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 premiums 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, accounting, and high executive positions. There are occasional 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 are 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 other employment

The few mathematicians and statisticians not employed by educational 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 nonprofit 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 electronic equipment on our economic life is of the same magnitude as the effect of the H-bomb on our military strategy"

(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.

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 prediction, 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.

2. They have "memories" of many thousands of words (either

numbers or instructions).

3. They are 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 alternative 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 mathematicians has been multiplying very rapidly-in mathematical terminology, "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 techniques, 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 foreseeable 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 working in applied mathematics require a knowledge of the field to which the mathematics is applied. Developments in pure mathematics are

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. If 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 universities 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 possibilities 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 current 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

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 mathematics are 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 statisticians 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 statistical methods are the biological and medical sciences, psychological testing, education, and public health. For instance, when the major