Executive Summary

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 Mathematics in Industry (MII) study, performed by the Society for Industrial and Applied Mathematics (SIAM) with support from the National Science Foundation and the National Security Agency, seeks to:

1. examine the roles of mathematics outside academia;
2. characterize the working environments of nonacademic mathematicians;
3. summarize the views of nonacademic mathematicians and their managers on the skills needed for success and the preparation provided by traditional graduate education;
4. suggest strategies for enhancing graduate education in mathematics, nonacademic career opportunities for mathematicians, and application of mathematics in nonacademic environments.

The findings of this report involve both mathematics as a discipline and mathematicians as practitioners of that discipline.

The MII steering committee, which directed and conducted much of the study, consists of seventeen applied mathematicians from industry, government, and academia. Approximately 500 mathematicians, scientists, engineers, and managers in the United States participated in the three-year MII study reported here. The findings and suggestions are derived from telephone interviews with several hundred recent advanced-degree holders (master's and Ph.D.) in mathematics working in nonacademic jobs; follow-up telephone interviews with many of their managers; and in-depth site visits by groups of steering committee members to commercial and industrial organizations and federal laboratories, chosen because they use mathematics, modeling, and computational simulation.

The study's first result is to confirm the remarkable range and variety of the applications of mathematics in industry and government. Many different success stories testify to the crucial value-added of mathematics in important real-world problems, including materials processing, automobile design, medical diagnosis, development of financial products, network management, and weather prediction. We stress that mathematics in these settings is often not labeled explicitly as "mathematics"; a final product represents a deliberately indissoluble blend of several d isciplines. As expressed during one of the site visits, "Mathematics is alive and well, but living under different names".

The overwhelmingly interdisciplinary nature of nonacademic mathematics has obvious implications about the work environment for mathematicians in industry and government, as well as about qualities considered desirable by employers; these provide the focus of our second set of findings. Some of the most important traits in nonacademic mathematicians include:

• skill in formulating, modeling, and solving problems from diverse and changing areas;
• interest in, knowledge of, and flexibility across applications;
• knowledge of and experience with computation;
• communication skills, spoken and written;
• adeptness at working with colleagues ("teamwork").

The qualities that distinguish these mathematicians from other scientists and engineers are seen by their managers as falling into two broad categories:

• highly developed skills in abstraction, analysis of underlying structures, and logical thinking;
• expertise with the best tools for formulating and solving problems.

Some interesting and mainly consistent views emerged about graduate education in mathematics. The mathematicians surveyed tended to agree that they were well educated for several important aspects of nonacademic jobs: thinking analytically, dealing with complexity, conceptualizing, developing models, and formulating and solving problems. However, many felt inadequately prepared to attack diverse problems from different subject areas, to use computation effectively, to communicate at a variety of levels, and to work in teams.

Based on these results, the MII steering committee offers several sets of suggestions and strategies guided by two related purposes: (1) broadening the graduate curriculum and educational programs, and (2) creating mechanisms for actively connecting academic and nonacademic mathematical scientists. These suggestions are intended not only to provide students with increased flexibility in their career choices, but also to develop a deeper understanding of real-world applications of mathematics. Some suggestions are straightforward and small-scale, while others involve cooperation among academic departments and formal affiliations with nonacademic institutions. Our objective is to present a range of strategies that can be adapted to suit particular needs and circumstances.

The topics of nonacademic employment and applications of mathematics have recently received great attention because of their relationship with two phenomena: the current crisis in the academic job market, and the perceived sharpened attention of U.S. funding agencies to work on applications. In some instances, discussion of these issues conveys grudging acceptance of unpleasant necessities that will, if all goes well, pass away; then the mathematics community can return to business as usual. The MII steering committee emphatically does not take this view. Even if the academic job market improves and funding pressure eases, we are convinced that mathematics and mathematicians should change permanently along the lines indicated in our multiplicity of suggestions. We also believe that the traits valued in nonacademic mathematicians are important and worthwhile in a far wider context.

In many areas of mathematics, history shows clearly that the flow of ideas and inspiration between mathematics and applications runs strongly in both directions. The richness of real-world applications of mathematics as well as the contributions and insights of nonacademic mathematicians should be encouraged to enhance research, teaching, and practice throughout mathematics, science, and engineering.