State of the Art Reviews. Mathematical Sciences: A Unifying and Dynamic Resource

摘要

The expository report reviews world trends in Mathematics and assesses the position of American mathematics in the world mathematical community. It emphasizes four major trends: (1) mathematical sciences research is strong worldwide and the United States is maintaining the leading role; (2) mathematics is unifying internally; (3) applications of mathematics in both traditional and new areas are flourishing and involving more central areas of mathematics; and, (4) mathematics is the driving force behind new areas of computation science and is in turn profoundly influenced by high-speed computing. These trends which demonstrate the vitality of the mathematical sciences as well as the changing nature of this critical discipline are illustrated in a series of six vignettes. The report closes with a brief epilogue, which records the key recommendations of the 1984 National Research Council report, Renewing U.S. Mathematics: Critical Resource for the Future and remarks on the response to and impact of that important document.