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Joint Policy Board for Mathematics
Testimony on the FY 1997 National Science Foundation Budget Request

This testimony was delivered by AMS President-Elect Arthur Jaffe on 10 May 96 before the House Appropriations subcommittee on VA, HUD, and Independent Agencies. For more information, please contact Lisa Thompson, JPBM Congressional Liaison.

Good afternoon, Mr. Chairman and Members of the Subcommittee. I am Arthur Jaffe, President-Elect of the American Mathematical Society, and Landon T. Clay Professor of Mathematics and Theoretical Science at Harvard University. Thank you for this opportunity to comment on the FY 1997 budget request of the National Science Foundation. I speak on behalf of the Joint Policy Board for Mathematics, a joint effort of the American Mathematical Society, the Mathematical Association of America, and the Society for Applied and Industrial Mathematics. With a combined membership of over 57,000 mathematical scientists and educators, our members' concerns span fundamental and interdisciplinary research on mathematics; the applications of mathematics to science, engineering, industry, and business; and mathematics education at all levels.

Mr. Chairman, the Joint Policy Board for Mathematics urges you to provide full funding for the National Science Foundation's research and education programs. We believe that the national impact of these programs warrants the small, 3.3 percent increase the NSF has requested for FY 1997.

Support for research and education in mathematics, basic sciences, and engineering ranks among the most productive investments Congress can make in the future of our country. The mathematicians, scientists, and engineers supported by the NSF today develop new ideas and make new discoveries which become the building blocks for our society and for our economy tomorrow. The United States spends less as a percentage of GDP on civilian research than our major competitors. The federal government remains the major source of support for fundamental research and education, as the private sector continues to emphasize short-term payoffs over building long-term strength.

Working with less than 5 percent of the total federal R&D budget, the NSF plays a central role in the funding for fundamental advances in mathematics, science, and engineering and assumes major responsibility for many critical components of science and technology. The NSF is the only federal agency that supports basic research across the broad spectrum of traditional fields underlying our leading position in science and technology. In doing so, it also facilitates bridging the interfaces between different scientific disciplines. The NSF works diligently toward the achievement of excellence in education in science, mathematics, and engineering, and it is strengthening its programs to promote the integration of research and education at U.S. universities. Furthermore, the NSF pursues partnerships and encourages the participation of other federal agencies, of the states, and of industry in its activitiesoethereby leveraging its comparatively small budget.

The NSF supports only the most promising ideas for research among the many fine proposals that emerge from the Nation's colleges and universities. Furthermore it provides a key to our future predominance in science by encouraging our most brilliant and original undergraduate, graduate, and postdoctoral students to pursue productive scientific careers. For these reasons, the NSF is particularly deserving of the limited funds which you have to distribute.

Let me now offer a few examples demonstrating the national value of the NSF.

NSF Support for Research in the Mathematical Sciences

We are in the midst of a golden age of mathematics research, and today American mathematics is the envy of the rest of the world. The spectacular advances made in recent years are the consequence of NSF support for many areas of mathematics over the past 45 years. The NSF and its Division of Mathematical Sciences (DMS) play a central role as they provide virtually the only federal support for fundamental mathematical research. This research provides the underpinnings of our understanding of nature; it provides the fundamental framework to enable a broad range of advances in science, engineering, and business; and it contributes to the future of our technology-based economy. Some of the most revolutionary applications of mathematics emerge in completely unexpected ways from basic research by the most talented and original mathematical scientists supported by the DMS. In addition, DMS provides effective mechanisms for connecting mathematical scientists with fields and problems of immediate national importance, including those of industry.

We have witnessed two exciting themes in this recent progress. One theme is the flourishing of mathematics focused on classic questions generated from within the field. The second theme is the flourishing of work connecting mathematics with science. In both these areas we observe torrents of new ideas and results.

Three years ago, Princeton mathematician Andrew Wiles announced a solution to the 350-year-old Fermat problem. Today, insights emerging from this work have opened up a floodgate of new results and possibilities both in number theory, where they originated, as well as in several other related fields. In fact, number theory lies at the heart of modern cryptography. It is hard to believe that the basis of a company valued at more than $250,000,000 is the following observation: you can quickly multiply very large numbers together on a computer, but if someone presents you with a 200 digit number that was made by multiplying together two 100 digit numbers, then all the computers in the world working together may not be able to figure out what the original numbers were. The company is RSA Data Security, and its encryption algorithm is the basis of all secure commerce on the Internet. Today we believe that the 200 digit RSA codes on the Internet are still secure. But who knows? A dramatic breakthrough could immediately change the rules of the game. Future mathematical research will make or break these codes.

Other amazing progress has come about from various connections between mathematics and physics, an area in which I myself work. Most of us have heard of Newton's apple, which symbolizes the marriage between mathematics and physics. This ancient, traditional relation has suddenly blossomed in the past few years, with the work of physicists and of mathematicians fueling a minor revolution in mathematics. For example, a new mathematical theory has been discovered which incorporates the quantum nature of physics directly into our view of space and time; this is called quantum geometry. In another direction, particle physicists have conjectured that their equations expressing the laws of nature can be modified in a new way; amazingly, these ideas touch base with exciting current problems in mathematics. This raises the possibility of a new level of understanding at both the frontiers of mathematics, as well as at the frontiers of cosmology and particle physics. The early harvest has been exciting, but only the surface appears to have been scratched in these areas. The dream of workers in this area is to discover new laws of nature whose importance rivals quantum theory and relativity found early in this century.

Other connections to science and to engineering also hold the potential for having great impact. One such problem that DMS is seeking to address involves large data sets. Some impressive tools exist for collecting large amounts of scientific data, and often it is being collected faster than it can be analyzed. For example, the Human Genome Project will accumulate a database of 3 billion base pairs of human genetic code; an earthquake study in Los Angeles generates data at 35 billion different points; and satellites in one remote earth sensing project can amass 200 billion characters of information in just one scan.

Finding the best ways to organize large amounts of data so it can be distilled and interpreted is hindered by a lack of basic knowledge and structural models of databases. Basic research in core mathematics and computer science is needed to build the models and devise efficient techniques for extracting useful information. These questions arise in a variety of scientific fields including astronomy, communications, computer science, ecology, meteorology, molecular biology, particle physics, and geography; they also occur in record keeping in government and in business, such as in banks, in the Census Bureau, in the Social Security Administration, and in records of telephone and credit card use. The problem is inherently mathematical, and one of many in this field being attacked by NSF-supported researchers.

Another connection highlights the commitment by the NSF to build productive partnerships with other government agencies. Recently DMS established a collaborative program with DARPA to support the mathematical modeling and simulation of advanced materials processes, with a focus on prototyping of thin films (a layer of lubricant oil is an example of a thin film). The program was motivated by the needs of materials science researchers for advanced mathematical tools that would enable computational experimentation with designs and scale-up strategies. The predictive capabilities of the sought-after tools will reduce the need for expensive trial-and-error methods that now hinder the development of new materials and their processing equipment.

The Leadership Role of NSF in Mathematics Education

It is impossible to separate science education from scientific research. The NSF also provides most of the federal funding that enables the mathematical community to work toward the improvement of mathematics education at all levels. The Education and Human Resources Directorate, sometimes in collaboration with DMS, maintains an integrated set of programs that promote more effective, and more inclusive, mathematics education in schools, colleges, and universities throughout the country.

For instance, the NSF Systemic Initiatives program promotes partnerships among schools, universities, state and local governments, teachers, business, and policy leaders in an effort to improve K-12 mathematics and science education. Mathematical scientists are involved in many of the initiatives; for example, they work to improve the preparation of K-12 teachers.

While the K-12 programs of NSF attract much deserved applause, I'd like to emphasize that the Division of Undergraduate Education (DUE) is also essential to collegiate educators with innovative ideas for expanding student access and learning in mathematics, science, and engineering. The core programs of the DUEoecurriculum development, laboratory improvement, and faculty enhancementoeare especially important in these efforts.

As a follow-on to the remarkably successful calculus education program that JPBM has discussed in this forum in previous years, DUE is now sponsoring a program called "Mathematics Across the Curriculum." Because mathematics pervades all fields of knowledge and all modern technological jobs, it has become imperative to demonstrate the integration of mathematics into all fields of study and to enable students to make appropriate use of mathematics. With funds from this program, Dartmouth College leads a consortium of colleges and universities in undertaking a project to integrate the undergraduate study of mathematics into courses in some 16 different fields, ranging from art, music and philosophy to physics, engineering, and the social and biological sciences. Overall, 90 faculty from the consortium institutions are working to design 22 new interdisciplinary courses and revise ten others. This unprecedented cooperation among faculty from diverse departments is expected to enrich the entire collegiate curriculum.


Mr. Chairman, there are many other projects I could describe to demonstrate the extraordinary impact NSF programs have on science, technology, and education. None of them, of course, would change the fact that you face very difficult choices about dividing the federal budget. We are not asking you to stray from your commitment to balance the budget by 2002; but we are asking that as you make your decisions you keep in mind that the National Science Foundation is about discovery. Discovering new ideas and exploring their potential provides a key to solving many problems we face in the United States. I hope that you will keep sight of this investment in our future as we work through these difficult budgetary times.

In conclusion, I again urge the subcommittee's continued support for the research and education activities of the NSF. Thank you for this opportunity to express our views for the record regarding FY 1997 appropriations for the National Science Foundation.


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