Why should anybody but mathematicians care about the standing of U.S. mathematics in the world? To laymen and to policy-makers and legislators, the answer is far from obvious. A major virtue of this report is that it provides answers they can understand. It explains why virtually all aspects of our society, economy, and national security are increasingly dependent on mathematics, and not just the mathematics already discovered. The dependency also extends to continuing breakthroughs by the "pure" mathematics community.

The report carries a mixed message. The U.S. mathematics community holds a dominant position in the world, but several adverse trends are undermining it. A few are beyond the immediate control of the United States or any other country, affecting mathematics adversely everywhere. Others are peculiar to the United States. Some, such as weak K-12 mathematics education in the United States, are problem areas beyond the scope of this assessment, primarily because they are not very sensitive to National Science Foundation resource allocation policies. Others, however, can be significantly affected by NSF policies.

If we wake up to discover that we have allowed the dominant position of U.S. mathematics to erode, we will pay a heavy price in foregone progress in technology, science, and economic productivity. Only if policy-makers, legislators, and the mathematics community understand this danger alike can they act effectively to avoid it. At least two actions are clearly urgent: a) providing more resources for mathematics and b) using resources in more effective ways.

How objective is a report that makes such a straight forward demand for more resources? The exceptional quality of the panel members alone should remove all concern about parochialism, but it should also be noted that none is supported by the NSF, although one receives support from the Department of Defense. Most are internationally distinguished foreign mathematicians with no potential claim on NSF funding. The panel also includes some "stake holders," i.e., mathematicians and a scientist working in industry, finance, and another university science discipline. They have helped widen the panel’s concerns beyond the narrow interests of the pure mathematics community. Notwithstanding the inherently ambiguous nature of the task given the panel, the report has a strong claim to objectivity.

As the chairman and the most thoroughly non-mathematician on the panel, I want to express a word of gratitude to Dr. Donald Lewis, director of the Division of Mathematical Sciences, NSF, for his intellectual guidance and assistance throughout the assessment process.

William E. Odom
Lieutenant General, USA, Retired