NSF’s specific objective in the area of the mathematical sciences should be to build and maintain an academic community in mathematics that is both intellectually distinguished and relevant to society. This objective contains an important shift in emphasis, in keeping with the NSF’s Strategic Plan, which is the explicit inclusion of societal relevance as both a criterion for performance and an objective in the academic mathematical sciences.

Traditionally, U.S. departments of mathematical sciences have focused on problems in mathematics that are intellectually challenging for their own sake. In the last three to five years, however, shifts in emphasis have begun to appear. Underlying these shifts is the belief that mathematics has enormous benefits to offer to the country, to other areas of science and technology, and to industry, commerce, and government. These areas, in turn, have much to offer the mathematical sciences in providing challenging mathematical problems, jobs for mathematics students, and opportunities for mathematicians to work with professionals of varied disciplines. Therefore, NSF’s broad objective in mathematics should be to build and maintain the mathematical sciences in the United States at the leading edge of the mathematical sciences, and to strongly encourage it to be an active and effective collaborator with other disciplines and with industry.

NSF should also ensure the production of mathematical students sufficient in number, quality, and breadth to meet the nation's needs in teaching, in research in the mathematical sciences and in other disciplines, and in industry, commerce, and government.

NSF should approach these objectives through the following strategies:

• Show an increase in funding for the mathematical sciences to bring the number of researchers supported in this discipline to a level comparable to those in the physical and biological sciences and engineering;

• Encourage activities that connect mathematics to other areas of science, technology, business, finance, and government;

• Strengthen the connections between "pure" and "applied" mathematics;

• Broaden the exposure of professional and student mathematicians to problems in other fields;

• Make the mathematical sciences more attractive to U.S. students so the mathematical sciences can better complete for the brightest young people; and

• Maintain and strengthen abstract mathematics, which is fundamental to the health of the mathematical sciences.

Recommendations for NSF

Encourage broader education for graduate and undergraduate students in the mathematical sciences. NSF should focus its support on Ph.D. programs that simultaneously broaden education, decrease the teaching load of graduate assistants, and shorten time to Ph.D. NSF should encourage and, to the extent possible, fund programs at both the graduate and undergraduate levels that broaden exposure of students to mathematical problems in areas other than mathematics.

Provide funding for doctoral and postdoctoral students and younger researchers at levels comparable to those in the physical and biological sciences. Relatively low funding for research by graduate students in the mathematical sciences lowers morale and reduces the attractiveness of the discipline to bright young people. The scarcity of postdoctoral fellowships slows the professional development of potential academics. NSF should encourage postdoctoral students to immerse themselves in another discipline at the postdoctoral level.

Promote interactions between university-based mathematical scientists and users of mathematics in industry, government, and universities. NSF should increase support for programs that involve academic mathematical scientists in multidisciplinary and university/industry research. Particularly important is to support endeavors that distill mathematical challenges arising from new scientific and technological developments and to encourage research that addresses these challenges.

Strengthen research in abstract mathematics. A strong core of abstract mathematics is essential to the health of the mathematical sciences in the United States and in turn to all science. Because excellent abstract research is often motivated by problems encountered by users of the mathematical sciences, researchers need to maintain good communication with users.

Recognize its unique responsibility, as the principal federal funder of U.S. mathematical sciences, to sustain their position of leadership.

Milestones for NSF Activities

Over a period of three years, NSF should aim to:

Demonstrate substantial increases in funding for graduate students and postdoctoral fellows in mathematics. These increases would shorten the time to a graduate degree by requiring that students spend less time teaching, provide a broader and more flexible education, and make the field more attractive to U.S. students.

Show an increase in interdisciplinary activities involving mathematics. This increase would encourage the dissemination of mathematical concepts into communities of users, expose mathematicians to problems and opportunities outside conventional mathematics, and build partnerships between mathematical scientists and researchers in other disciplines.

Encourage activities aimed at broadening undergraduate and graduate curricula, with the objective of widening the range of curricular choices, raising the attractiveness of mathematical careers to students, and increasing the vocational flexibility of future mathematicians.

Show an increase in funding in the mathematical sciences to bring the number of mathematical scientists being funded to a level comparable to that in the physical and biological sciences. This is especially important for retaining young academic researchers.