## Introduction

Industrial mathematics is a specialty with a curious case of double invisibility. In the academic world, it is invisible because so few academic mathematicians actively engage in work on industrial problems. Research in industrial mathematics may not find its way into standard research journals, often because the companies where it is conducted do not want it to. (Some companies encourage publication and others do not; policies vary widely.) And advisors of graduates who go into industry may not keep track of them as closely as they keep track of their students who stay in academia.

In the business world, industrial mathematics is invisible because it is often not called “mathematics.” It is called “analytics,” “modeling,” or simply generic “research.” Credit for mathematical advances may go to “information technology” when it should really go to the people who use the technology and figure out how to employ it effectively.

Of course, for members of the Society for Industrial and Applied Mathematics (SIAM), it will be no revelation to read that mathematics can make a huge difference for private enterprises and, through them, for society as a whole. But we hope that this report will find its way to people who are not members of SIAM, and who perhaps have not been exposed to the kind of work that mathematicians in industry do. In particular we hope that this document will be useful, in different ways, to students who want to learn about industrial careers; academic mathematicians who advise and teach those students; university administrators who want to encourage partnerships with industry; and business managers who want to find out how mathematics can benefit their companies.

For readers who want to know what industrial mathematics is, we recommend skipping the rest of this introduction and going straight to part two, where you will learn about eight general areas of application of the mathematical sciences (broadly defined to include computing and statistics) to industry. You will also find 18 case studies that illustrate the excitement, vitality, and importance of mathematics in industry.

### 1.1 The SIAM 2011 Mathematics in Industry Study: Background

In 1996, SIAM published the first *SIAM Report on Mathematics in Industry* [MII 1996]. This report, and a set of regional workshops that followed its release, helped to clarify the perception in academia of the role of mathematics and mathematicians in industry. It provided an overview of employment opportunities for graduate students, and mathematics departments still refer to it in their career information for students. It has also been cited in subsequent reports by the Smith Institute, the Organization for Economic Development, and the European Science Foundation on the subject of mathematics in industry, (See [Smith 2004], [OECD 2008], and [ESF 2010].) Anecdotally, the report has been used to motivate the need for (and predict the success of) courses and programs in industrial mathematics and computational science.

Many of the recommendations and insights in the 1996 report remain valid today. However, the landscape of mathematical and computer sciences in industry has changed. Organizations now collect orders of magnitude more data than they used to, and face the challenge of extracting useful information from it. Computing technology has continued to advance rapidly, and companies are making more and more aggressive use of high-performance parallel computing.

Another important trend is the transition of the US economy from one led by the manufacturing sector to one in which services are more important. In 1996, manufacturing accounted for 15.4% of US GDP, while the combination of finance, insurance, and scientific and technical services jointly contributed 12.5%. By 2010, the order had reversed, with manufacturing accounting for 11.7% and finance, insurance, and professional and technical services accounting for 15.9% [BEA 2011].

Since 1996 the US government and private foundations have funded several programs that have addressed the sharing of knowledge among scientists in academia, government, and industry. For example, the National Science Foundation established its GOALI (Grant Opportunities for Academic Liaison with Industry) program. The US Department of Energy expanded its Computational Science Graduate Fellowship (CSGF) program and Scientific Discovery through Advanced Computing (SciDAC) program. It also launched the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program, which enables businesses to obtain access to supercomputers and, just as importantly, access to expertise in using them. The Sloan Foundation funded efforts to develop a Professional Science Master’s (PSM) degree, including degrees in mathematical and computational sciences. Several universities and colleges began building centers and programs in mathematics and computational science with a real-world focus.

Finally, the business press has discovered the importance of mathematics, statistics, and computer science to innovation. See, for example, [Baker 2006], [Baker 2008], [Lohr 2009], [Baldwin 2010], [Cohen, N. 2010], [Cohen, P. 2010] and [Hardy 2010]. During the recent mortgage credit crisis, credit swap models and quantitative models in general received criticism from inside and outside the business press ([Patterson 2010], [Taleb 2007], and [Triana 2007]). Nevertheless, this does not seem to have dimmed the enthusiasm within the business press. Corporate management and their shareholders read these articles and books, and we expect that this will create an environment in which they will be receptive to the potential value of mathematical and computer sciences.

In view of all of these changes since 1996, SIAM felt that it was time to update the old report to reflect the new business and economic environment and the new opportunities available. We are also taking the opportunity to include something that was not provided in the original report, a suite of detailed case studies illustrating the variety of ways in which mathematics is being used in industry today.

### 1.2 Scope and Methodology

We began by conducting five small focus groups of industrial scientists. In total, the session participants included 21 mathematical and computational scientists from nine industrial sectors. The goal was to get a broad overview of the current state of mathematics in industry and to inform our questions for the next two phases of the project. We then developed, tested, and administered an online survey of recent PhDs in mathematics and statistics who took jobs in industry. Our questions probed their backgrounds, their group’s tasks, and to what extent their degrees are utilized on the job. We also requested their suggestions for current students. There were 550 PhD graduates from June 2004 through July 2007 who took jobs in industry and for whom we could identify an employer. Of these we were able to find 200 valid e-mail addresses. The survey received a typical online survey response rate of 30 percent.

Finally, and separately from the online survey, we conducted in-depth interviews with 56 senior mathematical or computational scientists (of which 21 were senior managers) in industry from 23 corporations. In total, through the focus groups, the online survey, and the in-depth interviews, we solicited the opinions of 145 industrial mathematicians from 14 industrial sectors.

There are four significant changes to the scope of this report as compared to the 1996 report. First, we included PhD graduates from statistics departments in our survey. The previous study included such graduates only if they received their degrees from a joint mathematics and statistics department. Second, we did not survey the immediate supervisors of the graduates, as we did in 1996. However, in our in-depth interviews and site visits, we interviewed senior-level managers and addressed the same questions as we did in 1996. Third, our interviews and site visits did not deal exclusively with mathematicians and statisticians, but included all mathematical and computational scientists no matter what department they received their PhD from. Finally, we did not interview or survey Master’s graduates for this report. With funding from the Sloan Foundation, SIAM undertook a survey of applied mathematics Master’s programs in 2002, [Crowley and Seitelman 2003], and we have not felt it necessary to repeat that effort here.

In this report, however, we do discuss the rise and development of the Professional Science Masters (PSM) degree. SIAM was involved in the early stages of the PSM movement. The SIAM Education Committee produced guidelines for a professional Master’s degree in applied and industrial mathematics, [“SIAM Guidelines” 1998], using the 1996 Mathematics in Industry report [MII 1996] as a reference.

Finally, we will mention that many of the case studies in section 2 of this report were suggested by or grew out of the onsite interviews. In all cases, the interview information has been supplemented by publicly available information from published articles and company press releases. We include six (out of 18) case studies from companies with which we did not have direct contact with. Those case studies are based entirely on published articles and company press releases.