the mathematics report indicates that the United States is the world leader in mathematics. If the mathematics community requests additional resources, some policymakers might question the request on the grounds that the United States is already the world leader in that field. That concern has been expressed in connection with the life sciences. However, as the mathematics panel indicated in its report, the United States could drop from being ''the world leader" in mathematics research unless additional investments were made in some key subfields and unless more US students chose to enter the field. Thus, an assessment that the United States is the leader in a field does not necessarily imply that no additional resources are needed for the field.