This material is based upon work supported by the National Science Foundation under Grant No. DMS-9121741. The Government has certain rights in this material. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

References Editor's Note: This document does not reflect the formatting of the original report and does not include the appendices. A reprint of the full report may be obtained by contacting Dr. James W. Maxwell at the AMS, jwm@ams.org.

The last two years have seen recent doctorates in the mathematical sciences facing an increasingly difficult employment market, at the same time that the profession is concerned about the future supply of U.S. citizen doctorates. The factors creating today's tight market are reduced hiring by departments because of the current economic recession, the sudden availability of highly qualified foreign nationals from former Soviet bloc countries, and the increase in the supply of doctorates in the mathematical sciences in the last two years. Although doctorates in other sciences are experiencing employment difficulties, mathematics doctorates are especially hurt by reduced academic hiring because the majority seek academic employment.

Indications are that the 1992-93 season can be expected to be similarly bad, if not worse; the numbers of new doctorates are anticipated to stay at the 1991 level, numbers of positions available are down, and we probably will continue to see immigration of Soviet mathematicians as well as a large proportion of non-U.S. citizen new doctorates choosing to stay in the U.S.

The Task Force projects that the U.S. job market will demand around 800 new mathematical sciences doctorates per year over the next 10 to 15 years from the nation's doctorate-granting mathematical sciences programs. The projection is naturally susceptible to job-market perturbations because of economic conditions, changing attitudes regarding support of higher education, the supply of doctoral mathematicians from other parts of the world, college enrollment patterns, choices made by individuals about time of retirement, and other short-term factors that cannot be predicted with assurance.

The Task Force concluded that some long-term actions are necessary both for the scientific health of the mathematical profession and to prepare mathematicians for the future employment market. There are long-term needs of the profession which must be addressed to improve the flexibility needed to accommodate future fluctuations in supply and demand. The Task Force recommends that the AMS can and should play an active role in bringing about change that is needed. Specifically, the AMS should:

Advocate for the broadening of doctoral programs in mathematics to recognize the value of nonacademic employment and the matching of talent with the teaching needs of the community, to produce doctorates with wider employment options;

Advocate for a larger pool of postdoctorate positions which imaginatively combine teaching and/or industrial components so as to enable continued development of mathematicians.

The Task Force also recommends the following actions which can be implemented quickly to alleviate some of the current stress:

The AMS should collect additional data on mathematicians beyond the first year after the doctorate, so that the community has a better understanding of what happens to its new doctorates.

The AMS should strengthen and augment existing employment services in the following ways:

- continue refinement of electronic employment services (e-MATH)
- strengthen the Mathematical Sciences Employment Register by increasing nonacademic employer participation;
- expand the Employment Register to meetings of societies such as SIAM; support current efforts to improve the matching algorithm used at the Employment Register;
- conduct seminars and workshops on academic and nonacademic employment opportunities and on employment-seeking skills for doctoral candidates;
- organize retraining and continued professional development opportunities;
- develop a standardized cover sheet useful to departments for applications for academic employment.

**The Task Force**

The spring of 1990 saw the first community-wide expressions of concern over the difficulty graduating PhD candidates were experiencing in finding satisfactory employment. Although the Annual AMS-MAA Survey of 1989-90 new doctorates [1] which took place over the summer and fall of 1990 showed no relative increase in unemployment among new PhD's over previous years, the anecdotal reports of difficulty in finding employment increased in frequency and intensity as the 1990-91 academic recruiting season progressed. In response to these concerns, the AMS-MAA Data Committee conducted a survey of thirty of the top doctorate-producing mathematics departments during March and April of 1991 [2]. The results of this survey confirmed and sharpened the widespread concerns about employment, and the AMS established a Task Force on Employment. The charge to the Task Force was to review the current employment situation within the academic mathematics community, to identify the problems in the functioning of this labor market, and to make recommendations to the AMS, to mathematics departments, and to the larger mathematical community on ways to address the problems that were found. Members of the Task Force are: S.-Y. Cheng, Ronald M. Davis, Helen G. Grundman, D. J. Lewis (Chair), Bernard L. Madison, James W. Maxwell (ex officio), Donald E. McClure, Calvin C. Moore, and Carol S. Wood. The work of the Task Force was supported in part by National Science Foundation Grant No. DMS-9121741.

Members began their work by examining available data, conducting a panel discussion at the August 1991 mathematics meeting in Orono, meeting with representatives of federal agencies in September, participating in discussions at the October Chairs' Colloquium and the January 1992 Baltimore meetings, and meeting in February to formulate their recommendations. A survey of academic hiring experiences was conducted in late 1991 in order to learn more about the impact of factors such as immigration and budget cutbacks; the results were released in advance of this full report in order to report the findings as soon as possible to the mathematical community [3]. The report of the Academic Hiring Survey, 1991-92, can be found in Appendix A.

This report presents the findings and recommendations of the Task Force. The first sections present what is known about the current employment market and what can reasonably be projected about future employment markets. The next section offers recommendations that the Task Force feels address long-term needs of the profession in order to help bring about a better balance between supply and demand and to mitigate those imbalances which will undoubtedly occur from time to time. The final section recommends various new and expanded employment services that the AMS can undertake with little delay. Some of these recommendations are already being implemented by the Society.

**Historical Background**

First, we should acknowledge that for many of us the current difficult employment market is not new. The previous prolonged downturn in employment opportunities for new PhD's is usually marked as beginning in 1970. Twenty years later we find ourselves in the midst of a downturn approaching the severity of the earlier one, which reached its nadir in 1975. A number of recommendations made by the group charged with similar work to that now undertaken (the Committee to Advise on Analysis of Employment Data) appeared in the Notices of the AMS in the early 1970's and some are repeated in the following sections. Few of these recommendations ever received serious attention by the community, perhaps because the employment crisis eased as graduate enrollment and subsequent doctorate production decreased, and the situation slowly but steadily improved during the decade of the eighties. In 1992, however, it seems prudent to approach the current employment downturn as a situation which is unlikely to go away of its own accord, and as an occasion for taking actions to avoid such severe fluctuations in the future. We believe that many of the following recommendations are consistent with calls for reform coming from various segments of the mathematical community.

The 1991 Annual AMS-MAA Survey provided firm evidence of the difficult market from the perspective of the job candidate [4]. In fall 1991, 12 percent of the 1990-91 new doctorates whose employment status was known were reported to be unemployed and still seeking employment. The only time the fall unemployment rate has been this high was during the early 1970's (10 percent in 1973, 11 percent in 1974, 14 percent in 1975, and 10 percent in 1976). Between 1977 and 1990, the figures have been between 4 and 7 percent.

By March 1992, 5 percent (54) of the 1990-91 new doctorates were still unemployed and seeking employment [5]. For the years 1977 to 1990 the median of the comparable unemployment figures is 2 percent unemployed and the maximum is 3 percent. Spring unemployment figures are not available for years prior to 1977.

When compared to the national unemployment figures, 5 percent unemployed may seem small, but the unemployment figures reported (disturbing as they are) do not tell the full story. A qualitative review of the data indicates significant underemployment of those new doctorates who did find employment, as reflected in the number of one-year positions reported. Comparisons with prior years is not possible, but the Task Force suspects that this underemployment has significantly increased in recent years and that it will haunt the employment market over the next several years.

**Recommendation:**

The Task Force therefore recommends that the AMS undertake a longitudinal study to monitor the future employment experiences of the group of new doctorates taking postdoctoral and other temporary postions.

Three factors were recognized by the Task Force as contributing to the difficult market:

an increased number of new PhD's;

reduced hiring because of cuts in university and college budgets;

increased numbers of highly-qualified doctoral mathematicians from abroad seeking employment in the U.S.

The number of 1990-91 doctorates in mathematics, statistics, applied mathematics and operations research awarded by U.S. institutions increased by 18 percent from 1989-90 [4]. At the same time, the number of positions for which doctoral faculty were recruited was down significantly for 1991-92, by more than 15 percent in doctorate-granting mathematics departments and more than 30 percent in master's-granting departments [4]. Finally, immigrants from Eastern Europe and the former Soviet Union accounted for 13 percent of the new hires during 1990-91 in doctorate-granting departments [3].

In addition to the three factors identified above, all of which have had a substantial impact over a short period of time, a fourth factor has had a gradual, growing impact on the employment market:

increasing numbers of non-U.S. citizen new PhD's entering the U.S. job market for mathematical scientists.

The change in numbers from year to year has not been sharp, but the cumulative effect of the steady increase is great. There are two elements of this change: (i) the increase in absolute numbers of non-U.S. citizen new doctorates, notably from Asian countries [4], and (ii) an increased tendency of non-U.S. citizens to remain in the U.S. after receiving the degree. Data on these trends are summarized in this report's later section on the role of non-U.S. mathematicians.

The Task Force strongly suggests, based on available data, that the 1991-92 employment market currently underway will prove at least as difficult as the 1990-91 market. Estimates suggest that the number of 1991-92 new doctorates will be as high as the 1990-91 total [3]. These new doctorates must compete for positions with a swelling number of recent PhD's who have taken temporary positions in the last two years. Furthermore, there is little reason to expect the 1992-93 market to be any better. The national economic downturn which forced reductions in the number of positions under recruitment for 1990-92 has continued, and there is little prospect that a turnaround will occur soon enough to have a positive impact on academic hiring in 1992-93.

Any attempt to forecast the demand for new doctoral-level mathematical scientists must be critically examined to understand the assumptions on which it is based. Depending on the scenario that one assumes, expressed, for example, in terms of demand for new faculty members, general economic conditions, demographic trends, etc., one can arrive at widely varying projections for total demand. This presents a dilemma for departments and institutions attempting to plan for the appropriate level of support for a graduate program: they need to foresee appropriate levels of PhD production four or five years hence, and, at the same time, they cannot necessarily foresee the true state of the factors that will decide what the overall demand for new PhD's will be.

The current condition of the job market is a case in point. Two or three years ago, even though job seekers at the time witnessed early signs of a changing market, the popular press more commonly focused on impending shortages of doctorates in many areas of science and engineering. With shortages predicted for the second half of this decade and with a job market that had been hot up to that time, few people imagined that we would now be experiencing relatively high levels of unemployment and a very difficult market. The assumptions on which the projections of shortages rely do not yet prevail, and perhaps they never will. At the time the projections were made, the short-term impact and possible long-term implications of a general economic downturn, of junk bonds and the Savings and Loan liability, and of the end of the Cold War were not generally foreseen nor well understood.

While we recognize that short-term perturbations of the job market for PhD's in mathematics can dominate medium-term or long-term trends and render any prediction incorrect, it is still useful to understand some things about the size and the dynamics of the doctoral mathematicians' job market. The job market can be viewed as a compartmental model, with some flow of individuals into and out of the market (e.g., new doctorates coming into the market and retirees moving out) and with some internal flow between compartments (e.g., an individual moving from a nonacademic to an academic position). The separate compartments correspond to major, relatively homogeneous sectors of the job market, e.g., faculty positions in four-year colleges and universities, positions for mathematical scientists employed in government, positions for mathematical scientists in business/industry, etc.

The largest compartment in the job market remains teaching or teaching-and-research in four-year colleges and universities. According to the 1990-91 CBMS Survey [6] there are approximately 16,000 full-time doctoral faculty in mathematics and statistics in U.S. four-year colleges and universities; "mathematics" includes departments with other titles in which mathematics is the primary discipline. In terms of the hiring of new doctorates, this sector of the market is also the largest. According to the 1991 Annual AMS-MAA Survey, among new doctorates in mathematical sciences from U.S. institutions who took first jobs in the U.S., 64 percent took jobs in a four-year college or university, 15 percent took other academic positions (two-year college, research institute, research center, etc.), and 21 percent took positions with government or business/industry [4].

Information is known about rates of attrition due to various causes and about the demographic profile of the faculty members. Under reasonable (but nonetheless debatable) assumptions, we can predict the numbers of positions which should become available in this sector over the next 10 to 15 years. We focus on the number of faculty positions in four-year colleges and universities which may be filled by candidates who do not already hold positions in this sector of the market. This may include (i) new doctorates, (ii) people moving from outside of academia into a faculty position, and (iii) new entrants to the U.S. job market from abroad, but does not include people moving from one university to another, i.e., flow within the compartment.

We shall consider the time period 1992 through 2008, over which projections of the college-age population are known. The following facts are known about factors affecting availability of faculty positions:

**1.** Attrition due to death and retirement typically ranges from 1.5 to 2 percent [1, 6 ]. Today, 36 percent of faculty are age 50 or over [6]. If we assume that almost all of the age 50 or over faculty will leave their positions before year 2008, then it is reasonable to assume that the attrition rate will remain in the 1.5 to 2 percent range over this period. When projections of total faculty supply and demand are made, it is commonly assumed that most vacancies due to retirement or death will be filled. This may be a reasonable assumption in the long run, but it is not a valid assumption during periods of economic restraint, such as the current one. Reports from the recent special survey of academic hiring directed by the Task Force show that many institutions are using early retirement incentives as a method of reducing faculty size; positions freed by retirement today are not necessarily being refilled today.

**2.** The U.S. population of 18-year olds is expected to rise from approximately 3.3 million today to approximately 3.9 million in 2008. The population size is reaching its interim low point now and will start to rise by 1995. The growth will be fairly steady, at a rate of about 1 percent per year. We assume that this will imply some growth in mathematics enrollments and commensurate growth in faculty size. While this seems a "reasonable" assumption, it actually oversimplifies the situation and is not borne out historically. For example, over the 1980's the population of 18-year olds dropped about 19 percent, course enrollments in mathematics in four-year colleges and universities rose 6 percent, and doctoral faculty size grew 20 percent [6]. Further, the socio-economic profile of the college-age population will be rather different in 2008 from that of today and this may have implications for enrollments in different areas of study and for allocation of educational resources. It is not feasible to anticipate all of the factors that will affect mathematical sciences enrollments and the related demand for mathematical sciences faculty. The U.S. Department of Education recently projected that college enrollments will rise a total of 13 percent over the next ten years [7].

The government projections go beyond the naive assumption that enrollments are proportional to the total 18-22 year-old population; they recognize changing patterns of college-attendance rates among women, among older segments of the population (older than the traditional 18-22 year-old segment), and among minority groups. Even if the naive assumption is incorrect, the more analytical projections of college enrollment reinforce our assumption that there will be more students in mathematical sciences courses over the next 10 to 15 years.

**3.** Attrition from faculty ranks for reasons other than death or retirement is of approximately the same order of magnitude as death/retirement attrition, i.e., in the range of 1.5 to 2 percent annually [8]. From data reported in the Annual AMS-MAA Surveys over the period 1983-88, among positions vacated by doctoral faculty, 18 percent were due to death or retirement, 16 percent were due to transitions to nonacademic employment, and 5 percent were due to transitions to an employer outside the U.S.

To project demand for new faculty, we take as our starting point the current 16,000 doctoral faculty in mathematics and statistics. Since we can only hope to project the order of magnitude of the yearly demand, we assume approximately linear growth and ignore the second-order effects of the changing faculty population size. Under the assumption of 1.5 percent annual attrition due to deaths and retirements (240 positions), 1 percent annual growth in faculty size due to increased enrollments (160 positions), and 1.5 percent attrition due to movement to nonacademic employers (240 positions), roughly 640 positions would be open each year to new entrants to four-year college and university faculties. With attrition rates of 2 percent each for deaths/retirements and for movement to nonacademic positions, roughly 800 positions would be open each year to new entrants to four-year college and university faculties.

Data from the Annual AMS-MAA Surveys document how positions for new entrants to this sector of the job market have been filled. Over the period 1983-88, 63 percent of new entrants to doctoral faculty positions were new doctorates, 13 percent came from nonacademic positions, 13 percent came from institutions outside the U.S., and 10 percent came from other sources. During the same period, among new entrants to this sector of the job market who held previous employment in the mathematical sciences, about 10 percent came from outside the U.S. In striking contrast, the 1991-92 academic hiring survey showed that about 25 percent of the new hires who had held previous employment in the mathematical sciences came from positions outside the U.S. [3]

How does a demand for 800 new doctoral faculty in four-year colleges and universities translate into demand by the U.S. job market for new PhD's? If we assume that 63 percent of these positions will be filled by new doctorates (as in the period 1983-88), then roughly 500 positions will be available in this sector for new doctorates. If we assume further, that traditional employment patterns will be followed by new doctorates (as in 1990-91 with 64 percent of the positions assumed within the U.S. to be in this job sector), then roughly 790 new PhDU's will be absorbed by all U.S. employers. Substantial numbers of new doctorates, of course, still assume positions outside the U.S.; in 1990-91, 15 percent of the positions taken by new doctorates were outside the U.S.

The actual experience of 1990-91 new doctorates is comparable to the projections. The employment status was known in February 1992 for 1,005 of the 1,074 new doctorates from U.S. institutions. Among these, 797 took positions in the U.S., with 509 of the U.S. positions being in four-year colleges and universities. A total of 144 new doctorates were known to have taken positions outside the U.S. and 45 were known to be unemployed and still seeking employment.

**I. Shifts in Graduate Programs**

Since it is impossible to predict with any accuracy the demand for new doctorates in the mathematical sciences, the mathematics graduate departments need to be sure that their programs provide their doctorates with sufficient flexibility that if one job market is restricted or closed down their doctorates are in a position to enter other job markets. Too narrowly oriented or highly specific programs can limit the opportunities of graduates of such programs.

As long as mathematicians remain dependent on academia as the near-exclusive employer of their talents they must anticipate repetitions of employment shortfall as at the present time. Further, when a group narrows its employment possibilities it necessarily restricts the size of the income of its members. For the improved welfare of its members it is imperative that the mathematics community broaden the focus of its graduate programs so as to provide greater opportunity and flexibility in the career choices of its doctorates. The changes needed in the curriculum should not be difficult to identify and implement. A more significant change will be required in the attitude and orientation of faculty and students. Our experience in the 1970's supports the belief that employment outside academia can be expanded. We need the orientation of our programs to be such that employment outside academia is not viewed as second best. This need was already recognized in the 1970's:

"... we must make fundamental changes in the nature of graduate work in mathematics which will prepare most of our students for something other than academic life." [9]

"Perhaps what is needed is sound graduate education in core mathematics with provision for continuing education, both before and after the doctorate, in the applications of mathematics." [10]

As enrollments of domestic students declined in the 1970's we managed to forget this earlier advice. When foreign students began to enter our doctoral programs in large numbers we continued our emphasis on academia, expecting them to return to universities in their country of origin. Having them stay and having failed to broaden our programs, we are experiencing the problems of the 1970's once again.

In most cases it is difficult to design undergraduate programs that lead directly to employment in commerce or undustry. On the other hand there is considerable evidence that such is possible at the master's level. Indeed there is strong evidence that graduates of professional master's degree programs directed to local industry are very much sought. Many U.S. students seek programs that are not too long and that have the likelihood of leading to employment. Professional master's programs conducted in concert with doctoral programs provide doctoral students with opportunities to obtain a broader and more flexible degree. The inclusion of a professional master's degree within our degree programs should increase our enrollments, provide for broader doctoral programs, and provide increased employment opportunities for doctorates both in industry and academia.

The Board on Mathematical Sciences issued a report on U.S. doctoral programs in April of this year [11]. The Task Force believes that the report offers numerous recommendations for structuring graduate programs in ways that would improve the employment prospects of graduates produced by programs incorporating these recommendations. The Task Force urges those inviduals responsible for directing their department's graduate program to give serious consideration to the recommendations within the Board's report.

**Recommendations:**

- The Task Force recommends that the design of graduate programs should be reexamined to focus on the goal of producing doctorates with realistic employment expectations who are better prepared to take advantage of the job market available to them. It is a fact that the majority of PhD's in mathematics spend a substantial portion of their professional efforts in mathematics instruction. It is therefore particularly important that U.S. graduate programs develop the teaching and communication skills of all students.
- The Task Force recommends that the AMS promote and help expansion of professional master's programs.
- The Task Force recommends that the AMS promote and help expansion of internship programs for undergraduate and graduate students as a long-term means of expanding interest in and opportunities for nonacademic employment.

**II. Need for more postdoctorates**

The present time is a propitious one for expanding the postdoctoral opportunities for new doctorates. New doctorates are increasingly aware of the value of traditional postdoctoral experience in securing tenure-track positions in doctorate-granting departments. The number of highly-qualified new doctorates presently available means that an expansion of postdoctoral positions would not lead to shortages in post-secondary education or in industry and government. Furthermore, a flexible supply of such positions would allow the academic market to respond to fluctuations in the supply of candidates and simultaneously increase the capabilities of new PhD's and their long-term value to the mathematics profession.

What is being suggested here is not simply an increase in the number of typical postdoctoral positions, but also a rethinking of the purpose behind such positions. In the biological and physical sciences and in medicine a postdoctoral position is seen as a necessary continuation of the educational process. Why not in mathematics? A structured program that mixes the opportunity for an indepth research experience with other forms of professional development offers far more to the individual and, ultimately, the profession than a sequence of one- or two-year temporary teaching positions with a heavy teaching load and no real provision of opportunities for professional development. This is especially true for domestic students, some of whom begin graduate school with considerably less mathematics knowledge than their counterparts from other countries.

The research component of a postdoctoral position could be complemented by a component of professional development taking numerous forms. For example, the goal could be to improve the recent graduate's teaching skills or breadth in mathematics. In another direction, the position could involve outreach to other disciplines or to industry. Another possibility is a position stressing curricular development or activities in pre-college education.

The funding possibilities for these positions are varied. In some cases, redirection of departmental or institutional funds already available is all that is needed. At some institutions a postdoctoral position could be funded by a slight decrease in graduate enrollment, with the postdoctorate (for whom the department does not have to pay tuition) covering teaching duties that would have gone to graduate students. In other cases incremental funding would need to be sought from institutional sources and outside agencies. Departments should consider including postdoctoral positions in grant proposals for any project where they may be appropriate. A position requiring little or no departmental service from the new PhD, instead allowing for professional development, could be offered at a somewhat lower level of compensation than a typical tenure-track position.

One area of activity that has not yet adequately tapped the talents of recent PhD recipients is that of curricular reform. New PhD's could provide needed expertise in classroom technology while adding fresh insights to these projects. As many schools try to incorporate the use of computers into their teaching, it should be remembered that a good number of recent graduates have expertise in computers and even experience both as students and as instructors with the use of computers in education. Similarly, various experiments in pedagogy could utilize the skills of recent PhD's. Development of a new generation of mathematicians who see involvement in educational issues as part of their mathematical careers would improve the mathematical health of the U.S. Institutions and federal or state funding agencies could provide support for such involvement, either for the educational or for the research component of the postdoctoral experience, as fits their own goals.

Many institutions and funding agencies are very interested in encouraging interactions between different disciplines. Mathematics departments should take advantage of this by working to establish cross-departmental postdoctoral positions. A postdoctoral position is an ideal vehicle for providing new PhD's with valuable opportunities to pursue their interests in the interplay between different disciplines.

Another avenue for funding is through corporations, some of whom may be interested in setting up joint postdoctoral positions which would include time at both the academic institution and at the business site. Both the institution and the corporation would benefit from having a researcher who might not otherwise be available to either. Companies would benefit through greater recognition in the academic community, while departments would benefit through additional funding and strengthened relations with the corporate sector. The Institute for Mathematics and Its Applications at the University of Minnesota has had success in setting up split-support postdoctorates incorporating time both at IMA and at cooperating industries.

No doubt there are many other possibilities for designing new postdoctoral positions and for funding them. The key in designing these positions is to focus on the goal of continuing the recent PhD's professional development. To this end, approximately half of each appointment should be for research; other duties need to be controlled to allow sufficient time for the establishment or further development of a research program. When possible, new appointments should be for at least two years, minimizing time lost by both the department and the appointee in frequent job searches.

An increase in the number of postdoctoral positions would mean that a greater number of new PhD's would have time to further establish themselves before competing for permanent jobs. Evidence from the Academic Hiring Survey suggests that postdoctorate experience is a distinct advantage in securing tenure-track positions at doctorate-granting departments [3]. Additionally, the availability of postdoctorates designed with non-traditional research components would expose recent graduates to a wider range of employment options. As a result, these mathematicians would have a better sense of just where they want to fit into the mathematical community. Further, those making hiring decisions would have much more useful information about their candidates than was available at graduation, or would have been available had the candidates been simply teaching during the interim.

**Recommendation:**

The Task Force recommends that departments of mathematical sciences look for ways to create postdoctoral positions that combine research with other forms of professional development. The AMS should facilitate this as much as possible and should lead an effort to approach funding agencies for support of the various types of postdoctorates appropriate for each agency.

**III. Role of non-U.S. mathematicians**

The U.S. job market for PhD mathematicians has traditionally been entered at two stages in the careers of the foreign mathematicians. One stage is as mature mathematicians, educated at the doctorate level abroad. In the current market such mathematicians come to the U.S. mostly from Europe, with a sizable increase in those from the former Soviet Union in recent years. The other stage of entry to the U.S. has been as graduate students, earning a PhD in the U.S. and remaining here, either for a few years' postdoctoral work, or permanently. Currently many of these students come from Asia, notably the People's Republic of China. The U.S. has traditionally welcomed mathematicians at both stages, and relied upon them to add strength and range to the mathematical vigor of this country.

Over the past ten years there has been a steady increase in the supply of non- U.S. citizen new PhD's entering the U.S. job market. Two factors contribute to the increased numbers seeking positions.

First, more non-U.S. citizen new doctorates are being produced. According to the Annual AMS-MAA Survey [4], the number of non-U.S. citizen new doctorates has risen every year since 1978-79. According to the Survey's fall counts, the number of doctorates awarded to non-U.S. citizens by U.S. institutions increased from 283 in 1980-81 to 581 in 1990-91. Most of the increase occurred since 1986 and it is largely due to increased numbers of graduate students from eastern Asia, especially from China and Korea. Between 1980-81 and 1985-86, the total non-U.S. citizen count increased by 70, up 25 percent; from 1985-86 to 1990-91, the total non-U.S. citizen count increased by 228, up 65 percent. The number of new doctorates awarded by U.S. institutions to citizens of eastern Asian countries increased from 82 in 1980-81 to 132 in 1985-86, up 61 percent; between 1985-86 and 1990-91, this number increased to 328, up 148 percent in the 5-year period and a four-fold increase from the count ten years earlier.

Second, there is a greater tendency of non-U.S. citizens to stay in the U.S. than in the past. According to reports of the NSF Survey of Earned Doctorates [12], the proportion of non-U.S. citizen temporary residents who intend to stay in the U.S. after receiving their degrees, among those who had definite postgraduation plans for which the location was known, increased from 54 percent in 1980 to 68 percent in 1989; the data have not yet been reported for 1990 and 1991. There is considerable year-to-year variation in the reported proportion, but a trend is clear: the proportion is consistently higher during the last half of the 1980's than it was during the period 1970-80.

We would clearly have experienced serious faculty shortages throughout the 1980's were it not for the supply of non-U.S. citizen PhD's produced in the US. Only 478 of the 1990-91 new doctorates were U.S. citizens, a number far too low to fill the available positions, even in the current tight market [5].

The influx of mature mathematicians has gone uninterrupted for many years, but fluctuates significantly with the political and economic situations in their home countries, making reliable predictions of that component of the job market difficult. The impact of the pool of senior mathematician "superstars" suddenly available to the U.S. from the former Soviet Union may be diminishing, but continued pressure comes from the even larger pool of younger mathematicians for whom the U.S. now seems to be most desirable as a place to work and live. The strengthening of the U.S. research community in this way is not without cost, however, both here, in the discouraging lack of appropriate positions for U.S. doctorates, both citizen and noncitizen, and abroad, with the apparent weakening--or, some feel, dismantling--of several of the world's leading centers of mathematics. There is also the risk that a department or administration will neglect other institutional needs in favor of a "big name", in an effort to raise the prestige of the department. But the influx of mature mathematicians has long been viewed by the U.S. community as a benefit, and our openness to all mathematicians has been a source of strength for our profession. It is not clear that bad economic times are sufficient reason to change this view.

Since the early 1980's the U.S. has experienced an increase in the number of graduate students from the People's Republic of China. This exceptional group of students enhanced and enriched our graduate programs, and were all the more welcome after a decline in the number of U.S. students entering our graduate programs in the early 1980's. After the Tiananmen Square event in 1989 the strict visa restrictions were suspended, at least until 1994, and these students entered the U.S. job market in greater numbers than expected. It is impossible for the Task Force to predict visa policies beyond 1994, but we expect that the current students will apply for postdoctoral positions here, and thus their impact on the market for new doctorates will not soon abate. Moreover, the influx of Chinese students has not been substantially slowed by various restrictions on foreign study by the government of the People's Republic of China. With the uncertainty about the continued viability of graduate education in the former Soviet Union, we could even see a rise in applications to graduate school from that region in the next few years. Meanwhile, it would be very shortsighted for the U.S. graduate faculty to allow its delight in the high level of education of its foreign students to result in neglected development of the talented pool of U.S. students. This neglect would put the U.S. community at the mercies of the world economic and political scene. While the decade of the 1980's saw steady increase in the number of foreign graduates taking U.S. employment, there is no guarantee that this supply will continue to be available to the U.S. market. In the case of Asian students, for example, the economic strengths developing in the Pacific Rim countries have expanded the academic job market there, with improved salaries and research environments. Already a number of Asian students have returned to this region quite successfully.

**Recommendation:**

Recognizing the significant role played by non-U.S. citizens in our graduate programs, and their importance in the U.S. labor market, the Task Force recommends that U.S. graduate programs fulfill their responsibility to develop the communication skills of their foreign students and the cultural understanding necessary for U.S. market needs.

**IV. Expansion of Nonacademic Employment Market**

If the employment market for mathematics PhD's is to have any long-term stability, then the market must be expanded and there must be some method built into the system to adjust for temporary increases and decreases in the PhD production. This is necessary since the PhD production machine -- about 170 institutions with over 290 departments in the mathematical sciences -- is very large compared to the number of degrees awarded annually: at current production levels, an increase of one degree per institution produces a 17 percent increase in production.

The nonacademic employment market for mathematics PhD's is relatively unknown, but we do know that around 20 percent (less than 200) of the new PhD's report taking nonacademic positions each year. In 1990-91, statistics or applied mathematics departments produced 87 of the total of 140 new doctorates reported to have taken nonacademic employment in government or business and industry. These same departments accounted for 327 out of a total of 1074 new doctorates reported by U.S. institutions in 1990-91. Said another way, only 52 of the 747 new doctorates from doctorate-granting departments of mathematics were reported to have taken nonacademic employment within the U.S. As many new PhD's in the early 1970's discovered, it is not necessarily an easy task to enter the nonacademic market. Part of the problem is that many companies do not know how valuable mathematicians could be to them in solving their problems. But when nonacademic employers have a core of professional mathematicians on their staff they are more likely to seek additional mathematicians.

Compared to other scientific disciplines, the mathematical sciences doctoral programs are small and are narrowly focused on academia. During the decade of 1980-89, the biological sciences produced five times as many doctorates as did the mathematical sciences, while chemistry and physics produced approximately three and two times as many, respectively. About 50 percent of the new doctorates produced in the mathematical sciences take their first job in academia (excluding postdoctorate positions), compared to 11, 6 and 10 percent respectively for the biological science, chemistry and physics [13].

Beyond the need for jobs for new PhD's, there are at least two reasons why expanding the nonacademic employment market is important:

Mathematics PhD's can be valuable contributors to the nation's nonacademic workforce.

The nonacademic workforce is directly tied to the nation's economy and responds directly to growth of that economy. (Long-term workforce expansion is clearly dependent on long-term economic growth.)

**Recommendations:**

The Task Force recommends that the AMS use the various means available to it to make clear to the mathematical community the value of, and the opportunities for, nonacademic employment.

In particular, the AMS should seek to charge the AMS-MAA-SIAM Joint Committee on Employment Opportunities (JCEO) with responsibility for coordinating the efforts of the three societies to reach their constituencies with this message. Furthermore, the AMS should work to see that the resources necessary for the JCEO to fulfill this expanded charge are provided jointly by the three societies.

Some specific recommendations for immediate efforts to improve awareness and availability of nonacademic employment opportunities are contained in the section "Recommendations for Short-Term Actions". Some of the recommendations are already being implemented.

Finally, the AMS should take every opportunity to promote industrial internship programs as a means of fostering awareness among nonacademic employers of the value of mathematicians to their concerns.

**V. Expansion of Academic Employment Market**

In the last few decades, university mathematicians have sought to have research opportunities comparative with other sciences. In particular they have sought comparable teaching loads. This meant significantly reducing teaching loads from those of the 1960's. However, rather than insisting on enlarging their faculties to meet the reduced teaching loads, mathematicians accepted substantially larger class sizes and heavy use of teaching assistants and adjuncts without considering the impact on the quality of instruction provided. Today there are few universities where the quality of lower-level mathematics instruction is not heavily criticized. This perceived lowering of the quality of beginning instruction is perhaps a major factor in the reduction in the percentage of domestic students taking a doctorate in mathematics. At the same time the increased number of teaching assistants has led to an increase in the number of doctorates produced.

Comparison of college mathematics instruction with that in the sciences is almost certainly comparing apples and oranges. Lower-level science benefits from well-prepared and well-delivered demonstrations coupled with "hands on" lab experiments. Lower-level mathematics instruction is much more skills training akin to that provided in language and composition courses, requiring almost daily "hands on" effort by the student coupled with instant feedback from the instructor. As such, it seems essential that elementary instruction be done in small classes. If mathematicians were able to convince themselves and administrators that the quality of instruction would improve substantially if the student/faculty ratio were reduced, it would probably mean that mathematics would get a greater share of the institution's budget. Departments under siege from criticism of the quality of their instruction would do well to examine whether they could make the case for more regular faculty.

A number of mathematics departments have recognized that an undergraduate degree in mathematics is an excellent prerequisite for graduate study in other disciplines. They have accordingly designed mathematics undergraduate programs that prepare students to enter other fields of study and, in so doing, have increased (often more than doubled) the number of undergraduate majors. Other mathematics programs have designed curricula that prepare undergraduates to enter employment on completion of the bachelor's degree, again increasing the number of students taught and making the case for more mathematics faculty.

The principal reasons why more regular full-time faculty members are needed are:

- Between 1970 and 1990 the mathematics enrollments per faculty member increased by approximately 13 percent [6].
- The national imperative to improve mathematics learning has led to reforms predicated on reduced class sizes.
- In 1990 there were approximately 20,500 part-time faculty members: 13,700 in two-year institutions and 6,800 in four-year institutions [6].
- A significant percentage of mathematics faculty members do not have doctoral degrees: 23 percent in four-year institutions and 83 percent in two-year institutions [6]. Consequently, increasing the academic workforce for doctorates in mathematics by a significant number, say 5,000, could be supported. The increased availability of mathematics PhD's now presents an opportunity to do so. However, departmental faculties will have to make arguments and commitments that convince administrators to allocate or reallocate scarce money for new or enhanced positions. Two questions must be confronted:
- Will increasing the doctoral faculty significantly improve mathematics instruction?
- Where will colleges and universities get the money to finance the increase?

Money available to colleges and universities is not projected to increase significantly over the next few years. The total number of faculty positions is likely to be nearly constant, so increases in mathematics positions would probably require reallocations from other disciplines. The arguments for reallocations will need to be compelling, including firm commitments by mathematics faculties to institutional priorities that are likely to be focused on improving mathematics teaching for all students.

**Recommentation: The Task Force recommends:**

Departments should take advantage of available faculty candidates to improve mathematics instruction.

When doctoral programs are preparing graduates for academic positions care needs to be taken to see that they are thoroughly prepared to address the needs and priorities of the full range of prospective academic employers.

The Task Force recommends the following enhancements to existing AMS employment services and additional employment services, most of which could be implemented quickly, and some with little cost, to alleviate the pain of the current crisis. Actions have already been taken to implement some of these recommendations and their status is noted.

- The Task Force recommends the encouragement of a wider use of electronic employment services. Action has already been taken by opening the e-MATH service for free listings of positions to be filled by fall 1992, opening late in the current recruiting season. This service will provide rapid dissemination of information on late-breaking openings. The service began mid-April and was publicized through a direct mailing to all mathematical sciences departments at two- and four-year institutions, and nonacademic employers, together with announcements in the Notices of the AMS and Employment Information in the Mathematical Sciences (EIMS). All current subscribers to EIMS will receive the up-to-date list of positions by regular mailings during the summer. Appendix C contains a copy of the announcement of this service.
At this time, the Task Force does not recommend the use of e-MATH as a central clearinghouse database of applications. Appendix D contains the report of Task Force investigations and deliberations on this proposal.

- The Task Force recommends that the AMS develop a standard application form acceptable by all departments of mathematics. This form would replace the various department-specific forms which applicants must often fill out and would give departments a common core of easily extracted information for use in managing their application pool. AMS staff are investigating ways to implement this recommendation.
- The AMS should explore new methods to facilitate the employment process. One area of potential need is the filling of postdoctoral positions, especially if the number of such positions is expanded. Another area might be the provision of up-to-date information on who is still on the market, especially during the later stages of the employment season.
A proposal which received much deliberation before being rejected by the Task Force called for the development by the AMS of a matching program for postdoctorates, modeled on that used for the medical community in the national resident matching program. The Task Force felt that there were many problems in adapting this model to the needs of the much less homogeneous mathematical community, and recommends that this model not be pursued at this time. However, should their recommendation for more mathematical postdoctorates be followed, there would need to be consideration of some controlled process for matching suitable candidates to positions.

- The AMS should seek to provide opportunities for continuing professional development and career expansion.
The expectation is that there will be an increasing number of recent PhD's presently employed in nontenure-track positions who will soon be competing with new PhD's for a small number of tenure-track positions at doctorate- granting institutions. In past years the relatively small number of such individuals were left to their own resources to locate employment and often to adapt their preparation to fit into different educational institutions. Today, with the substantial numbers of such individuals, it is incumbent upon the mathematical community to assist non-tenure track faculty and individuals in temporary positions in seeking employment opportunities in settings other than PhD-granting institutions and in adapting to fit into those settings.

To that end, the AMS should investigate, in conjunction with other societies, mechanisms to prepare both prospective PhD's and those in temporary positions to move into settings other than doctorate-granting institutions. The Task Force envisions short but intensive workshops or training sessions, located in settings other than national meetings, where attendees would not only receive information about a specific employment area and its relationship to other areas, but also extensive training that would enhance marketability in that area. The Task Force is aware that the AMS Short Course Series was introduced in the 1970's in part to expose research mathematicians to applications of mathematics, but their recommendation here is for a lengthier model. Some suggested topics are 1) Teaching at a Two-Year College, 2) Teaching at Four-Year Colleges and Liberal Arts Colleges, and 3) Careers in Industrial, Business, and Government settings.

- The Task Force has strongly supported the improvements proposed by the AMS-MAA-SIAM Joint Committee on Employment Opportunities (JCEO) to the matching algorithm used at the Employment Register, and views the funding of this work by the Society to be a worthwhile investment in this unique employment service to the whole mathematical community. AMS staff are working with consultants on plans for a new system, anticipated for use at the January 1993 Employment Register.
- The Task Force recommends that JCEO investigate ways to increase the number of employers interviewing at the annual Mathematical Sciences Employment Register. Special efforts will be needed to attract nonacademic employers. Consideration could be given to running a version of the Employment Register at SIAM annual meetings.
- The Task Force suggests that JCEO organize workshops at annual meetings to provide graduate students with information on the employment opportunities for new PhD's in two-year colleges and the necessary skills to succeed in this environment. Development of a service such as this should be part of the charge to JCEO in cooperation with the American Mathematical Association of Two-Year Colleges.
- The Task Force suggests that the AMS explore the organization of workshops at annual and summer meetings on opportunities for nonacademic employment, the skills necessary for success in nonacademic employment, and how to be effective in seeking nonacademic employment.
- The Task Force recommends expansion of current AMS publications giving advice to those seeking employment, paying attention to the underemphasized areas of two-year college and nonacademic employment. Expansion could include more information on the nature of these two areas of employment, advice on how to be effective in seeking such employment, and a list of possible sources of nonacademic employment of mathematicians. The AMS could also consider the use of other aids to advisors as they prepare graduate students to enter the employment market, such as videotaped sessions on effective presentations, interviewing and the search for suitable positions.

[1] 1990 Annual AMS-MAA Survey, First Report, Notices of the AMS, November 1990, and Second Report, May/June 1991.

[2] McClure, Donald E. Report on Preliminary Survey of Employment Situation for 1990-1991 New Doctorates, May 1991. Unpublished report prepared for the Executive Committee and Board of Trustees of the AMS.

[3] McClure, Donald E. Academic Hiring Survey, 1991-1992, Notices of the AMS, April 1992.

[4] McClure, Donald E. 1991 Annual AMS-MAA Survey, First Report, Notices of the AMS, November 1991.

[5] McClure, Donald E. 1991 Annual AMS-MAA Survey, Second Report, Notices of the AMS, July/August 1992.

[6] Albers, Donald J. et al. Statistical Abstract of Undergraduate Programs in the Mathematical Sciences and Computer Science in the U.S.: 1990-91 CBMS Survey. MAA Notes No. 23, 1992.

[7] "Enrollment projections revised upward in new government analysis". *The Chronicle of Higher Education*, January 22, 1992.

[8] Madison, Bernard L. and Therese A. Hart. *A Challenge of Numbers: People in the Mathematical Sciences.* National Academy Press, 1990.

[9] Young, Gail S. "The Problems of Employment in Mathematical Sciences." *Notices of the AMS*, August 1971.

[10] Anderson, Richard D. et al. "Statement on Employment of PhD's in Mathematics". *Notices of the AMS*, April 1971.

[11] Board on Mathematical Sciences. Educating Mathematical Scientists: Doctoral Study and the Postdoctoral Experience in the United States. National Academy Press, 1992.

[12] NSF. Science and Engineering Doctorates: 1960-1989. Surveys of Science Resources Series, NSF 90-320.

[13] Thurgood, D. H., and J. M. Weinman. Summary Report, 1990: Doctorate Recipients from U.S. Universities. National Academy Press, 1990.