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Mathematics turned inside out: the intensive faculty versus the extensive faculty

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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.

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Notes

  1. Ladder staff are faculty members who have been given tenure or a promise to be considered.

  2. Clark (2006) amusingly describes the “academic-charisma” that universities seek in faculty members.

  3. A good example of the importance of the academic job market to disciplines is the Annual Survey of the Mathematical Sciences in the United States, which in spite of the ambitious title is only an accounting of supply and demand for mathematics department faculty (Phipps et al. 2009).

  4. The American Mathematical Society (2010) posts the MSC on the world wide web. Fairweather and Wegner (2009) discuss the latest revision. The MSC changes very infrequently at the 2-digit level, most recently in 2000 when class 04 was combined into 03.

  5. In comparison, the American Institute of Physics database had 216,747 papers on “quantum” subjects, thereby illustrating the selectivity of Zentralblatt editors in choosing only mathematically relevant papers. Roth (2005) describes publication databases for the physical sciences.

  6. Clark (2006, Chap. 2) refers to the academic catalog as “the single most condensed academic document, the royal road to the academic subconscious.”

  7. Only three institutions with very high research activity have over 50,000 students (Carnegie Foundation 2010).

  8. Only faculty members with primary appointments outside mathematics departments are considered in case of joint appointments. When a university has two mathematics departments then only faculty outside both are considered.

  9. Information science has been called a meta-discipline in this sense (Bates 1999). Fields that draw expertise from more than one other field have also been called meta-disciplines, for example see Mihelcic et al. (2003). In the latter sense some fields may be meta-disciplines only temporarily while they are nascent.

  10. Stigler (1986) describes this history, and Hald (2007) derives the theory in the historical context. Gauss, whose career coincided with the formation of academic departments, is remembered for his mathematical and physical discoveries. He taught mostly astronomy and geodesy (Dunnington 2004, pp. 405–410).

  11. If Hotelling is accurate, then the treatment of statistics in mathematics departments is a good example of intra-disciplinary considerations trumping those of the academic community (Calhoun 2000, pp. 74–75).

  12. See recommendations of the National Science Board (2004, II, 2–20) and several studies quoted therein.

  13. D. M. Bressoud is president of the Mathematical Association of America. W. E. Kirwan is chancellor of the university system of Maryland and a former mathematics department head.

  14. For example see the recent collection of articles edited by van Kerkhove and van Bendegem (2007).

  15. A Gedankenversuch is a thought experiment in physics that is interesting from the standpoint of theory but is impossible to encounter in reality.

  16. This particular professor of finance is not heavily published on mathematics subjects while the professor of computer science is.

  17. As described by Klein (2002) and Schoenfeld (2004). In the United States, K-12 refers to kindergarten followed by 12 years of pre-university instruction.

  18. L. A. Steen is a former president of the Mathematical Association of America.

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Acknowledgments

I wish to thank the editor, Prof. C. Musselin, and the reviewers for comments and suggestions that greatly improved this paper.

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    Joseph F. Grcar

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Appendix: Institutions

Appendix: Institutions

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Grcar, J.F. Mathematics turned inside out: the intensive faculty versus the extensive faculty. High Educ 61, 693–720 (2011). https://doi.org/10.1007/s10734-010-9358-y

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Mathematics Subject Classification (2010)

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