Mathematics Turned Inside Out: The Intensive Faculty Versus the Extensive Faculty

TL;DR

This paper reveals that in U.S. research universities, the extensive faculty outside mathematics departments conduct most research and teach advanced mathematics, challenging traditional views of departmental boundaries.

Contribution

It highlights the significant role of the extensive faculty in mathematics research and education, which has been overlooked in policy and sociological studies.

Findings

Extensive faculty conduct most mathematics research.

They teach advanced mathematics independently of departments.

Their interests dominate the most published areas of mathematics.

Abstract

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.