  Research universities in the United States have larger mathematics faculties
outside their mathematics departments than inside. Members of this "extensive"
faculty conduct most mathematics research, their interests are the most heavily
published areas of mathematics, and they teach this mathematics in upper
division courses independent of mathematics departments. The existence of this
de facto faculty challenges the pertinence of institutional and national
policies for higher education in mathematics, and of philosophical and
sociological studies of mathematics that are limited to mathematics departments
alone.
