Executive Summary

In 1996, the Society for Industrial and Applied Mathematics (SIAM) published the SIAM Report on Mathematics in Industry, which was based on a study supported by grants from the National Science Foundation and the National Security Administration. That report, and a set of NSF-funded regional workshops that followed it, helped raise the awareness of mathematicians in academia about the role of mathematics in industry. The study was widely cited and used to motivate curricula and programs that focused on industrial and governmental problems.

Since 1996 there have been many changes in the types and scale of challenges that industry and government are facing. For example, the deciphering of the human genome and the availability of molecular dynamics simulations are beginning to transform the pharmaceutical industry. These changes create new opportunities for graduates with backgrounds in statistics, data mining and simulation. The financial sector has grown hugely since 1996 as an employer of mathematicians. Even though the credit crisis of 2007-8 brought “quants” into some disrepute, companies are still eager to hire graduates who have true insight into both mathematics and finance. Also, the US economy is moving from one that is based on manufacturing to one that is based on services. This creates employment opportunities for mathematicians in businesses that provide consulting services in the realms of business operations, science, and engineering.

In view of these changes, we felt that it was time to update the 1996 report and look at the way mathematical sciences are used in industry today. We also wanted to hear about the experiences of recent PhD graduates who have chosen to pursue industrial careers. Accordingly, we conducted focus group meetings with industrial scientists, an online survey of recent doctoral degree recipients, and onsite interviews with 56 senior scientists and managers from 23 corporations. In total, we have interviewed or surveyed 145 mathematical and computational scientists from 14 major industrial sectors.

Our most important conclusion is that the mathematical and computational sciences continue to find many applications, both traditional and novel, in industry. Some of these applications have very dramatic effects on the bottom line of their companies, often in the tens of millions of dollars. Other applications may not have an easily measured impact on the bottom line but simply allow the company to conduct business in a 21st-century data-rich marketplace. Finally, some applications have great value as contributions to science. We want to emphasize that technology transfer, including the transfer of mathematical ideas, is not a one-way street; a technology designed for or by one company often ends up enriching science as a whole.

The centerpiece of this report is a set of case studies from a variety of applications, including business analytics and optimization, manufacturing design and virtual prototyping, quantitative drug design, financial risk analysis, production planning and supply chain management, and information retrieval and data mining. We intend these case studies to be inspiring and informative for a wide range of readers: from students wanting to know “What is mathematics used for, anyway?” to academic departments seeking to understand how to prepare students for non-academic jobs, to mathematicians in industry who would like to explain the value of mathematical methods to their managers. Often we find that mathematicians in industry do not feel respected by their colleagues in academia; we hope that the impressive range of applications discussed here will convince academic mathematicians that industrial problems can be difficult, substantive and fascinating.

Mathematical scientists in industry work in a highly interdisciplinary team environment. Their contributions tend to be attributed to the dominant discipline of the team. In 1996 we wrote, “Mathematics is alive and well, but living under different names.” This comment is still apropos. Unfortunately, it means that a new mathematical approach to an industrial problem may be difficult to sell to higher management, which might not be prepared to appreciate it. One mathematical scientist and manager whom we interviewed recalled the reaction of a senior management to a suggestion for improving production-line efficiency. The senior manager responded: “These are the five things I am evaluated on; your idea does not help me in any of them.” Because of such attitudes, mathematicians in industry need to develop communication and entrepreneurial skills that may not have been as critical in academia. It is not enough to have a good idea; they need to sell it in a language management will understand.

This report explores the implications of this interdisciplinary environment for the skills and traits considered essential by employers in industry and government. Our interviewees emphasized communication skills, the ability to work effectively in a team, enthusiasm, self-direction, the ability to complete projects, and a sense of the business.

In this study we also took a closer look at the technical skills that graduates need, which tend to fall into three overlapping domains: mathematics, computation, and specific application domains. Useful mathematical skills include a broad training in the core of mathematics, statistics, mathematical modeling, and numerical simulation, as well as depth in an appropriate specialty. Computational skills include, at a minimum, experience in programming in one or more languages. Specific requirements, such as C++, a fourth-generation language such as MATLAB, or a scripting language such as Python, vary a great deal from company to company and industry to industry. Familiarity with high-performance computing (e.g. parallel computing, large-scale data mining, and visualization) is becoming more and more of an asset, and in some jobs is a requirement. The choice of an application domain to focus on depends strongly on a graduate’s career goals and the requirements of his or her potential employer. In general, a student’s level of knowledge has to be sufficient to understand the language of that domain and bridge the gap between theory and practical implementation.

We conclude the report with a range of suggestions and strategies for enhancing the graduate curriculum and creating mechanisms for connecting academic, government, and industrial scientists. Some suggestions are intended for students; for the most part they are not new, and yet some of them are still ignored surprisingly often. For example, we highlight the great importance of industrial internships or direct work with a mentor from industry during the graduate years. Other recommendations are directed at academic departments and their industrial or governmental partners. Some are straightforward and easily implemented on a local scale, while others involve collaboration on an institutional, national, or global scale.