**EXECUTIVE SUMMARY**

The modern world increasingly depends on the mathematical sciences in areas ranging from national security and medical technology to computer software, telecommunications, and investment policy. More and more American workers, from the boardroom to the assembly line, cannot do their jobs without mathematical skills. Without strong resources in the mathematical sciences, America will not retain its pre-eminence in industry and commerce.

At this moment, the U.S. enjoys a position of world leadership in the
mathematical sciences. But this position is fragile. It depends very
substantially on immigrants who had their mathematical training elsewhere and in
particular on the massive flow of experts from the former Communist bloc. The
latter, at least, will not continue because there is little talent left to drain
and even less new talent being trained.

Young Americans do not see careers in the mathematical sciences as
attractive. Funding for graduate study is scarce and ungenerous, especially
when compared to funding for other sciences and with what happens in Western
Europe. Further, it takes too long to obtain a doctorate because of the
distractions of excessive teaching. Students wrongly believe that jobs that
call for mathematical training are scarce and poorly paid. Weaknesses in K-12
mathematics education undermine the capabilities of the U.S. workforce.

Based on present trends, it is unlikely that the U.S. will be able to
maintain its world leadership in the mathematical sciences. It is, however,
essential for the U.S. to remain the world leader in critical subfields, and to
maintain enough strength in all subfields to be able to take full advantage of
mathematics developed elsewhere. Without remedial action by the universities
and National Science Foundation (NSF), the U.S. will not remain strong in
mathematics: there will not be enough excellent U.S.-trained mathematicians,
nor will it be practicable to import enough experts from elsewhere, to fill the
Nation’s needs.

Since the time of Pythagoras, mathematics has been one of the intellectual
pinnacles of civilization. Although many mathematicians develop their subject
as a purely logical structure, with no reference to the outside world, every
area of mathematics, however pure it appears, has important applications: good
pure mathematicians will always deserve support. For the benefit of the Nation
and of U.S. mathematics, however, there must be more effective interaction
between mathematicians and the users of mathematics. All participants in
mathematics must share the responsibility for improving this interaction.

Since the National Science Foundation's role is to support scientific
activities within universities, we recommend that it encourage programs that:

- Broaden graduate and undergraduate education in the mathematical sciences.

- Provide support for full time graduate students in the mathematical sciences comparable with the other sciences.

- Provide increased opportunity for postdoctoral study for those who wish to become academic researchers as a means to broaden and strengthen their training as professional mathematicians.

- Encourage and foster interactions between university-based mathematical scientists and users of mathematics in industry, government, and other disciplines in universities.

- Maintain and enhance the historical strength of the mathematical sciences in its academic setting as an intellectual endeavor and as a foundation for applications, sustaining the United States' position of world leadership.