International Benchmarking of US Mathematics Research (1997)

The United States is clearly preeminent in mathematics today. The field is thriving in terms of both quality and opportunities. Not only are there stellar researchers in all fields at American institutions, but they are backed by a broad and active research community. Mathematical research in the United States has many links with science, engineering, and technology and is broadening its contacts with education at all levels. But this position of eminence is fragile. Increasing demands are placing a strain on the mathematics community.

In making judgments about mathematics, the International Benchmarking of US Mathematics Research Panel kept these points in mind:

• Mathematics is the language and tool of most of the sciences.

• Mathematical results often have a long life.

• Mathematical research is conducted on a very broad front, and seemingly disjointed branches often turn out to be intimately related.

• Ideas of abstract mathematics often are crucial ingredients in practical applications.

• Mathematics is one of the pillars of education in kindergarten, elementary school, highschool, and college.

The present strength in US mathematics is due to:

• Continued attractiveness of the United States to talented people around the world.

• A strong system of graduate education.

• Diversity and flexibility of the US research enterprise.

• Sustained funding for research from universities and the federal government.

The United States continues to attract some of the best graduate students and postdoctoral fellows from all over the world; a substantial portion of active research mathematicians now in the United States come from outside the United States. But we are in danger of losing our preeminent position if we do not face some critical issues and challenges. Some critical issues and challenges must be faced:

• US leadership in mathematics rests on the health of research universities, which today are experiencing severe financial pressure and conflicting demands.

• The United States is not taking sufficient advantage of its native mathematical talent: while graduate enrollment from abroad thrives, the number of American students applying to graduate school in mathematics is diminishing.

• Serious thought is needed about how to make better connections between mathematics and other fields, because mathematics is crucial in much interdisciplinary research.

• US industry has reduced its commitment to long-range research in mathematics.

In 1993, the Committee on Science, Engineering, and Public Policy (COSEPUP) of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine issued the report Science, Technology, and the Federal Government: National Goals for a New Era. This report recommended that the United States be among the world leaders in all major fields of science and maintain clear leadership in selected fields. A similar recommendation was made in a later National Research Council (NRC) report, Allocating Federal Funds for Science and Technology, published in 1995—that the United States “strive for clear leadership in the most promising areas of science and technology and those deemed most important to our national goals. ”

Both reports stated that quantitative measures, such as dollars spent and number of scientists supported, were inadequate indicators of leadership and that policy decisions about programmatic issues or resource allocation would be better informed by comparative international assessments. Independent field-specific panels were suggested as the best means for obtaining such evaluations. Each panel would consist of researchers in the particular field, researchers in closely related fields, and research users who follow the field, and each panel would include researchers from outside the United States.

In late 1996, COSEPUP began an experimental study of the effectiveness and outcome of such panels. The present report—an evaluation of US research in mathematics—was prepared by the first panel and will be followed by studies in materials science and immunology. Each panel has been asked to address the following questions:

• What is the position of the United States in research in the field relative to that in other regions or countries?

• What key factors influence relative US performance in the field?

• On the basis of current trends in the United States and abroad, what will be the relative US position in the near term and the longer term?