The variety of math-focused jobs in business, industry, and government is increasing, a trend recently highlighted in the popular press. For example, a*Career Cast ***article **about the best jobs of 2015 has quotes from happy “mathy” employees. Math fares similarly well in this **top 10** from *Business Insider*. A*Fortune ***article** claims that every business will need, in some sense, to become a math shop. The new challenge is to connect students trained in the mathematical sciences to these jobs.

*Image from Harvey Mudd College.*

At the same time business jobs are increasing, the number of tenure-track academic jobs is **shrinking**. Newly minted PhDs **may have** to **take** one or more postdocs and then take an adjunct or visiting position. Mathematical sciences students often gravitate toward these academic jobs, because it is a traditional career path. As students, they live in the academic world and have professors as role models. Unlike fields such as engineering, where industry experience and consulting are fairly common for academics, mathematics professors might not be able to advise their students about careers outside academia.

Internships can bridge gaps between people at academic institutions and people in business and government institutions. By engaging with internships, mathematical sciences students learn that they are eligible for a broad range of jobs—especially when they combine their degree with programming, data science, and strong communication skills. Students from the mathematical sciences—defined broadly to include pure and applied mathematics, statistics, and operations research—will play a major role in the 21st-century workforce.

The mathematical preparation for internships can begin early, especially as mathematical modeling more frequently enters the K–12 curriculum (more about that trend in my last **blog post**). Through modeling, students can become aware of the practical power as well as the intellectual beauty and strength of mathematics. If the modeling problems are chosen well, students will use mathematics to solve big, messy problems that they care about. These quantitative and logical thinking skills can be later applied in their jobs to solve problems in feasible and (as much as possible) optimal ways.

An undergraduate class in mathematical modeling led me to a career as an applied mathematician—an occupation I had never heard of before I took the course. This first significant experience with mathematical modeling took place in a capstone experience during my senior year at Oberlin College. My professor, Bruce Pollack-Johnson (now at Villanova), gathered a group of students from his operations research classes for a practicum at NASA in Cleveland. Our problem was to figure out how to make sure the astronauts, life support and operations, and scientific experiments would have enough energy on the yet-to-be-built space station. It uses solar panels and must rely on batteries when it cannot be oriented to receive enough sunlight. We knew the problem was important, and in the end our supervisor told us they might implement some of our ideas.

In that practicum we learned how big and messy real problems can be. We experienced the excitement of tackling a critical problem. We went to NASA to learn about the space station and ask questions about what had already been tried. We learned that we had to work with limited information and create a model that would be flexible enough to accommodate the inevitable changes NASA would make before (and after) the launch. Before the class, I already knew that mathematics was useful. But the typical classroom story problems that are so abstract compared to adult work life did not give me a sense of how mathematics was used in practice. When a graduate from my college who worked at NASA encouraged me to think about pursuing a career there, I couldn’t imagine myself in such a position. Nevertheless, the practical experience and seeds of encouragement took hold—and stuck.

Throughout this experience I had access in my favor. I had been accepted to a small liberal arts college, could afford to attend, and had performed well enough as a mathematics and English double major to qualify for the senior-level practicum course. We had a professor who figured out how to create this opportunity for us and who supported our team through the problem-solving process, so that we were able to make suggestions to NASA by the end of the semester. We had a college that allowed our professor to teach a capstone with only a handful of students enrolled. This intensive internship-like experience became my most inspiring mathematics course in college. I want more students to have access to these types of opportunities, because they are engaging and because the skills they teach are in demand. They should be available to everyone who has the interest and can develop the appropriate skills, not just those in positions of privilege.

Industrial mathematics workshops can provide large groups of students with access to these experiences. When I was a graduate student at North Carolina State University my colleagues and I participated in **such a workshop**; my team solved a problem related to HIV treatment, which motivated us to delve into differential equations models, control theory, and the complexity of data from human subjects. We also gained communication skills by presenting our findings, writing a technical report, and typesetting it in LaTeX. We learned how to find ways for each team member to contribute given our limited skills. We had to work within a very short timeframe using software (Matlab) that was new to most of us. Several of us continued to pursue biological and health-related problems as part of our PhD research. Some students in our program pursued academic jobs, some went to government labs, and others went to industry. All of these outcomes were viewed as successes, and we were prepared to pursue the paths of our choice because our mathematics skills were enhanced by teamwork, programming, and communication.

Faculty members also have opportunities to learn about industrial mathematics with their students. As a postdoc at Duke, I visited the United Kingdom and participated in a tradition called * study groups *(generally called

*in the United States and Canada). In these intensive multi-day sessions, mathematicians and their students tackle problems presented by industry representatives. Students see their faculty mentors outside their usual professorial roles. If the solution presented by the team seems viable to the company, the group sometimes continues to work on the problem after the workshop. Thus, study groups can lead to continued associations between academic scholars and industry contacts, as well as internships or positions for faculty’s graduate students.*

**math-in-industry****workshops**At Harvey Mudd College, I serve as a mentor in a course called “Clinic,” a similar course to the one I had at Oberlin but implemented as a capstone in engineering, computer science, mathematics, and physics to a majority of the seniors at the college. In teams of about four, students work on a problem for an industrial sponsor for a year with the guidance of an industry liaison and a faculty mentor. The students serve as project managers and take ownership of the project and its deliverables. They work on soft skills such as communication, project timeline management, data visualization, documentation, meeting efficiency, and presentations. At the end of the year they travel to present their results to the company. Several other institutions, such as Olin College, University of California Los Angeles, and Worcester Polytechnic Institute now have related programs, but they are not ubiquitous, especially in mathematics departments.

As I had at Oberlin, Harvey Mudd College students have privileged access. We have longstanding relationships designing projects with sponsors and experience mentoring teams so our students are able to produce work of value to the company. Because our college is highly selective and well known to industry, our students have little trouble obtaining internships. And while a majority of our undergraduate students go on to pursue graduate work, many of them upon graduation also spend some of their first decade of work in business or government positions. Some return with their companies to sponsor “Clinic” projects. While our program has been successfully replicated and adapted at other institutions, it requires a great deal of institutional investment in terms of faculty mentoring time and staff support. Summer internships can provide students with similar experiences and the added benefit of more time on site.

As Vice President of Education for the **Society of Industrial and Applied Mathematics** (SIAM), I have been thinking about how to provide more mathematical sciences students with internship opportunities. Students from top schools and departments that have invested in business or government connections will likely have no problem landing a well-paid internship in a desirable location. But that is a small fraction of the total number of mathematical sciences students.

To reach students nationally we can create infrastructure that connects mathematical sciences students to internships and jobs. Those jobs are probably not called *mathematician *, and instead have titles such as Analyst, Engineer, Data Scientist, and Senior Researcher. The opportunities need to be located in places the student can live. And if internships become commonplace, the pay might vary greatly according to the student’s experience and the type and location of the work.

A mathematical sciences internship website, in addition to job postings and applications, can communicate to companies the **kinds of** industrial **problems**mathematical sciences students can solve. At the same time, it can educate mathematical sciences students to seek skills such as programming, data sciences, and communication that enhance their career opportunities. A site can suggest ways to incorporate new courses and internship opportunities into degree programs and connect students to intensive training through Math in Industry Workshops and programming or data science courses.

Infrastructure that bridges the gap between students and jobs can also provide materials and information to help faculty connect with local businesses and government agencies. Many large companies have existing internship programs, but might not yet recruit in mathematics departments. Small and medium-sized companies may not have internship programs or academic connections. A national network of faculty ambassadors, like the faculty already participating in the **Preparation for Industrial Careers** (PIC MATH) program, could help create local internship opportunities and new collaborations between academic institutions and local businesses.

The more faculty and alumni that have experience and connections in business and government, the more mentoring will be available for students. Voices supporting a variety of career paths for mathematical sciences students can also help us redefine success. Statistics and operations research have a long tradition of preparing students for a variety of jobs, but in mathematics departments, a tenure-track academic job in a top university is the traditional measure of success. Students can make significant contributions in many careers. This training can start young with mathematical modeling, build with internships, and culminate in a workforce prepared to solve big, messy problems with tools from the mathematical sciences.

Faculty will continue to train students for academic careers. Some will pursue tenure-track positions in the institutions of their choice, but an increasing number of our students will take positions very different from our own. Let’s learn about those options and share them with our students. Then, when a student takes a good job and enjoys a successful career, let’s call that a win.