**VII. OBJECTIVES, RECOMMENDATIONS, AND MILESTONES FOR NSF
**

**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.