## Testimony on the FY 2003 Budget Request for the National Science Foundation

### Tom Manteuffel, Ph.D.

President, Society for Industrial and Applied Mathematics

Good morning. My name is Tom Manteuffel, and I am a Professor of Applied Mathematics at the University of Colorado at Boulder. For nearly two years now, I have also had the privilege of serving as President of the Society for Industrial and Applied Mathematics, or SIAM, which is an organization of about 10,000 applied mathematicians and computational scientists from academia and industry.

I am here to stress the importance of balanced funding in science, for the economy and for national security, and to urge you to increase the budget for the National Science Foundation. SIAM is here today to support the position advocated by the Coalition for National Science Funding, an organization made up of universities and scientific organizations, and to explain how funding for all disciplines is important to the SIAM membership.

But first, I'd like to thank you and the other Members of this Subcommittee for the strong support you've shown NSF in recent years. This has made a tremendous difference in the ability of many disciplines to move forward. Especially, at this exciting time when many scientific and engineering fields are making great strides in addressing critical problems confronting our society and our world.

Opportunities abound for significant progress in the disciplines central to the interests of the SIAM membership. As science of the 21st Century becomes ever more complex, the need for computational and applied mathematics is increasingly evident. As stated in a recent NSF Mathematical Sciences report,

"The mathematical sciences identify and study structures; they formulate powerful concepts that can unify and clarify phenomena in the natural and technological worlds, in the other sciences as well as within mathematics itself; they organize and design efficient ways to compute; they form the very language of science"

The NSF has recognized the critical importance of the mathematical sciences and has taken important steps to shore up its investment in this area.

And yet, we still maintain some serious concerns with the proposed overall NSF budget request, because too many other research areas at NSF actually decline in real dollars. Given the interdisciplinary nature of research today, it is important to recognize that declines in one area of science affect progress in others.

Let me draw my argument from computational sciences. The same argument can be made for many other areas of science and engineering, but I wish to draw from the area with which I am most familiar.

You have often heard that today's challenges faced by science and engineering are so complex that they can only be solved through a partnership between the various modes of sciences and engineering; experiment, theory and computing. All three approaches are needed to understand the complex phenomena investigated today by scientists and engineers, but each approach in turn requires the mathematical sciences. Moreover, many significant problems of national interest can only be advanced through computational modeling.

Most people recognize that the rapid growth of computational techniques in science, engineering and in business is being driven by the phenomenal growth in computing power. This is, of course, true. But, it is only half the story. What is not widely understood is the complex set of relationships that are necessary to effectively apply this computational power, namely, the partnership between mathematics, computer and computational sciences, and the application areas in science and engineering. In many cases, more than half of the improvements and speedups in computational modeling actually come from improved mathematical models, algorithms, and software. The field concerned with the development of these techniques is now referred to as, Computational Sciences, Mathematics & Engineering, or CSM&E.

This field concerns the whole computational process, including: the development of mathematical concepts, models and techniques; the analysis and development of computational algorithms; the mapping of computational algorithms onto current high-end architectures; the development of software engineering tools and systems; and the specification of future advanced-computing capabilities.

In particular, a major research focus has been on achieving progress on the so-called, "Computational Grand Challenge Applications". The Grand Challenges phrase was coined to denote fundamental problems in science and engineering with broad economic and scientific impact whose solution can only be advanced by research incorporating the most advanced computing models, systems and software.

Let me cite just a few examples of where CSM&E contributes to advancing the state-of-the-art of Grand Challenge Problems:

**Selected Grand Challenge Problems**

- Health Sciences: Designing effective new drugs requires the capability to model proteins. Known as proteomics, this research depends heavily on mathematical formulations and computational techniques.
- Information Sciences: Many methods to assure reliability, security, and trust in computing infrastructures, such as the computer internet (Web), have their roots in some of the more complex "pure" areas of mathematics.
- Homeland Security: Prevention, detection and response technologies, ranging from distributed pathogen identification, data management and data mining, and simulation and risk assessment, to signals analyses and reconnaissance, all involve complex mathematics and computation.
- Medical Imaging and Visualization: Techniques for enhancing perception for various technologies, such as, magnetic resonance imaging, computerized axial tomography, and positron emission tomography are derived using deep mathematics and complex computations.
- Geophysical Sciences: Understanding the effects on our environment, oceans, atmosphere, and global climate, is a case-study of complex mathematical interactions.
- Engineering Sciences: Predicting the onset and effects of earthquakes and other shocks is only possible through massive computational models linked to empirical data.

Today, with the vigorous support of this Committee and the Congress, NSF is in a position to provide leadership on the computational Grand Challenges and SIAM and the mathematics community will be there to collaborate to help advance all disciplines.

This nexus between mathematics, computation and important science and engineering problems is what places the SIAM membership in a position to appreciate the need for balanced support for all disciplines in the NSF budget. The fact that most SIAM members regularly collaborate across disciplines brings home to me why it is so important for SIAM to advocate for an increase in the overall NSF budget.

**NSF FY '03 Budget Request**

Let me briefly highlight the main budgetary and programmatic components that support CSM&E research. The central element in this support comes from the NSF's Division of Mathematical Sciences (DMS), the core support for all mathematical sciences. For many years, federal support for our core discipline was stagnant. This affected collaborations across all sciences and engineering: important lines of research were unexplored; fewer college students saw any real opportunities in the field of mathematics and did not pursue graduate education; and preeminence in the field began to shift from the U.S. to other areas of the world.

Thanks to strong leadership here on Capitol Hill, and at NSF, the tides have begun to turn at NSF. The President has requested an increase of $30 million for NSF's Division of Mathematical Sciences in FY 2003; this follows a similar increase of $30 million in FY 2002. While we continue to see science funding losing to inflation at other federal agencies, such as the Departments of Defense, NSF has recognized the centrality of mathematics and has increased its investment in the mathematical sciences research, both in the core discipline and in conjunction with other scientific fields.

The investments that NSF makes in DMS are leveraged through the entire range of science and engineering. From this perspective, the increases of $30 million two years in a row are an excellent investment in our future.

The FY 2003 request for NSF's mathematical sciences program incorporates several components that provide leadership:

- Focused mathematical sciences research teams, interdisciplinary training groups, and other collaborative mechanisms will lead to advances in broad areas of science and engineering;
- New and continuing national institutes in the mathematical sciences will work at the interface between the mathematical sciences and other disciplines; and
- Grants for Vertical Integration of Research and Education in the Mathematical Sciences (VIGRE) will support undergraduate, graduate and postdoctoral education and training activities and curriculum development. This will help to improve and reform the research and training opportunities in the mathematical sciences.

As I said at the beginning of my testimony, these are exciting times for the mathematical sciences. Scientists in other fields are using the results of mathematical research to explore and develop fascinating new lines of discovery; as they do so, they encounter new problems that require a mathematical solution. This cyclical relationship is the key to advances that will help stimulate economic growth, continue our technological leadership and ensure our national security. I would like to thank you again for hearing from me today. I hope that you will continue your strong support of NSF, and that you will support the President's FY 20003 request for the mathematical sciences and CSM&E and I urge you to increase the overall NSF budget.