III. CRITERIA FOR ASSESSMENT


The National Science Foundation is the major non-university source of research support for the academic mathematical sciences in the United States. Assessing the performance of NSF in this area is then equivalent to assessing the performance and health of U.S. academic mathematics and the impact of academic mathematics on users of mathematics in university, industry, and government.

At the same time, assessing the value of mathematics by measuring the return on public investment cannot be done by simply comparing the amount of expenditure on mathematics with the amount of wealth created. The "effects" of mathematics may not be immediate, or direct, or attributable to a single funded program. A more accurate assessment of the field requires one to accept the consensus view of all branches of science and technology -- that support for mathematics is essential -- and to ask whether that support is producing health within mathematics and a valued impact outside it.

The Panel concluded that the most accurate way to measure the impact of academic mathematics is to examine the three primary activities of mathematicians:

  1. Generating concepts in fundamental mathematics;
  2. Interacting with areas that use mathematics, such as science, engineering, technology, finance, and national security; and
  3. Attracting and developing the next generation of mathematicians.