SIAM News Blog

What Characteristics Make Mathematicians Suited for Industry?

By Bill Satzer

While the number of Ph.D.s in the mathematical sciences continues to grow, the availability of academic positions—especially those leading to long-term employment—remains stagnant. According to the American Mathematical Society’s recent survey, 52 percent of new math-based Ph.D.s in the United States held academic positions in 2014-2015. Three-fourths of that 52 percent were hired in postdoctoral positions. Nonacademic U.S. hiring was at 35 percent, a five-year high. If history is a guide, many of those postdocs will not find permanent academic employment.

What happens to these unemployed Ph.D.s? Does their training and experience in graduate school prepare them for the world they must now face? I seek to identify the characteristics that make mathematics Ph.D.s attractive candidates for positions outside the academic world and prepare them for nonacademic careers. Sometimes this environment is simply called “industry,” but I find that term too limiting and even misleading. Jobs that employ mathematicians now cover a broad spectrum—from government to retail sales (e.g., Amazon and Target); management consulting (e.g., McKinsey & Co.); manufacturing (e.g., Dow Chemical Co., DuPont, Corning Inc., 3M); data analysis and software development (e.g., Google); medical technology; pharmacology; drug development; and so on. But for lack of a better word, I’ll continue to use the term “industry” to encompass all non-academic employers.

I identify three general categories of attributes desirable for industrial employment: technical capability, communication skills, and flexibility. Ph.D. students typically focus most on technical skills and general technical aptitude. These are significant, but only part of the picture. Communication and flexibility matter quite a bit, and may be as important as technical capability.

The following analysis is based on my experience in industry, as well as conversations, interviews, and discussions with mathematics Ph.D.s working in industry; the people who hire them; and the people who work with them. Though the suggestions pertain to Ph.D.s in the mathematical sciences, many also apply to related fields, such as physics.

Applied mathematics plays an important role in the manufacture of goods such as aluminum. Mathematicians design prototypes, optimize and verify designs, automate processes, and help manage supply chains. SIAM photo.

Technical Capability

A mathematics Ph.D.’s most important technical skill is a capacity for sustained logical and analytical work. Writing a thesis tests one’s ability for extended, independent work, and the discipline and persistence necessary to carry it through. This is true regardless of a student’s specialization area, though specializations in more applied areas may make finding a nonacademic position easier. 

At the same time, there are general areas where a solid technical background—equivalent to what one would learn in an advanced undergraduate course—is highly desirable. These include probability and statistics, data analysis, mathematical modeling, and the basics of numerical analysis (particularly numerical linear algebra). Experience with mathematical software like MATLAB, Mathematica, or Maple can be very useful, as is familiarity with writing code in languages such as C. However, some companies—particularly those doing heavy-duty data work—may actually require experience in coding with Python, C, or something similar.

Many potential employers continue to view mathematics Ph.D.s as impractical or too specialized, interested only in the abstract and skilled only in proving theorems. Thus, evidence of breadth is important — serious interest, curiosity, and experience in areas unrelated to one’s Ph.D. specialty.

The ability to learn and continue learning is another essential strength. Being able to jump into a situation, assess it, and quickly gauge what one needs to know is invaluable. Adaptability in an unfamiliar work environment is a prime asset.

Recognizing that not every problem demands a full-scale attack and rigorous solution is also important. Sometimes new Ph.D.s want to demonstrate their analytical skills by pursuing a fully robust solution and a proof, but this often suggests a lack of perspective and perhaps poor judgment. The effort required to solve a problem can be highly dependent on the situation. Often the best results emerge from back-of-the-envelope calculations. Learning to evaluate a problem and justify the corresponding level of effort is highly regarded.

It is important to note that rarely (and in my experience, never) is someone hired to fill a position as a mathematician. A mathematician’s value to a company is not as a mathematician, but as an individual with a versatile skill set who happens to be a mathematics Ph.D. Scientists, engineers, and mathematicians are hired for industrial jobs with the expectation that they have, or will develop, relatively broad capabilities in that industry to contribute technically to a company’s goals. Industrial managers assume that their employees are there to do the job and handle any technical issues that arise, regardless of the scientific or engineering discipline.

Communication Skills

 Unsurprisingly, Ph.D.s should be able to share information with colleagues—who come from a variety of backgrounds—in a nonacademic environment. Part of this is simply learning some of the technical language used by engineers, chemists, biologists, computer scientists, and others. I find that this helps in understanding and appreciating their perspectives. Sometimes the real technical issues and problems do not begin to emerge until the language issue is addressed. More than once, I’ve found myself working on a problem that I presumed was well posed in a technical area with which I had little experience, only to find that the problem described to me was not the right one at all. Resolving language and cultural differences between technical specialties in advance helps avoid the “correct solution-wrong problem” dilemma. The process of developing “shared knowledge” in a work environment begins with developing a shared vocabulary, shared goals, and perhaps a shared perspective.

Mathematicians often use their skills to help streamline production and distribution systems in industry. SIAM photo.
Relevant communication skills include both speaking and writing, formal and informal. For example, knowing how to assemble a concise presentation on short notice is a valuable skill. And clear, well-organized, and articulate writing is still rare enough not to go unnoticed.

While the aforementioned approaches largely apply to communication with fellow engineers and scientists, most companies have a variety of other personnel—including sales, marketing, manufacturing, financial, legal, and management groups—with whom one must interact. While the worldviews of other engineers and scientists may differ from yours, the perspectives of individuals from such diverse areas can be mind-bogglingly at odds with your own. Nonetheless, to work with them you’ll have to understand something about them, their goals, and the effects of their actions. Additionally, while academic work can be mostly solitary, teamwork is far more common in industry. This requires considerable adaptability to accommodate differences in technical language, culture, work style, and personality.

New Ph.D.s with teaching experience can use that experience to their advantage. Teaching, either one-to-one or in small groups, is very common in industrial settings, as people naturally educate one another in everyday situations. Knowing how to present ideas and concepts clearly and concisely, as well as how to identify and approach areas of misunderstanding, is a notable skill. This offers solid evidence of the ability to communicate to a potential employer.


It is increasingly common for people, especially technical professionals, to make one or two major career changes during the course of their working lives. Flexibility is a survival skill; it requires that Ph.D.s view themselves as broadly capable, engaged with the world, and open to challenge. To be successful in a nonacademic environment, new Ph.D.s must be willing to immerse themselves thoroughly in the projects with which they are involved. 

In some cases, the most critical need for flexibility arises when recent Ph.D.s realize how they must reinvent themselves and realign their expectations for nonacademic positions. Unfortunately, I have often witnessed new mathematics Ph.D.s in industry-based positions who feel that they have failed as mathematicians and disappointed their advisors and mentors because they were not doing what they were trained to do. The adjustment can be traumatic, but Ph.D.s must resolve this before they start actively looking for jobs. Uncertainty in job interviews is not a good strategy. The necessary self-assessment and realignment of expectations is best done as early as possible in one’s graduate school career.


New mathematics Ph.D.s have much to offer. To insure that they find personally fulfilling careers and put their talents to the best use, I’ve suggested a collection of skills and attributes that increase their desirability for positions in industry. These, I think, would be beneficial no matter the direction of their future careers.

Bill Satzer received his Ph.D. in mathematics from the University of Minnesota working on a problem in celestial mechanics under advisor Dick McGehee. Almost all of his career has been in industry; he recently retired from the 3M Company.

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