This report assesses the adequacy of United States resources in support of mathematics. Section I (the introduction) considers the support of research, the scope of mathematics, and relationships of mathematics to computer science and education. Section II discusses strengths and opportunities in the mathematical sciences by considering mathematics and technology, mathematics in and as science, trends, and the future. Section III examines various aspects related to inadequate support for mathematics, including reasons for decreased federal support and the consequences of inadequate support. Section IV presents and discusses various guidelines for future support, considering such areas as university-government cooperation, the breadth of support, employment prospects, and Ph.D. production. Section V offers recommendations to the federal administration, congress, universities and the mathematics research community. Appendices include: (1) a description of the varied approaches to research in mathematics; (2) a discussion of federal support, focusing on trends, analyses, and data sources; and (3) a paper by Arthur Jaffe ("Ordering the Universe: The Role of Mathematics") which considers the importance of mathematics to science and technology. One finding noted is that recent funding increases in the computer sciences actually mask a downward trend in federal support for mathematics itself. (JN)