## A Career in the Math Sciences at a National Lab (or What I Wish I'd Known in Grad School)

**October 19, 2010**

**Careers in the Math SciencesNatalia Alexandrov**

So, you are a mathematician about to start or already in grad school, wondering about your options after you finish. Now is the best time to wonder--you can prepare to make informed decisions long before you get your degree. In this article I give you an idea about working at a National Aeronautics and Space Administration (NASA) research center, through answers to questions students frequently ask. Some of my impressions are specific to NASA Langley Research Center, where I work, but much of the information applies to other national laboratories too. You should look into the specifics of any labs that interest you for details. Finally, a disclaimer: These are my personal opinions, colored by my experience and career choice at NASA. They do not, in any way, represent the official NASA position. *Q: What does NASA do and where does mathematics play a part?A:* NASA, an agency of the U.S. government, focuses on space exploration, scientific discovery, and aeronautics research. Its applied research activities mainly fall into three areas, with considerable interdependence among them: space (e.g., the shuttle and the space station, exploration of the solar system and the universe, astrobiology, bioastronautics); aeronautics (e.g., fundamental aeronautics, next-generation air transportation), and science (e.g., earth and atmospheric sciences, materials). Information about NASA's programs, projects, and centers can be found at the agency's website (www.nasa.gov).

As to be expected, mathematics is everywhere. Some areas of aerospace research, such as computational fluid dynamics, structural analysis, and multidisciplinary optimization, are explicitly mathematically intensive, relying on numerical partial differential equations, nonlinear optimization, approximations. Other areas, such as design and transportation systems, make use of expert knowledge and heuristic approaches, relying, for instance, on simplified models, rule-based simulations, evolutionary algorithms, and scenario-based analysis. Arguably, the complexity of "real-life" systems will always defy attempts at complete rigorous mathematical descriptions. However, the growing complexity of modern systems and the need for radically new solutions also mean that evolutionary, experience-based, and heuristic approaches alone are insufficient for designing new systems. This is good news for mathematicians. Optimal or even feasible solutions for complex, massively multidimensional new systems can be counterintuitive and require rigorous mathematical methods to supplement expert decisions.*Q: What can a mathematician do at NASA? What career paths are available?A:* NASA scientists and engineers work in several general settings: research and development, systems analysis, systems engineering. As a rule, every activity, even in fundamental research, has an applied goal consistent with some aspect of NASA's mission.

Traditionally, the NASA staff is composed mainly of engineers and scientists. As a mathematician, you can follow one of two paths (in addition to administration, which is not considered here). You might become an expert in a specific discipline and devote your career to it, in essence becoming an engineer or a scientist with good mathematical skills. Many exciting technical areas are amenable to such a strategy. Alternatively, you could choose to be a mathematical generalist, continually learning about new areas at sufficient depth to contribute to research in many applications and disciplines. I have chosen the latter and have never yet met an uninteresting problem! My impressions are based on this choice.

Your role as a generalist mathematician (should you choose to accept it) could span the range of problem-solving activities--from interacting with experts in a field in order to formulate problems amenable to solution, to method and theory development, to computational tool development, to actual solutions, to opening new method and application areas, based on your discoveries.

NASA mathematicians have a great degree of flexibility in pursuing new problems and solutions. Depending on your curiosity, persistence, and willingness to learn and establish collaborations with disciplinary experts, you are free to explore both the depth and the breadth of as many disciplines as you wish, as long as you are productive. Despite very busy schedules, all the scientists and engineers I have met at NASA have been willing to help me learn about their fields and have welcomed collaborations on problems of interest.

My work with colleagues in computational fluid dynamics, for instance, has been especially rewarding and fun for me. I am not sure just how much fun it was for this very busy group when, having spent considerable time showing me how to run their CFD codes, they had to contend with my daily visits that always started with, "the grid broke again!" But they were invariably gracious as we unraveled the causes. I have come to appreciate the complexity and beauty of their subject. In turn, I like to think that they have come to appreciate optimization, at the very least as a great diagnostic tool.

Formal opportunities to work in different groups and positions arise often. Staying in a single group also affords tremendous opportunity for variety, if that is what you like. You are free to bring new aspects and areas to your position. In my recent work in transport systems, for example, I had an opportunity to develop research announcements in such areas as complex network topology optimization and predictive modeling for complex systems, leading to new lines of investigation and new collaborations with NASA and external colleagues.*Q: What are the most important areas in need of mathematical attention?A:* In my opinion, predictive modeling (of everything) with quantified uncertainty and confidence is the most important area in need of development. Numerical modeling is ubiquitous, more so all the time. How much are the answers worth? When can computational simulations really replace experiments? Should they?

In some disciplines (e.g., aerodynamics), the models themselves are well developed but require quantification of uncertainty. Other systems defy traditional mathematical modeling. For instance, very large complex systems with autonomous but interacting components (sometimes referred to as "complex adaptive systems"), such as transportation, have not yet been modeled in the sense of "physics-based" modeling. Their boundaries are unclear; they have never been formally designed but rather have evolved over time, subject to demands and constraints.

Consider the actual air transportation system. As it grows in complexity, increasing automation is required. An automated system must be provably safe and sustainable. How can we construct proofs about the safety of such a system? Clearly, rigorous mathematical methods are the only way to prove statements about safety. Active efforts are under way at NASA to develop methods for reasoning about complex systems so that questions about safety, performance, sustainability, and impact can be answered in ever larger contexts (e.g., environmental).

In general, traditional systems analysis and engineering begin with a definition of the boundary of the system under consideration. New methods for predictive modeling of realistic systems with uncertain boundaries are crucial.

Another general problem is the need to anticipate algorithms that will allow us to take advantage of coming breakthroughs in hardware. Arguably, we have not yet taken full advantage of parallel and distributed computing. What would we do with quantum computing if it arrived?

This is just a sample of general methodological problems of interest to NASA and all other national laboratories. You can find details of specific problems at the agency and lab websites.

*Q: What are useful skills to develop?A:* Different application areas require different specific technical skills, but good formal mathematical training will ground you in general problem solving and allow you to acquire missing expertise quickly, as long as you remain flexible and curious. Given that you will almost certainly have to learn the application subject matter "on the fly," training in either pure or applied math will serve you well. You are likely to benefit from courses in such areas as analysis; mathematical modeling, including numerical solution of differential equations; linear and nonlinear optimization; and graph theory. Strong computing skills are a necessity.

Beyond mathematical skills, learning to communicate with scientists and engineers during the process of problem formulation and solution is one of the most useful skills a "generalist" can acquire. This is both a technical and a social skill. Subject matter experts often think in subject-specific terms, while we (mathematicians) think in variables, functions, etc. It is always up to the mathematician to do the translation. Patience and flexibility go a long way. It helps to keep in mind that, as mathematicians, we are often naïve about the realities of applications; engineers are justifiably cautious about new "recipes"--after all, they managed to build a lot of good things by themselves. It is worth the time and effort it takes to inject explicit mathematics into applications that have traditionally relied on it implicitly.

The ability to work in different modes is also important: Sometimes you will be a member of teams of various sizes, and sometimes you will work completely independently. In any case, you will do a great deal of writing, and writing well is an invaluable skill.

Finally, a sense of accountability is essential. Deadlines are more firm in some areas than in others, but in any area, you are accountable for your promises. This does not imply that you will go to jail for not proving a theorem on time! But it does mean that you will need to periodically assess your progress and justify your results. It may also mean abandoning a research direction that has not yielded results after a certain amount of time and, perhaps, revisiting it in the future.*Q: How is working in a national lab different from working in industry and academia?A:* In comparing national labs and academia, it is tempting to pass along comments from colleagues in research universities: In academia you are free to pursue any problem you wish, whereas at a national lab your work will be guided by the mission of the lab. As a corollary, one of the main criteria for quality work at a university is acceptance by your peers, while at a lab it is some measure of the applicability of your research to a real problem. Teaching and advising students are academic activities.

Strictly speaking, much of this is true: For instance, the likelihood that a person at an aerospace research center will work on a problem in agriculture is not high. The distinctions, however, can be tenuous and depend greatly on individual career paths.

In principle, at a university you can work on anything you wish, although fiscal realities mean that you will likely be working in areas of interest to funding agencies. Conversely, even though at NASA you will work on problems that support the agency's mission, you are, as a rule, free to pursue new areas of research and even, if you are persistent enough, to open new active areas of research; you do have to demonstrate the relevance of the work to the ultimate mission. NASA researchers have many opportunities to teach and mentor students; with rare exceptions, I have worked with one or two students every year. There are also opportunities to collaborate with external researchers. And, depending on the research area, publishing can be as important as at a university.

Moves in new research directions have originated in a number of ways for me. A new direction might start with a colleague's request for help, bringing with it a new awareness of an interesting area. This is how I became involved in modeling of transport systems. A move might also start with a personal interest, not even related to work. My "outside" interest in biology and medicine led me to a recent involvement in the NASA Human Research Program. Pointers from management or project requests for expertise can bring you into new areas as well. In all cases, your work has to be funded, which means that eventually you will have to convince a specific funding organization of the relevance of your research.

And this brings me to the one unwelcome similarity: If you think that working at a national lab will excuse you from proposal writing, you are mistaken! You will likely be submitting as many proposals as your colleagues at research universities.

Distinctions include the increased accountability at national labs (e.g., the potential need to abandon unproductive lines of inquiry mentioned earlier) and a number of controls on information dissemination. For instance, you will need to have your papers reviewed before sending them to a journal.

It is difficult to comment on specific differences between working at national labs and in industry, because there is such a broad range of possibilities in industry, from small technical consulting firms to high-tech giants, each with its own conditions and culture. The general difference lies in the basic goals: National labs are concerned with matters of public interest, while commercial interests are paramount in industry.

*Q: Do I need to be a U.S. citizen and do I need a security clearance?*A:* Some DOE labs, including Livermore, Los Alamos, and Sandia, do require citizenship. Most DOE labs, however, including Argonne, Oak Ridge, Berkeley, Pacific Northwest, Brookhaven, and Idaho, do not. Prospective employees should check on the individual policies of labs of interest to them. The majority of work at NASA is not classified and does not require a security clearance. If you are not a U.S. citizen, you may still be able to collaborate with NASA via one of the affiliated research institutes (e.g., the National Institute of Aerospace, www.nianet.org). Other laboratories may have similar affiliated organizations. (*Revised from the print edition; see below.)

*Q: Where can I find more information?*

A:The main NASA website (www.nasa.gov) contains a wealth of information about current research directions and programs, as well as pointers to the NASA centers. The NASA Technical Report Server (ntrs.nasa.gov) gives you access to recent reports. But the best way to get a feel for working at NASA is to take advantage of the student programs. The Langley Aerospace Research Summer Scholars program (http://www.nianet.org/larss/) offers opportunities for both undergraduate and graduate students to spend a summer at NASA Langley working with a researcher. The NASA Graduate Student Researchers Program (http://fellowships.hq.nasa.gov/gsrp/nav/) is an agency-wide fellowship program for graduate study in science, mathematics, and engineering related to NASA research and development. The award recipients are encouraged to spend part of the year at NASA. Once you are looking for a job, you can place your CV at www.usajobs.gov, which advertises jobs in government labs. You can sign up for announcements of NASA Research Opportunities (http://nspires.nasaprs.com/external/) and ask your faculty adviser to sign up as well. Your adviser can respond to calls for proposals and, if appropriate, include you as a member of a team.

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*Q: Anything else?*

A:Finally, because you are reading this, I assume that you are a student member of SIAM and have attended SIAM conferences. This is an excellent way to meet researchers from national labs and find out about research and work opportunities. I encourage you to remain a member of SIAM and also recommend that you attend conferences and read papers from conferences of other professional societies, where researchers from the labs you are interested in are likely to publish.

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*Natalia Alexandrov is a research scientist in the Aeronautics Systems Analysis Branch, Systems Analysis and Concepts Directorate, of the NASA Langley Research Center. Her doctorate is from the Department of Computational and Applied Mathematics at Rice University. She is a member of the SIAM Committee on Membership and an Associate Fellow of the American Institute for Aeronautics and Astronautics. Readers can contact her at *[email protected].

**Career Clarification (from November 2010 issue)**

The statement "As a rule, you must be a U.S. citizen to work at a national lab" ("A Career in the Math Sciences at a National Lab," *SIAM News*, October 2010, page 4, print edition) merits some clarification. Foreign nationals interested in jobs at national labs should be aware that some Department of Energy labs (e.g., Livermore, Los Alamos, and Sandia) require U.S. citizenship. Many other DOE labs---including Argonne, Oak Ridge, Berkeley, Pacific Northwest, Brookhaven, and Idaho---do not. As suggested in the article, readers interested in opportunities at any lab should check that lab's requirements.

Susan Minkoff ([email protected]), of the University of Maryland Baltimore County, is the editor of the Careers in the Math Sciences column.