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Careers in the Math Sciences

By Hans Kaper 

This column is addressed not so much to students and junior faculty as to more experienced mathematical scientists who are looking for new challenges and wish to use their accumulated knowledge and experience to serve the community. That is how I saw myself, after a long career as a researcher (including a stint as division director) in the Mathematics and Computer Science Division at Argonne National Laboratory.

In 2001, having served on a number of review panels and a Committee of Visitors for the Division of Mathematical Sciences at the National Science Foundation, I was asked whether I would be interested in joining DMS as a program director. (Then, as now, several positions were about to open up.) At Argonne, working as an applied mathematician in a multidisciplinary research environment, I had become familiar with all sorts of mathematical and computational problems in physics, materials science, chemistry, and engineering, and found inspiration in diverse applications for my research, mainly in the area of differential equations. Becoming a program director would be an interesting opportunity to put this accumulated knowledge to work in a different environment, so I accepted the invitation and became a “rotator”—a temporary staff member, on assignment from my home institution. The idea was to give it a try for a year and see whether I would like it. As it turned out, I loved it; I stayed for three years and then signed on for another three.

In this column I describe some of my experiences as a program director in applied mathematics (I was one of four), and as a participant in some larger programs within DMS and in several NSF-wide multidisciplinary programs. I hope to convince you that serving the community as a rotator can be both challenging and exciting.

At the Micro-level—DMS Applied Mathematics Program

As program director in the DMS applied mathematics program, my primary responsibility was to manage a portfolio of research projects within a given budget. With four program directors and about 300 proposals submitted to the program each year, each of us handled between 75 and 90 proposals (the numbers increase as you become more experienced). During my tenure, I handled all proposals dealing with applications of dynamical systems and many proposals in various other areas of applied and computational mathematics (materials, inverse problems, and so on). By “handling” I mean making sure that the proposals are in compliance with the required format, that they are appropriate for the program, that they are reviewed fairly and expertly, and that the review process is thoroughly documented. If you think that a proposal may be of interest to other programs, within the division or in other divisions, you contact the program director and coordinate a joint review.

Putting review panels together is serious business, because you want to make sure not only that the panelists’ expertise matches the proposals under review, but also that the panel has enough diversity (in more ways than one). Fortunately, our community takes its responsibilities seriously, and I found that, although not all panelists were equally adept at putting their thoughts in writing, the opinions were always informative and helpful. As program director, you learn to read between the lines. I certainly enjoyed this part of the job and admit that running a panel was one of my favorite activities. I also enjoyed taking a panel to dinner one evening at a local restaurant, as was the custom. My favorite restaurant was Taste of Morocco, where the food was different, the atmosphere relaxed, and the biggest surprise came at 8 o’clock, when the belly dancer made her entrée. Panelists who were unaware of this extra attraction reacted in various ways, but all remembered the occasion.

Sometimes we had to solicit extra reviews if a panel could not reach consensus on the merits of a particular proposal. But once the recommendations of the panel and the reviews were in, it was time for tough decisions: to consider each proposal and decide whether to recommend a declination (a “dec”) or an award. Although the success rate is higher in DMS (about 30%) than in most other divisions, there are always more declinations than awards. When a proposal is declined, you need to be sensitive to the expectations of the principal investigator, or PI, who needs to be made aware of the reasons for the declination. These reasons can vary. Only the “best” projects can be funded (the standard expression is that a proposal needs to be “compelling”), but as program director you need to keep in mind that a portfolio needs to be balanced by topic area, by seniority of the PIs, by geographic distribution of the institutions, and so on. This is where experience and judgment come in.

Of course, it is always a pleasure to recommend an award, especially if the project is proposed by a junior researcher. The budget, which is part of a funding recommendation, requires something that is euphemistically called “negotiation.” In most cases, the negotiation is one-way; considering the scope of the proposed project, you give a bottom-line figure to the PI, who must then figure out how to allocate the dollars to the various budget items.

If the division director concurs with your recommendation, it goes to the NSF Division of Grants and Agreements, which formalizes the award in a contract between NSF and the proposer’s university. Details may be tweaked, but in the end it is your recommendation as program director that is decisive. I found this part of the work most satisfying; it seemed to strike a nice balance between autonomy and responsibility.

At the Meso-level—Division of Mathematical Sciences

DMS has a team of about 30 program directors. Some are permanent, some are rotators; the split, about 40–60 during my time at NSF, has shifted lately to about 50–50. There are good reasons for this arrangement; ideally, permanent program directors are the institutional memory, and rotators bring in the fresh ideas. In fact, it works pretty much as stated. In DMS, the permanent program directors and rotators worked very well together. Some of us were more outgoing than others, and some worked harder than others, but nobody considered DMS a sinecure. I appreciated the help I got from my permanent colleagues when I first came to DMS. They guided me through the labyrinth of data bases and helped me conquer the vagaries of Windows.

As a DMS program director, you are expected to participate in the management of various programs that have been developed to foster collaboration and communication among mathematical scientists. I was particularly interested in the Focused Research Groups (FRGs), a program that funds teams of researchers to address well-defined problems or problem areas in the mathematical sciences. Proposals submitted to this program go through a more extensive review process than proposals from individual researchers, and the eventual recommendation must be endorsed in a joint meeting of all the DMS program directors. The panel reviews and any supplementary ad hoc (mail) reviews must be strongly positive, and somehow you have to make the argument that “your” proposal is as compelling as strong proposals from other areas of mathematics. It is a bit like comparing apples and oranges, and your responsibility is to convince your colleagues that your shining apples are as deserving of support as their bright oranges. The colleagues are friendly, but the competition is stiff, and you have to know how to make your case.

Major programs in DMS are handled by a “Management Team,” which consists of two to five program directors, depending on the size of the program. In my second term I became a member of the Institutes Management Team, which is responsible for overseeing the portfolio of Mathematical Sciences Institutes supported by DMS. This was a fascinating and most rewarding experience. The institutes are the “major facilities” of the mathematical sciences research community and the jewels in the crown of DMS. Each institute has its own character, and collectively they demonstrate the breadth and depth of current mathematics and statistics. I particularly enjoyed participating in site visits to review the organization of programs and the quality of governance. These visits were very illuminating, as well as exciting and—because of the high visibility of the institutes within the universities—a bit intimidating. Lots of good things happened, but nothing is perfect, and the challenge was always to make every visit a constructive experience for all involved.

At the Macro-level—National Science Foundation

Managing a portfolio of research projects in applied mathematics was only part of my job. I quickly became involved in several activities beyond DMS. This was probably natural, given my prior experience in a multidisciplinary research environment. In my first term I particularly enjoyed my involvement in the three ongoing NSF-wide initiatives: Nano-science and Technology, Information Technology Research (ITR), and Bio-complexity. My responsibilities included participating in the management of these programs, handling proposals, organizing reviews, and negotiating with colleagues in other disciplines about funding recommendations. These activities gave me first-hand experience in managing a broad portfolio of research proposals in areas in which I had only limited expertise.

Programs like Nano, ITR, and Bio-complexity reflect a national research agenda, which is set by the U.S. Congress and implemented at the level of NSF. As a program director, you don’t have much influence over the goals of such programs, but you do have significant influence over how they are implemented and managed. Other NSF-wide programs emerge from the research community, and this is where I found that program directors can have a much more direct influence. As program director, you are in touch with the research community, you pick up ideas, and discuss these ideas internally with colleagues in NSF, usually in NSF working groups. The ideas are tested out in workshops with outside experts, worked out in white papers and reports, and, if all goes well, eventually endorsed and supported by upper-level management.

During my tenure at NSF I participated in several such working groups. A working group in the Mathematical and Physical Sciences (MPS) Directorate on cyberscience eventually led to the NSF-wide program Cyber-enabled Discovery and Innovation (CDI), another to the MPS-wide program Approaches to Combat Terrorism (ACT), the latter with significant support from the intelligence community. Both programs ran for several years and supported several interesting research projects in the mathematical sciences. One of my lasting legacies is a Dear Colleague Letter (still active but in need of updating) issued jointly with my colleague Eduardo Misawa in the Engineering Directorate soliciting proposals from mathematicians and engineers for collaborative research in complex systems.

The Global Perspective

After serving a little more than six years as program director, I asked myself whether I had made a difference. My answer was unambiguous: yes. I had been able to support good science that will eventually benefit society and help up-and-coming scientists who may become leaders in our discipline. At a personal level, I had become familiar with a broader range of mathematics. It was often hard work, but most of it had been rewarding. And I had really enjoyed interacting with my colleagues, who were smart, interesting, and focused on doing a good job for the research community. Without hesitation, I recommend that you give it a try. If your expectations are realistic, and you approach the job with curiosity and an open mind, you will find it an enriching experience.

Hans Kaper is an applied mathematician who wears many hats. He is currently affiliated with Georgetown University and is co-director of the “Mathematics and Climate Research Network” (MCRN). Kaper is a corresponding member of the Royal Netherlands Academy of Sciences and a Fellow of the Society for Industrial and Applied Mathematics, class of 2009. He is editor-in-chief of SIAM News, chair of the SIAM Activity Group on Dynamical Systems, and a member of the SIAM Committee on Science Policy. Kaper received a PhD in Mathematics and Physical Sciences from the University of Groningen, the Netherlands. He can be reached at

Sue Minkoff (, of the University of Texas at Dallas, is the editor of the Careers in the Math Sciences column.

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