Today's Challenge: Keeping Up with the Demand for Mathematics

June 10, 2001

Talk of the Society
Thomas Manteuffel and James Crowley

What are we, after all?

It sounds like a simple question, but the SIAM leadership has considered it in several different contexts over the last several months, leading to interesting discussions about the future of applied mathematics and computational science and SIAM's role in that future.

Perhaps the question has arisen because of our recent efforts to reach out to new (for SIAM) disciplines. This year, for example, we have organized conferences in three new areas: data mining, imaging sciences, and life sciences (more about each below). In fact, our organization seems to be pulling in many new directions. But this is the strength of our discipline: that it is relevant in many contexts. The exploration of new application areas to learn where mathematics can make an impact is what has drawn many of us to applied and computational mathematics, and it is the common mathematical themes that glue us together.

Unique Set of Researchers
SIAM held its first conference on data mining in Chicago, April 5-7 (see organizing committee co-chair Robert Grossman's report). This conference brought together a unique combination of researchers with a common interest in data mining. Easily outnumbering the 19 academic mathematical sciences departments represented were the 76 corporations and firms (Merck, Nokia, AstraZenica, Daimler-Chrysler, Fidelity Investments, Booz-Allen & Hamilton, SAS, General Motors, Numerical Algorithms Group, and Blue Martini Software, to name just a few), 15 national labs, and various other academic departments (mainly computer science and electrical engineering, but also physics, economics, psychology, and business, among others).

A broad area with many diverse applications, data mining can be described as research targeted to the extraction of information from massive data sets. Some data sets, like semantic information extracted from the Web, have been considered largely the domain of computer science and artificial intelligence. Other examples include large sets of data generated from telephone transactions (see "Massive Graphs Pose Big Problems," SIAM News, April 1999 ), genetic databases (where the interest might lie in the extraction of functional information), astrophysical or geophysical data collected from sensor arrays, and even the outputs of large-scale computational simulations.

Readers will easily recognize the last of these examples as a problem involving significant mathematics, the others perhaps less so. What the SIAM conference on data mining did was to bring together a diverse group of scientists, many from a part of computer science not traditionally associated with SIAM, along with more traditional applied and computational mathematicians.

Whether the primary interest is scientific discovery or practical solutions in a specific domain, there is much to be gained by the scientific exchange of information across different disciplines and across different problem domains. This is what SIAM has to offer.

Imaging and Life Sciences
In Boston this fall, SIAM will host back-to-back conferences in the imaging sciences (September 22-24) and the life sciences (September 24-26). Each of these conferences will be conducted by a new activity group. Each will bring applied and computational mathematics to bear on problems in specific application domains, and will bring together researchers from applied mathematics, computational science, and the application domain.
Concerns are expressed whenever SIAM reaches out to new areas: Will more traditional applied mathematics (or, more precisely, traditional applied mathematicians) be lost in the enthusiasm for the new areas? But applied mathematics and computational science are dynamic fields that continually embrace new applications in order to remain vital and relevant. New application domains suggest new problems, leading to new research activity that often depends on established expertise and extends the research in new directions.

The life sciences promise to be a driving force for computational science in the future. For decades after World War II, applied mathematics and computational science were driven by problems in fluid dynamics arising in aerospace applications. In the coming decades, that role may be usurped by the life sciences. This is an area with rich intellectual content, and it is one to which mathematics and computation have much to contribute. SIAM's role is to make the community aware of new opportunities and to provide media for the exchange of scientific information.

Evidence of the increasing interest in mathematics and computing in the life sciences can be seen in the U.S. agencies that fund research. The Department of Energy's Science Office is planning to launch a new effort in biological and environmental research---"Genomes to Life" ( Philippe Tondeur, director of the Division of Mathematical Sciences at the National Science Foundation, has been collaborating with the U.S. National Institute of General Medicine to establish programs on the boundary between mathematics and biology. The National Institutes of Health expect to announce the creation of the National Institute of Biomedical Imaging and Bioengineering in the near future. Clearly, this is an area in which the demand for mathematics is growing at a rapid pace and one to which mathematics has much to contribute.

Strategy Sessions
Surprisingly, discussions of future directions and trends were a major part of the most recent meeting of SIAM's Committee on Science Policy, held May 6 and 7 in Washington. Program directors from several federal agencies, invited to attend the meeting, made it clear that the demand for mathematics is increasing in new areas of application. In fact, said Douglas Cochran, the new program manager of the Applied and Computational Mathematics Program at the Defense Advanced Research Projects Agency, "We can't keep up with the demand for mathematics."

As SIAM's president and executive director, then, we see activities and opportunities for applied mathematics and computational science in many new and emerging areas. The point is not that there is no longer a need for research in more traditional areas, but rather that we have abundant opportunities for growth if we are willing to accept the new challenges.

And this leads us back to the question that opened this article: Who are we, and where do we---as an organization and as a discipline---wish to go?
In order to answer---or at least begin to discuss---such far-reaching questions, we have initiated a strategic planning effort that will continue over the next eighteen months. The effort began with a late-April workshop for the elected officers, the executive committee of the board, and a small subset of the SIAM staff at which we outlined some broad goals. The questions raised in this article were a key component of the discussions.

The goals established at the workshop will be presented to the SIAM council and board for further discussion, and implementation plans will be developed. As the process continues, we will keep the membership informed. Members will be encouraged to share their opinions on these issues. Meanwhile, as always, we welcome your comments and questions.

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