From the Director

Moving forward

Doug Arnold

IMA Director 2001-2008

With a mathematician's insistence on precision, I point out that the column name, From the Director, is a bit inaccurate for this issue. A few days ago, on July 1, Fadil Santosa became the fifth director of the IMA. Fadil was the first choice of the selection committee, after an extensive national search which brought in a gratifyingly large number of first rate applicants. I am delighted that the IMA will move forward in his capable hands.

In this, my last column, I take the opportunity to reflect on the closing of a wonderful chapter of my life. For the past seven years, a huge portion of my time, energy, and even my identity, were invested in the IMA. Its primary mission of advancing interdisciplinary mathematical research became my primary mission. Its challenges were my challenges and its outcomes reflected on me.

The IMA is always a hive of activity, and, by any measure, I have had a busy seven years. During this period we hosted 8,000 visitors and 60 IMA postdocs; we ran 7 thematic year programs, 130 workshops, tutorials, and short courses, 24 public lectures, and 80 industrial problems seminars; 20 new books appeared in the IMA volume series. It certainly took a lot of work—by me and by others—to support all these people and organize all this activity. In fact, at the IMA we like to think that it is the rare visitor who has an inkling of all the efforts that go into making their stay at the IMA smooth and productive. To use one crude indicator of organizational activity, my email files—the messages I thought significant enough to keep—contains about 100,000 messages relating to IMA business over the past seven years.

However when I look back on these years, I do not think so much of the long days and the detailed planning, the emails and telecons and meetings, the proposals and reports. What sticks with me is the exciting scientific atmosphere of the IMA: the great lectures I got to listen to and the great mathematicians and scientists I had the opportunity to meet and to talk with, the palpable excitement and discovery that fills the offices and hallways at the IMA, the feeling of witnessing the cutting edge which comes not infrequently during discussions sessions, and the significance of our role in helping to guide the mathematical world's research agenda as we plan our programs. My term as IMA director has supplanted my time at graduate school as the period of my life when I felt I learned the most, and is unquestionably the period in which my efforts have had the greatest impact. Quite simply, it has been my great good fortune and an immense privilege to have had the chance to lead the IMA.

I spent two years in my early and mid-career as an IMA visitor, and I have long understood what a great and special institution it is. Thus my coming as director in summer 2001 is sort of a mathematician's variation on the career path famously pitched by the owner of the Remington shaver company: “I liked it so much, I bought the company!”  But it is a truism that an institution such as the IMA can never rest on its laurels: it must progress or it will fail. Although I have stayed true to the vision and the mission which have guided the IMA since its inception, I have also led the IMA in many changes, and take great satisfaction in what we have accomplished. I make no effort here to be exhaustive, but will discuss a few of these changes.

The director of the IMA plays an important role in the selection of topics for the annual thematic program, collecting and integrating ideas and input from the community, learning about a field and its major players, developing a sense of where an investment of the IMA's resources are most likely to have the largest impact, and guiding the discussion and decision-making process. The recent programs, in Imaging, Applications of Algebraic Geometry, Mathematics of Molecular and Cellular Biology, and Mathematics and Chemistry (about to begin), are remarkably broad, while not diluting the IMA's focus on high-impact interdisciplinary mathematics. The imaging program engaged an established subject of applied mathematics and helped to move it in new directions and rekindle excitement at its research frontiers. The recent founding of a new SIAM Journal on Imaging Science is an indication of the energy in this area, partly as a result of the IMA program. The algebraic geometry program brought many mathematicians and ideas to the IMA for the first time, helping to gulf the unproductive gap between so-called applied and pure mathematics. It became clear to those of us in residence at the program that large parts of algebraic geometry provide extraordinarily effective and often under-utilized tools for applications. I do not believe the subject will ever be quite the same. While the past year's program fits squarely within one of the most well-recognized and active branches of modern applied mathematics, mathematical biology, next year's program is founded on the bold belief that the time is right to create a new field of mathematical chemistry that barely exists at present.

An innovation at the IMA that I have been privileged to lead was the creation of the New Directions short courses. I first discussed this idea at a meeting of the IMA Participating Institutions department heads, just before I assumed the directorship. There was strong agreement that universities across the country were eager to get their faculty more involved in interdisciplinary research areas, but that the obstacles mathematicians faced in moving from more traditional research topics into such areas were daunting, even to the very accomplished. The New Directions program addresses this with two-week intensive courses in the most exciting interdisciplinary research areas. They are team taught by two of the leading researchers in the world in the area of the course, and the student body consists of 25 accomplished mid-career mathematicians. The IMA has run six such courses so far, and the quality has been simply amazing, the response from the participants fantastic.

The IMA is in a unique position to advance public understanding and appreciation for the role of mathematics, and public outreach has become a major focus of mine. I used my position as IMA director to bring mathematics and its applications to the national press on dozens of occasions, reaching outlets as varied as CBS Sunday Morning TV, the Chicago Tribune, and Outdoor News. I also started the Math Matters public lecture series, where four times a year we bring distinguished mathematicians and scientists who are also superb expositors to the IMA to speak to a broad audience from the general public. We ask the speakers not only to talk about an area of contemporary mathematics, but also to illuminate the role math is playing in understanding our world and shaping our lives. This is one IMA program on which I kept very tight control, choosing most of the speakers myself and communicating with them about the type of lecture we sought. The series has had a remarkable success, and with advertising and word of mouth, the audience has grown to over 300 every time. To my surprise, the rather high level lectures are very attractive to high school students, who come in ever greater numbers, stoking my optimism and enthusiasm for outreach efforts.

Important too, are the changes over these years to the funding, size, and stature of the IMA. I had the good fortune to come to an institute that was working well, and had been doing so for nearly two decades. However, its activities were underfunded by many measures. This dates back to the late 1970s when the National Science Foundation released its first call for a national mathematical sciences research institute. The 1979 IMA proposal is a rare example of a grant proposal which successfully argued against the premise of the call for proposals. The Minnesota group proposed an interdisciplinary math institute, where mathematicians could come together with the users of mathematics from other fields. This was very different from what NSF had envisaged, which was a place where mathematicians could dig ever deeper into self-generated problems, far from outside distractions. NSF—to their great credit—accepted the Minnesota proposers' challenge and chose to deviate from their plan to create a single national math institute. They instead created two, one of which—the future IMA—was a sort of pilot for the heterodox but compelling vision of the proposal. Because of this background, the IMA started life severely underfunded. There was not funding available for two fully-funded institutes and the IMA received just 50% of what both the proposers and the NSF committee had estimated was the proper level.

In our 2004 renewal proposal to the NSF, I traced the impact of NSF's investment in the IMA since those days, and argued that the return on that investment has been tremendous. As I was able to demonstrate from the evidence, the IMA had played a huge role in transforming the culture of mathematical research, and its vision and working model, viewed as at the fringe in 1979, had become the mainstream, widely accepted and emulated by numerous newer math institutes across the country and the world. I also analyzed the opportunities for even greater impact that were being lost by inadequate funding. The NSF reviewers for this proposal—mail reviewers, panelists, and two separate site-visit teams—found the arguments compelling. The result was that IMA was renewed at the funding level we requested, which was 77% above the previous period. At last, 20 years after its founding, the IMA was fully funded. The impact of this new support level at the IMA has been tremendous. Our program size is much larger than before, we are much more able to attract the top leaders in a field as long-term visitors to our programs, new programs like the New Directions short courses are possible, and successful older programs run more frequently, like our Mathematical Modeling in Industry workshop for graduate students, which has moved from biennial to annual. Equally important is the boost in stature the IMA received from this tremendous vote of confidence from NSF, whose peer review process, after all, is generally regarded as the gold standard. Now, as the recipient of largest mathematics grant ever awarded by the NSF and simultaneously one of the longest funded NSF grantees, the IMA has become much more visible. As the division director for mathematical sciences said at the time of renewal, the IMA had become “a preeminent mathematics institute that serves as a model for other institutes worldwide”, “primer inter pares” in NSF's portfolio of math sciences institutes. This boost heightened our credibility with other funding sources and my own university's administration. It brought to the IMA regular delegations from nations seeking to found math institute. Most importantly, it made it much easier to recruit top talent to IMA programs as organizers and participants, and resulted in numerous exciting proposals sent our way.

Infrastructural changes are very important as well, and I made them a major priority of my term. The IMA increased its space for offices by about 40% and added a variety of meeting and conference space for our visitors. We just added a new seminar room with double the capacity of our current one. While the IMA space is certainly not the most impressive among math institutes, it is highly functional for its purpose. The IMA's information technology infrastructure is less visible to our visitors than bricks and mortar, but it affects their IMA experience in manifold ways, and we developed it into the best in the business in recent years. An extensive system of IMA-developed databases and web-based tools maintain information on our visitors, our programs, participant invitations and applications, visitor feedback and surveys, talks and related materials, etc. These are a great help in many ways. We use them to ensure a smooth visit for our participants. We mine them to help us assess and improve. We use them to organize the talk materials and video we collect, and make them easily accessible on the web. Speaking of video, toward the middle of my appointment we decided that webcasting and online video archiving technology had matured enough to warrant a major investment, and for some years now almost every IMA activity has been webcast live and archived in our online video library (give it a spin if you haven't already!).

While I have had the immense privilege to be director of the IMA these past seven years, the accomplishments I have discussed, and the many I have not, are of course the result of the good ideas and hard work of many people. Numerous exceptional people have worked with me as deputy and associate directors. The three-person management group has always worked as a team, and my accomplishments are their accomplishments as well. I have also been the beneficiary of the wonderful, one might say legendary, IMA staff, who manage to be tremendously efficient and authentically friendly at the same time, all the while making it look easy. The distinguished mathematicians who have served on our Board of Governors, Participating Institutions Council, and Industrial Advisory Board, as well as our human relations and other committees, have been an invaluable source of wisdom and support. I have already spoken of the strong support we receive from NSF. I am also very grateful for the personal guidance of the three NSF math division directors I have worked with, Philippe Tondeur, Bill Rundell, and Peter March, and of our program director, Hans Kaper. Besides NSF, IMA is supported by the University of Minnesota and its consortium of affiliated universities, corporations, and industrial labs, and their constant and generous support has been critical. Finally, but most importantly, is the huge intellectual support we receive from the many mathematicians and scientists who bring their energy and ideas to the IMA. They make what we do both possible and worthwhile. My heartfelt thanks to you all.

So what comes next? The IMA will without a doubt continue to move forward, and I am eager to see the ideas and innovations that will come from its new director. My own path forward is exciting and challenging as well. I will spend next year as a Guggenheim fellow on a sabbatical focused primarily on my research. Much of the time I will be with collaborators in Europe, and I will also take up residence—for the first time—in the School of Mathematics here at the University of Minnesota. I look forward to getting back to teaching and graduate advising the following year. Tomorrow I fly to the annual meeting of the Society for Industrial and Applied Mathematics (SIAM), which I will attend as the society's President-Elect. I expect that at SIAM I can put to good use many of the things I learned at the IMA. So in my life, as at the IMA, one chapter closes and another begins. Thank you for indulging these reflections on the past. Now let's get moving forward!