## Introduction

- Purposes and methodology of the SIAM Mathematics in Industry study
- Context for the SIAM MII report
- Possible audiences
- Outline of the report

### Purposes and methodology of the SIAM Mathematics in Industry study

Business, industry, and government provide not only a fertile domain for application of advanced mathematics, but also employment for a significant community of highly trained mathematical scientists. This first phase of the SIAM Mathematics in Industry (MII) study seeks to:- examine the roles of mathematics outside academia;
- characterize the working environments of nonacademic mathematicians;
- summarize the views of nonacademic mathematicians and their managers on the skills needed for success and the preparation provided by traditional graduate education;
- suggest strategies for enhancing graduate education in mathematics, nonacademic career opportunities for mathematicians, and application of mathematics in nonacademic environments.

The MII steering committee, which directed and conducted much of the study, consists of seventeen applied mathematicians from industry, government, and academia; their names and affiliations are listed in the Acknowledgments section. Approximately 500 mathematicians, scientists, engineers, and managers in the United States participated in the MII project over a three-year period. The findings and guidance for the suggestions of Section 5 are derived from telephone interviews with 203 recent advanced-degree holders (master's and Ph.D.) in mathematics working in nonacademic jobs; follow-up telephone interviews with 75 of their managers; and 19 in-depth site visits by groups of steering committee members to industrial and governmental organizations.

The telephone survey of mathematicians covered only those with highest degrees from departments formally labeled as "mathematics"; this includes "applied mathematics" and "mathematical sciences" but not "statistics", "operations research", or "computer science", although we certainly encountered many individuals who were trained in statistics and operations research within mathematics departments. Our definition of "nonacademic" institutions includes government laboratories (some of which are managed by universities on behalf of government agencies) and business or industrial organizations; we do not include academic research institutions.

A major aim throughout the telephone surveys was to gather quantitative data about working environments, important skills, and the value of graduate training for nonacademic mathematicians. The site visits provided impressions, anecdotes, and extended interchanges about the nature of applied mathematics and what it means to be a nonacademic mathematician.

### Context for the SIAM MII report

The present report does not arise in a vacuum; its themes have been explored in myriad forms and contexts, and are especially timely because of a recent confluence of trends and events.Within the mathematical sciences, the past five years have seen a crescendo of articles devoted to the prospects for nonacademic careers, driven by a substantial mismatch between the number of new Ph.D.'s and the number of academic jobs in mathematics. See, for example, [Lot95,McCl95].

Addressing the same phenomenon in a broader setting, the National Research Council (NRC) Committee on Science, Engineering, and Public Policy (COSEPUP) produced a widely discussed report, Reshaping the Graduate Education of Scientists and Engineers [NRC-Grad], in April 1995. Part of the impetus for that report was a growing impression that, throughout science and engineering, large numbers of U.S. Ph.D.'s cannot find jobs, especially in academia. The COSEPUP report explores two issues of particular relevance to the MII study: the nature of industrial employment and the resulting implications for graduate education.

Of course, these issues are not recent discoveries. For more than a decade, substantial and thoughtful studies have been written about U.S. mathematics education; see, for example, [CBMS92, David84, David90, NRC90, NRC-Doc]. Perspectives on nonacademic mathematics and the preparation required for nonacademic jobs have been considered in, for example, [Ben94, BKTSLD, Boy75, Ch91, Davis91, Fry41, Ster95, Weyl52]. Several authors from outside mathematics have also discussed the nature of industrial jobs in other disciplines and connections with graduate education; see, for example, [Hans91, Hold92, Horn92].

This MII report complements and extends the COSEPUP and other reports by concentrating in detail on applications of mathematics in industry and on the working environment for nonacademic mathematicians. It is widely perceived that graduate education in mathematics focuses almost exclusively on preparation for traditional academic research careers. Until now, however, reports have not systematically examined perceptions of industrial environments by mathematicians and their managers, nor asked for ratings by nonacademic mathematicians of their graduate education.

### Possible audiences

The steering committee believes that this report may be of interest to multiple audiences for various reasons.- Mathematical sciences departments. The report contains information about
nonacademic applications of mathematics and future opportunities for
mathematics; a detailed characterization of traits valued in nonacademic
mathematicians; an analysis of how well graduate education prepares
students for nonacademic careers; ideas for broadening the graduate
curriculum to provide students with greater flexibility in career choices
as well as a deeper understanding of real-world applications of
mathematics; and suggestions for faculty and departments to help build
closer ties to industry.
- Deans and university officials. Implicit in the report are policies and
strategies that might be useful if universities wish to encourage shifts
in curriculum or closer ties to industry.
- Students in mathematics and related disciplines. A picture emerges from
the report of careers in industrial mathematics, along with guidelines
about academic preparation. We also suggest actions for several kinds of
students: those interested in applications; those who wish to consider
the option of a nonacademic career; and those who wish to develop
connections outside academia.
- Industrial and governmental organizations who use or could use
mathematics. The success stories described in the report indicate the
many ways, some unexpected, in which mathematics can be applied to
produce concrete and measurable results. The managers surveyed, most of
whom were not mathematicians, consistently felt that mathematics could
provide a competitive edge for their organizations. We hope that this
report suggests new and evolving roles for mathematics in
industry.
- Federal and private agencies concerned with educational preparation. The
report presents data about mathematical careers and graduate education,
and suggests possible strategies to broaden mathematics curricula and
programs.
- Academic departments in disciplines where applied mathematics is important. Some of the findings clearly reveal close connections, ripe for expansion, between mathematics and other disciplines. The portrait of the industrial environment for mathematicians is likely to contain many points of similarity for graduates in other disciplines, and our suggestions indicate generic approaches to issues of concern throughout science and engineering—in particular, developing interdisciplinary programs, teaching communication skills, and creating links with industry.

### Outline of the report

Section 2 describes the roles of nonacademic mathematics in general and specific terms, including a list of success stories. The working environment for nonacademic mathematicians is discussed in Section 3, and a detailed analysis is given of the traits valued in nonacademic settings. Section 4 summarizes the views of nonacademic mathematicians and their managers about graduate education as preparation for nonacademic jobs. Based on these findings and their own experiences, the steering committee offers a variety of strategies and suggestions in Section 5, followed by a brief conclusion in Section 6.Within this report, we sometimes use the term "industry" to denote business and commercial firms, federal research and development laboratories, and commercial and not-for-profit research, development, and production facilities, i.e., activities outside the realm of education and academic research. It should always be clear from context when "industrial" refers specifically to industry.