialized in one of the physical sciences. However,
one woman in industry was supervising a large group of women com
puters; another was found on independent research work of a Gov
ernment research project. In the teaching field, women are appointed
to college faculties, but only a few reach the professorship level. They
seldom become heads of departments, either in colleges or in secondary
schools, except in colleges and schools for women. That it is pos
sible for competent, well-trained women to attain positions of respon
sibility is indicated by the achievements of a few. Listed in the 1938
edition of American Men of Science, among the 80 mathematicians
who have made outstanding contributions to scientific progress, were
4 women (%).
Because there are many more outlets for statisticians and because
there is a shortage in this field, advancement is usually more rapid
for qualified women in statistics than in mathematics. The posses
sion of the Ph. D. is important for recognition in this field, too. Be
cause of their background and understanding of the insurance busi
ness, men actuaries frequently move into high executive positions in
insurance firms ( /), but this is seldom true of women.
WOMEN IN MATHEMATICS AND STATISTICS
4-9
Organizations
Among the largest professional mathematical societies are the Math
ematical Association of America, the American Mathematical So
ciety, and the National Council of Teachers of Mathematics. Each
of the first two groups has more than 3,000 members. The teachers’
group has about 6,000 members, most of whom are women. Most of
these have mathematical training, although there may be some who
do not, since the only requirement for membership in all of these
groups is an interest in mathematics.
There are a number of professional societies for statisticians, some
of them confined to the special fields in which statistics is applied.
In addition to the Institute of Mathematical Statistics, which includes
statisticians interested in statistical theory and technique, there are,
for example, an Econometric Society and a Psychometric Society,
whose members have specialized in statistical measurements in the field
of economics and psychology respectively. All of these are of com
paratively recent origin and have had a great increase in membership
in a relatively short time. The American Statistical Association is an
all-inclusive group, which in 1946 had some 4,000 members, about 10
percent of them women. The Institute of Mathematical Statistics,
organized in 1935, had about 900 members in 1946; interest in statis
tics is the only requirement for membership in the Institute as well
as in the American Statistical Association (10). Membership in the
principal organizations of actuaries, the Actuarial Society of Amer
ica and the American Institute of Actuaries, on the other hand, is
restricted to those passing a series of examinations given jointly by
the two societies. Candidates become associate members upon passing
five examinations and full members or fellows after passing 3 more.
In these two groups combined, in which the membership is largely
duplicating, there are only about 565 fellows, including actuaries in
the United States and Canada. There are 562 fellows and 301 asso
ciates of the Actuarial Society, of whom 12 fellows and 11 associates
are women.
The Outlook
Although, during the war, production firms and Government proj
ects were important outlets for women trained in mathematics, the
emphasis, following the end of hostilities, shifted back to the more
usual channels. Teaching and employment with insurance and other
business firms again became the principal outlets for women college
graduates with mathematical training. The wartime shortage of liighschool teachers has continued, particularly in mathematics and certain
other fields {20). Placement officers in colleges throughout the coun
4-10
WOMEN IN MATHEMATICS AND STATISTICS
try in 1947 noted a continuing demand at the wartime level for women
mathematics teachers in secondary schools. At least 40,000 teachers
of mathematics were teaching in junior and senior high schools in
1947, according to the chairman of the Commission on Postwar Plans
of the National Council of Teachers of Mathematics. The preponder
ance of women in this organization is indicative of their numerical
importance in high-school teaching. Because men appear to be leav
ing this field, it will become increasingly important for women.
Most high-school teachers give instruction in more than one subject,
and existing teaching vacancies can often be filled only by persons pro
ficient in several related fields. Certain subjects tend to be grouped
together. Since mathematics teaching is usually combined with that
of the physical sciences, the woman who plans to teach high-school
mathematics will have wider opportunity if she is also able to teach
high-school science, particularly physics or chemistry.
In colleges and universities, too, opportunities for women mathe
matics teachers continued. The secretary of the American Mathe
matical Society stated in 1946 that there were not enough well-trained
women to fill all the first-class mathematical positions available to
them in colleges and universities. Some graduate work is practically
essential for appointment to college faculties, and, before the war a
Ph. D. was considered necessary to attain professorial rank. How
ever, the Women’s Bureau found, in 1947, that of a sample of women
with the rank of assistant professor or above in mathematics, less than
one-half had the Ph. D. Shortages will probably continue in
this field for several years; but as more persons with the Ph. D. be
come available it will become more difficult to attain professorial rank
without it. A report to the President in 1945 predicted that there
will be, due to the war, a total deficit of 1,200 Ph. D.’s in mathematics
by 1955 {21).
Most of the wartime research projects sponsored by the Government
were dropped after VJ-day. In the few that continued, the small num
ber of mathematical jobs were filled by the staffs of the institutions at
which the research was being done and by men with mathematical skills
who were being released from military service. The women’s military
services, which utilized women with mathematical training during
the war, were reduced to very small staffs. One, the SPARS, ceased
to exist, and the continuance of the others will depend upon the
passage of special legislation. In any case, only a few mathematical
jobs will be found in peacetime in these agencies.
Federal civil-service demand for women mathematicians continued
after the wTar. In 1947 a few women mathematicians were still em
ployed in such agencies as Ordnance in the War Department, the Naval
Research Laboratory, the Coast and Geodetic Survey, the National
WOMEN IN MATHEMATICS AND STATISTICS
4-11
Bureau of Standards, the National Advisory Committee for Aero
nautics, and the Tennessee Valley Authority. It appeared that the
demand from the Federal agencies would continue for some time to
outstrip the supply of those qualified. At the National Bureau of
Standards there were almost as many women mathematicians em
ployed in 1947 as there were during the war. On the other hand,
at the Coast and Geodetic Survey, women were being displaced as
men veterans returned. The Federal Bureau of Investigation, also,
had already dropped many of the women who had been hired for
cryptographic work during the war.
Women mathematicians and computers in 1947 were working on
the National Bureau of Standards mathematical tables project, lo
cated in New York. In the spring of 1947, this project employed seven
mathematicians, excluding the Director; three of them were women,
two of whom contributed work on a research level. There were also
24 women computers, about two-thirds of all the computers on the
project. However, in 194G, most of the vacancies on the computing
staff had been filled by male veterans. Turn-over is low, and it is
not expected that there will be many openings for men or women
computers there in the near future.
In industry, 14 of the 15 establishments covered in this study that
had women mathematical w-orkers on the pay roll during the war con
tinued to employ some of them following the war. The number of
women in mathematical occupations in these firms even during the war
was small, seldom over 25, although one very large corporation em
ployed about 100 women in mathematical work. These were computers
doing calculations for the technical staff; some of them have been
employed in these same jobs for many years.
Most of the industrial jobs available to women will continue to be
in computing, but this demand is almost negligible as compared with
that during wartime. Calls from industry for women trained in
mathematics were reported to be rare in 1947. A large aircraft com
pany, for example, which during the war asked one college for 100 or
more women at a time, was asking for groups of only a half dozen
after the war’s end.
Some of the employers expressed a preference for men, although
they planned to retain the women mathematical workers they had
hired during the war. As the women leave, however, men will be
hired to replace them. College placement officers also reported that
some well-qualified graduates had been dropped from industrial re
search jobs held during the war. Although many women are con
tinuing on their wartime mathematical jobs, it is difficult to say how
much of the gain will be in terms of permanent opportunities for
4-12
WOMEN IN MATHEMATICS AND STATISTICS
women. Much depends on the success of those who remain on the
jobs which opened up during the war.
From 1940, when there were in industry about 150 mathematicians
trained to or nearly to the Ph. D. level, to 1947, there was an appre
ciable increase in such personnel, according to the statement, of a
prominent research mathematician in the communications industry.
Not only is normal industrial research going forward, but a consider
able amount of postwar military research is continuing, partly in
industry, partly in Government laboratories, and partly in universi
ties. Many of the mathematical questions raised in this type of
research are akin to those raised in normal industrial research. A
substantial number of mathematicians are engaged in this work,
although few of them are women.
Although the demand for highly trained mathematicians in indus
try will increase, scientists seem to agree that it will never be compara
ble in volume to that for engineers, chemists, or physicists (^). Op
portunities for the woman Ph. D. in industry are few compared with
those on college faculties. However, entrance into industrial research
will be easier for women Ph. D.’s in the next few years than it is likely
to be later when a greater supply of men with the doctorate will be
available.
Employers complain frequently that men as well as women with de
grees in mathematics enter industry with no knowledge of applied
mathematics or of the problems and the terminology of the industry
(&£). Women who want a career in mathematical research in indus
try can increase their opportunities by taking some engineering or
other applied courses that will increase their understanding of the
practical problems requiring mathematical solutions in industry. For
consulting or research work in industry, a Ph. D. degree and a knowl
edge of the industry are essential.
Although the United States assumed world leadership in pure mathe
matics between World War I and World War II, mathematicians
in this country have tended to ignore applied mathematics, and not
much emphasis has been placed upon it by institutions of higher learn
ing. But the wartime situation emphasized the importance of applied
mathematics, which was used in the solution of problems relating to
aircraft design, explosion theory, exterior ballistics, and nuclear
physics, among others. Partly as a result of its prominence during the
war, universities are giving somewhat more attention to applied
mathematics than formerly. There is a School of Applied Mathe
matics at Brown University and an Institute of Mathematics and
Mechanics at New York University; and other universities are offering
courses in this field. In addition, it has been proposed that a unit,
to be known as the National Applied Mathematics Laboratories, be
WOMEN IN MATHEMATICS AND STATISTICS
4-13
established as part of the National Bureau of Standards. The pur
pose of the unit is described by the Bureau as follows: “It will spe
cialize in numerical and statistical analysis, and will undertake to offer
various services in these fields, and carry on a broad program of re
search and training. Particular emphasis will be placed on the devel
opment of high-speed automatic computing machinery and the mathe
matical theory needed for its effective use.” The projected program
for the laboratories also includes a training program, to consist of
instruction and work experience, for graduate students in applied
mathematics.
The industrial demand for statisticians, which increased tremen
dously within recent years, especially in the last decade (10), appears
to be continuing. This growth was further stimulated by the wartime
use of statistics in statistical control work and in planning. Sampling
methods, for example, developed by mathematical statisticians, made
it possible and safe to substitute inspection of only one of a number
of units produced in a war plant for the inspection of every unit. The
saving of time and manpower was tremendous. This is only one of
the many applications of statistics that has resulted in accelerating
the demand for statisticians.
The National Roster of Scientific and Specialized Personnel
reported that, in a 9-month period in 1945—46, for every 1,000 persons
registered in statistics, there were 30.7 vacancies reported to the
Roster, as compared with 4.4 vacancies per 1,000 registrants in mathe
matics and 23.9 in physics. The openings in statistics were divided
about equally between industry and Government; there were none
from colleges, which usually recruit directly (10).
The postwar demand for statistically trained personnel was studied
by the National Research Council’s Committee on Applied Mathe
matical Statistics, which in April 1946 made an inquiry concerning
requests for statisticians received by 30 leading authorities in this
field. Although undoubtedly some of the requests were duplicating,
their number and type illustrate the demand. About 140 requests
were received from business and industry, most of them to fill positions
in industrial quality control and in engineering, but there were also
many for sampling experts in market research organizations. The
educational requirements ranged from the bachelor’s degree to the
doctorate (10).
Almost as many requests, 135 in all, came from academic institu
tions for persons with Ph. D.’s in mathematical statistics, or in such
fields as agronomy, biology, economics, or psychology, if combined
with a minor in statistics. The positions offered ranged from instructorships to full professorships. One of the 30 authorities
reported 12 requests for men trained in agronomy and statistics;
4-14
WOMEN IN MATHEMATICS AND STATISTICS
another had received requests for mathematical statisticians from 21
colleges and universities (10).
Women mathematics teachers in 1947 numbered 355 in 330 colleges
and universities which comprise a United States Office of Education
enrollment sample of the 1,749 institutions of this type in the United
States. Most of them, 304, were teaching mathematics only; the others
were instructing in some other subject as well. If these institutions
are as representative of the faculties of all institutions of higher edu
cation as they are of enrollments, 1,710 women college teachers of math
ematics were employed in 1947, 85 percent of whom taught mathe
matics only. The others usually taught a science, such as physics or
chemistry, but sometimes a language, or economics, or some other sub
ject was combined with mathematics in the teaching schedule. A very
few combined the duties of counselor or dean with mathematics teach
ing. Two women included in the sample headed mathematics depart
ments. Unlike women teachers in some of the sciences, women mathe
matics teachers were found in all types of institutions, in larger uni
versities as well as in women's colleges.
Government was also represented among the requests for statis
ticians reported by selected authorities to the National Research
Council’s Committee on Applied Mathematical Statistics. Approxi
mately 90 requests for statisticians came from Federal and State
government agencies in a 6-month period. Most of these were from
the Federal Government (10).
In the fall of 1944, David M. Schneider made a survey of 164 govern
mental agencies in 23 States, representing all areas of the country.
He estimated that State agencies needed, at that time, a total of over
600 statisticians and nearly 1,100 statistical clerks. This included both
currently employed personnel and vacancies. Since there has been
a trend toward greater utilization of statistical personnel, it is likely
that the total need in State agencies is at least as great as it was in
1944. State departments of labor employ the largest number of
statistical clerks; public welfare departments and health departments
rank second and third in employment of statistical personnel, who
are also employed in State departments of highways, agriculture,
taxation, education, banking and insurance. Comments from the
States indicated that, although practically all municipal governments
perform some statistical functions, few technically trained statis
ticians are employed for such activities (11).
According to the National Research Council, in recent years the
growth in statistical opportunities has been especially great in the
fields of: (a) industrial statistics (quality control, research, and de
velopment); (i) research in the biological sciences; (c) collection and
WOMEN IN MATHEMATICS AND STATISTICS
4-15
analysis of government statistics; (d) market research and com
mercial sample surveys; and (e) psychological testing (10). However,
there are jobs for statisticians in many and varied fields, including
that of teaching to prepare additional needed statisticians.
The 1947 count of women faculty members in 330 institutions of
higher learning, as mentioned on page 4-14, revealed only 10 women
teaching statistics and 3 teaching biostatistics in these schools. This
would indicate that there are about 45 women teaching statistics pri
marily in all colleges and universities, two-thirds of whom are in
publicly and privately controlled universities and the others in
technical and professional schools. There are probably a great many
more who teach statistics courses along with other subjects such as
economics or mathematics. These would not show in the count, since
such faculty members would be listed as instructors or professors of
economics or mathematics.
I
Courtesy U. S. Department of Labor
Figure 2.—A mathematical statistician in the Bureau of Labor Statistics,
U. S. Department of Labor.
4-16
WOMEN IN MATHEMATICS AND STATISTICS
For at least a few years to come, then, there will be ample opportunity
for statistically trained women, who will not encounter as much dis
crimination in this relatively new and growing field as women in
many other professional fields have had to combat.
The inadequacy of present facilities and teaching personnel for the
training of statisticians has received attention in a special study of
the Committee on Applied Mathematical Statistics of the National
Research Council. In 1946, only 10 colleges and universities were
reported to have programs in mathematical statistics adequate for
the training of Ph. D’s {10). Among the schools at which outstand
ing work is being done in this field are Princeton, the University of
California, Columbia, and Iowa State College. Another school which
has recently emphasized this field is the University of North Carolina,
where an Institute of Statistics is directed by Prof. Gertrude Cox.
Only 14 institutions, including most of the 10 that were prepared to
offer the Ph. D. in mathematical statistics, were equipped also for
advanced training in applied statistics {10).
For Government workers and others living in Washington, D. C., a
variety of courses in statistics are offered at the Graduate School of
the United States Department of Agriculture. Evening classes are
held, and in addition to classwork, students can get experience in
sampling at the Bureau of Census and other agencies.
A specialized group of statisticians are the actuaries, whose oppor
tunities are limited chiefly to insurance companies, although there are
expanding opportunities for them in business and industry, because
of the increasing trend toward pension and retirement plans. In
addition, there are jobs in many State insurance departments, which
supervise and regulate the insurance business, and in such Federal
agencies as the Bureau of the Census, the Social Security Administra
tion, and the Railroad Retirement Board. There are also occasional
calls from Latin-American and other foreign countries for Americantrained actuaries. In spite of the limited number of organizations
which employ actuaries, this field is not overcrowded. There are over
350 life insurance companies in the United States and Canada; most
of them are growing in size, and their business is becoming more com
plex. There are only about 565 fellows of the Actuarial Society of
America and the American Institute pf Actuaries, and many more
are needed (1). “In the next few years the 350 insurance companies
in the United States will require several hundred more actuaries than
they now have,” according to the Committee on Applied Statistics of
the National Research Council {10).
Those who plan to enter this profession usually major in mathe
matics but often study economics or business administration in addi
tion. They frequently take the first three of the eight examinations
WOMEN IN MATHEMATICS AND STATISTICS
4-17
necessary to qualify themselves as Fellows of the actuarial societies
while they are in college, taking the other examinations later while
employed, usually with an insurance company (1). Only the woman
of superior ability should be encouraged to take the very difficult
actuarial examinations, which only a small proportion of the candi
dates pass.
Although women fill most of the'clerical jobs in insurance offioes
and some become actuaries’ assistants, they rarely become actuaries.
One young woman who worked as an engineering aid for an aircraft
company during the wTar and had excellent recommendations from
that company wTas recently hired by a firm of consulting actuaries and
hopes to become an actuary. But insurance companies have tradi
tionally preferred men for these positions, and only the exceptional
woman will pass beyond the position of assistant to an actuary. Two
women, one of them a Negro, are actuaries of small companies, al
though other’s have reached the mid-ranges of associate actuaries and
mathematicians in larger companies. This is a field in which women
must have unusual ability to succeed. A prominent actuary says that,
“A woman can succeed in this field, but she has to be 50 percent better
than her nearest male competitor to do it.” An outstanding woman
who has combined actuarial training with a Ph. D. in economics sug
gests that the woman actuary’s best chance for success lies in doing
the unusual, in finding a relatively unexplored area and specializing
in it. She attributes her own success to her ability to handle problems
which a person trained solely as an actuary or solely as an economist
would not be prepared to handle.
Although the shortage of Ph. D’s in mathematics and statistics
is expected to continue for some time, there appeared in 1947 to be a
satisfactory adjustment in the demand for and supply of women with
the bachelor’s degree in mathematics. According to reports from
college placement bureaus, even before the war, the number of women
mathematics majors graduating from college each year, although
small, was just about enough to meet the demand for people with such
training. Recent reports indicate a return to this tendency to equili
brium following the wartime distortion. But the shortage of statisti
cians, trained at both the bachelor’s and the Ph. D. level, will continue
for some years to come.
Women as well as men who have the capacity to do doctoral work
in mathematics, however, are needed in greater numbers than ever be
fore, and training is readily available in a number of institutions of
higher education. Theoretical mathematics is basic to scientific prog
ress, and the ability to contribute to knowledge in this field is so
exceedingly rare that an oversupply is almost inconceivable.
APPENDIX
Minimum Education and Experience Requirements for Application for
Beginning Federal Civil Service Position as Junior Professional
Assistant With Option as Mathematician ($2,644 a year)
(As taken from Civil Service Announcement No. 75, issued October 14, 1947,
closed Novemhf>r d. 1947)1
Applicants must have successfully completed one of the following:
A. A full 4-year course, in a college or university of recognized
standing, leading to a bachelor’s degree m mathematics. This study
must have included courses in mathematics consisting of lectures and
recitations totaling at least 24 semester hours, and courses in the physi
cal sciences (engineering, physics, geology, astronomy, chemistry, etc.)
totaling 12 semester hours; or
B. Courses in mathematics, in a college or university of recognized
standing, consisting of lectures and recitations totaling at least 24
semester hours; plus additional appropriate experience or education
in scientific fields which, when combined with the 24 semester hours
in mathematics, will total 4 years of education and experience and give
the applicant the substantial equivalent of the 4-year college course
prescribed under A above. The following are types of experience
which will be accepted in combination with education to complete the
4-year requirement:
Subprofessional or professional experience in the mathemati
cal or statistical analysis of observational data in the physical
or biological sciences which provided a working knowledge of the
theory and application of mathematical principles.
Research experience in such fields as physics, chemistry, en
gineering, biology, etc., which involved the evaluation of reports
and the organization of experimental data.
Subprofessional and higher grade laboratory work, produc
tion or manufacturing involving technical duties, and similar
types of work which provide a means of obtaining a working
knowledge of the theory and application of the scientific prin
ciples of a physical or natural science or of engineering.
In either A or B above, the courses must have included analytic
geometry, differential calculus, integral calculus, and in addition,
any four of the following: (a) Trigonometry; (b) theory of
equations; (c) vector analysis; (d) statistics; (e) higher algebra
1 For more complete and later information, consult latest announcements of the Civil
Service Commission posted in first- and second-class post offices.
4-18
APPENDIX
4-19
(beyond elementary college algebra) ; (/) differential equations;
(g) advanced differential calculus; (h) advanced integral cal
culus.
Minimum Education and Experience Requirements for Application for
Beginning Federal Civil Service Position as Junior Professional
Assistant With Option as Statistician ($2,644 a year)
(As taken from Civil Service Announcement No. 75, issued October 14, 1947,
closed November 4, 1947) 1
Applicants must have successfully completed one of the following:
A. A full 4-year course leading to a bachelor’s degree, in a college
or university of recognized standing, with (1) 20 semester hours in
statistics; or (2) 30 semester hours of college work consisting of a
combination including 6 semester hours in statistics and 24 semester
hours in any one or any combination of the following: (a) economics;
(b) agricultural economics; (c) sociology; (d) political science; (e)
social service; (/) education; (g) psychology; (h) home economics;
(i) biology; (j) public health; (k) agriculture; (?) mathematics; (m)
engineering; (n) physics; or
B. Courses as given under A above; plus additional appropriate ex
perience or education which, when combined with these courses, will
total 4 years of education and experience and give the applicant the
substantial equivalent of a 4-year college course. The following are
types of experience which will be accepted in combination with educa
tion to complete the 4-year requirement:
Progressively responsible clerical experience in (a) use of fre
quency distributions; (b) calculation of measures of central ten
dency, measures of variation and skewness, or index numbers; (c)
graphic analysis, time series analysis, or correlation analysis
under the direction of a professional statistician.
Progressively responsible experience in planning statistical
surveys; processing statistical data, including the collection, com
pilation, verification, and appraisal for consistency of numerical
data; and analyzing statistical data.
1 For more complete and later information, consult latest announcements of the Civil
Service Commission posted in first- and second-class post offices.
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(3) Bower, Julia Wells. The effect of the war on college women and mathe
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(16)
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SOURCES
4-21
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o
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